christopher/oeis · Datasets at Hugging Face

sequence_id stringlengths 7 7	sequence_name stringlengths 4 573	sequence listlengths 1 348	keywords listlengths 1 8	score int64 1 2.35k	offset_a int64 -14,827 666,262,453B	offset_b int64 0 635M ⌀	cross_references listlengths 1 128 ⌀	former_ids listlengths 1 3 ⌀	author stringlengths 7 231 ⌀	timestamp timestamp[us]date 1999-12-11 03:00:00 2025-07-19 00:40:46	filename stringlengths 29 29	hash stringlengths 32 32
A012401	Expansion of e.g.f.: sinh(arctan(x)log(x+1))=2/2!x^2-3/3!x^3-10/5!x^5+328/6!*x^6...	[ "0", "0", "2", "-3", "0", "-10", "328", "-2184", "5040", "-40104", "1311552", "-15123240", "72848160", "-748098000", "27513786480", "-450798649560", "3381295357440", "-44199243856320", "1837919010900480", "-39019174967975040", "402216681934690560" ]	[ "sign" ]	6	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2018-02-13T19:34:46	oeisdata/seq/A012/A012401.seq	95480dbc426236f896f880acce6c1ec3
A012402	arcsinh(arctan(x)log(x+1)) = 2/2!x^2 - 3/3!x^3 - 10/5!x^5 + 88/6!*x^6 - ...	[ "2", "-3", "0", "-10", "88", "336", "-5040", "5256", "202752", "-2094840", "26943840", "-534147120", "7877529840", "-41350410360", "-804692528640", "16885512006720", "-166653340523520", "3621340758072960", "-48704381263560960", "-2035821123825148800", "99959690241598844160", "-1979439236443512264960" ]	[ "sign" ]	9	2	1	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-11-27T11:28:39	oeisdata/seq/A012/A012402.seq	5304b392307324b3ed6cfcad5f439546
A012403	E.g.f. tanh(arctan(x)*log(x+1)).	[ "2", "-3", "0", "-10", "-32", "1596", "-10080", "27936", "-260928", "1924560", "33929280", "-686630880", "4846421760", "-42426084960", "778331473920", "-1890071554560", "-216298842931200", "4070252020032000", "-41366803088056320" ]	[ "sign" ]	16	2	1	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2025-06-01T22:21:19	oeisdata/seq/A012/A012403.seq	c444b1e490c154d752afac0804086226
A012404	arctanh(arctan(x)log(x+1))=2/2!x^2-3/3!x^3-10/5!x^5+448/6!*x^6...	[ "0", "0", "2", "-3", "0", "-10", "448", "-3444", "10080", "-62784", "2682432", "-44090640", "365238720", "-3190206240", "98622664320", "-2518618203360", "38819985684480", "-522802362915840", "13679170866554880", "-437041001210135040" ]	[ "sign" ]	6	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2016-11-28T18:29:14	oeisdata/seq/A012/A012404.seq	be7c78d0ff63034f780fb1341cd35f9f
A012405	Expansion of e.g.f.: cosh(arctan(x)log(x+1))=1+12/4!x^4-60/5!x^5+90/6!x^6-420/7!*x^7...	[ "1", "0", "0", "0", "12", "-60", "90", "-420", "15008", "-149184", "572040", "-4263600", "153746472", "-2274880608", "14574976416", "-151922927520", "6077379610368", "-119360435727744", "1090133783570880", "-14675613664063104" ]	[ "sign" ]	6	0	5	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2019-06-22T19:08:17	oeisdata/seq/A012/A012405.seq	b9723e7dd0b930ca8b47019ef1a66e62
A012406	Expansion of e.g.f.: sec(arctan(x)log(x+1))=1+12/4!x^4-60/5!x^5+90/6!x^6-420/7!*x^7...	[ "1", "0", "0", "0", "12", "-60", "90", "-420", "21728", "-270144", "1479240", "-9807600", "330821832", "-6651092448", "71604108576", "-744095308320", "20714430198528", "-548875353239424", "9233126375705280", "-138948347142163584" ]	[ "sign" ]	6	0	5	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2018-04-07T13:23:08	oeisdata/seq/A012/A012406.seq	a3d93bb7b2085963165f2465eb8a2848
A012407	sech(arctan(x)log(x+1)) = 1 - 12/4!x^4 + 60/5!x^5 - 90/6!x^6 + 420/7!*x^7...	[ "1", "0", "0", "0", "-12", "60", "-90", "420", "-4928", "-32256", "788760", "-4052400", "12074568", "-397549152", "2860681824", "80960836320", "-1570434928128", "8575093540224", "-83967092441280", "3671889608928384", "-27749577690072192" ]	[ "sign" ]	12	0	5	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2013-10-31T12:17:13	oeisdata/seq/A012/A012407.seq	fa17795061c7c2b9931f68eb5bce7f01
A012408	exp(arctan(x)exp(x))=1+x+3/2!x^2+8/3!x^3+25/4!x^4+100/5!*x^5...	[ "1", "1", "3", "8", "25", "100", "465", "2186", "10273", "58568", "428193", "2778382", "11360177", "71102044", "1639157169", "15866637762", "-85280723135", "-1590866608240", "41214840121921", "683822331420054", "-11338214469525167" ]	[ "sign" ]	4	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:48	oeisdata/seq/A012/A012408.seq	7474e4afa81906e7d8737aa8ce43aa00
A012409	E.g.f. sin(arctan(x)*exp(x)).	[ "0", "1", "2", "0", "-16", "-60", "-40", "336", "-2560", "-20976", "342688", "4002944", "-24866048", "-523996096", "3812202368", "103065059072", "-777384271872", "-26888473739008", "196597142376960", "8734488670474240", "-63053651090673664" ]	[ "sign" ]	16	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2013-05-17T11:44:21	oeisdata/seq/A012/A012409.seq	cbc1fe61a861046afc6cc1f8a6b0fa75
A012410	Expansion of e.g.f. arcsin(arctan(x) * exp(x)).	[ "0", "1", "2", "2", "8", "88", "560", "3880", "48064", "645376", "8447488", "129332480", "2305269760", "43823270528", "893173681920", "19883237893376", "476731844235264", "12171513901662208", "330755844515020800", "9543303550734733312", "291053885585803034624", "9354941906907855192064" ]	[ "nonn" ]	11	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2018-07-19T02:57:21	oeisdata/seq/A012/A012410.seq	5f925690f8fec1884fd54a056c1727d8
A012411	arctan(arctan(x)exp(x)) = x + 2/2!x^2 - 1/3!x^3 - 28/4!x^4 - 107/5!*x^5 + ...	[ "0", "1", "2", "-1", "-28", "-107", "470", "10243", "51592", "-677879", "-15870422", "-76105753", "2647708780", "62662672733", "171362144382", "-21259413359701", "-489069754224624", "774485831879569", "300884931182492754" ]	[ "sign" ]	9	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2018-01-15T15:26:01	oeisdata/seq/A012/A012411.seq	7862fece688dfd13af676d1927c26327
A012412	cos(arctan(x)exp(x))=1-1/2!x^2-6/3!x^3-15/4!x^4+20/5!*x^5...	[ "1", "0", "-1", "-6", "-15", "20", "255", "70", "-3423", "46728", "501375", "-3625358", "-60112239", "420430556", "9211149311", "-79037179650", "-2033765765567", "18361020368016", "572833991092479", "-5418169914165654", "-201869115241158607" ]	[ "sign" ]	4	0	4	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:49	oeisdata/seq/A012/A012412.seq	7285fe1cb0ff48a489a3f96426d0b5ed
A012413	sinh(arctan(x)exp(x)) = x + 2/2!x^2 + 2/3!x^3 + 8/4!x^4 + 80/5!*x^5 +...	[ "0", "1", "2", "2", "8", "80", "320", "16", "1920", "99776", "416128", "-5760896", "-13486592", "1070744064", "3323114496", "-195141029888", "-464796680192", "51108813787136", "107290616242176", "-16422323853352960", "-25773434486882304" ]	[ "sign" ]	13	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2013-11-21T12:46:01	oeisdata/seq/A012/A012413.seq	f888a5ab20302d313c1974f62f0ccc31
A012414	Expansion of e.g.f. arcsinh(arctan(x) * exp(x)).	[ "0", "1", "2", "0", "-16", "-52", "200", "3752", "18496", "-190384", "-4797152", "-28063552", "661457920", "17348360768", "74504846208", "-4999196993152", "-124352680593408", "-83620707815168", "65968266617811456", "1541961961341134848" ]	[ "sign" ]	9	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2018-07-19T03:05:05	oeisdata/seq/A012/A012414.seq	e07c2f69c63773ce9b0d68d66f99393a
A012415	Expansion of e.g.f. tanh(arctan(x) * exp(x)).	[ "0", "1", "2", "-1", "-28", "-115", "230", "7051", "43080", "-172327", "-6067382", "-47080361", "309697324", "12289126629", "114505019694", "-1105109602973", "-48948382516592", "-522517588252495", "7065091754607762", "338212264324430255" ]	[ "sign" ]	17	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2024-08-04T04:14:47	oeisdata/seq/A012/A012415.seq	88d073192beee015183886ba4499e006
A012416	arctanh(arctan(x)exp(x))=x+2/2!x^2+3/3!x^3+20/4!x^4+173/5!*x^5...	[ "0", "1", "2", "3", "20", "173", "1190", "11039", "140968", "1855481", "26494858", "441706331", "8105309500", "159190672613", "3403623626286", "78823813121975", "1949180731782480", "51354602068725361", "1439864769232356882" ]	[ "nonn" ]	12	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2016-11-28T18:32:17	oeisdata/seq/A012/A012416.seq	5563f33cd6d873ba3343413f1b681f99
A012417	cosh(arctan(x)exp(x))=1+1/2!x^2+6/3!x^3+17/4!x^4+20/5!*x^5...	[ "1", "0", "1", "6", "17", "20", "145", "2170", "8353", "-41208", "12065", "8539278", "24846769", "-999642020", "-1683957327", "211007667650", "379515957057", "-52699680395376", "-66075776120255", "17106146184773014", "14435220017357137" ]	[ "sign" ]	6	0	4	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-12-15T12:33:12	oeisdata/seq/A012/A012417.seq	88dc4da9b921039b9ac2f36ee4ba31e6
A012418	Expansion of e.g.f.: sec(arctan(x)exp(x))=1+1/2!x^2+6/3!x^3+21/4!x^4+100/5!*x^5...	[ "1", "0", "1", "6", "21", "100", "1005", "9170", "73353", "794952", "11042745", "144625118", "1936131549", "31475441452", "562265168101", "9960214270890", "187956163443857", "3970728871687824", "88040662078595313", "1994667867977462454" ]	[ "nonn" ]	6	0	4	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2016-03-19T16:17:11	oeisdata/seq/A012/A012418.seq	0a956ded4a065c6ca16c75e4cbc094b0
A012419	Expansion of e.g.f.: sech(arctan(x)exp(x))=1-1/2!x^2-6/3!x^3-11/4!x^4+100/5!*x^5...	[ "1", "0", "-1", "-6", "-11", "100", "995", "2030", "-45943", "-568632", "-1189145", "54818082", "845395901", "1936128428", "-142744278261", "-2685086733290", "-6197620433007", "713212265955216", "15393015776009807", "26780979282600266" ]	[ "sign" ]	6	0	4	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2016-03-06T11:01:09	oeisdata/seq/A012/A012419.seq	2bb616018fd455135820e31300a1b857
A012420	exp(arctan(x)sin(x))=1+2/2!x^2-50/6!x^6+56/8!x^8+27178/10!*x^10...	[ "1", "2", "0", "-50", "56", "27178", "-2358884", "320163870", "-64993423408", "17229734819538", "-5720421047111484", "2329873846478810630", "-1143585527502409144520", "666071310836628939214906", "-454305678798485051002579924" ]	[ "sign" ]	6	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2016-06-19T10:06:12	oeisdata/seq/A012/A012420.seq	b2bfb325f0719a631441feec245a1301
A012421	sin(arctan(x)sin(x))=2/2!x^2-12/4!x^4+70/6!x^6+2856/8!*x^8...	[ "2", "-12", "70", "2856", "-406262", "53106460", "-8809933106", "1910193704272", "-531575014780398", "185190064964692804", "-78983931548861495466", "40480351020220065079928", "-24547642682771502545050854" ]	[ "sign" ]	4	0	1	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:49	oeisdata/seq/A012/A012421.seq	731e70642448b6fda6262c98bd132dfd
A012422	arcsin(arctan(x)sin(x))=2/2!x^2-12/4!x^4+310/6!x^6-17304/8!*x^8...	[ "2", "-12", "310", "-17304", "1700458", "-258909860", "56652535966", "-16866155567408", "6564236008307922", "-3237559423419911996", "1974150395798812732422", "-1458519974560491245318344", "1283942399735883713487058746" ]	[ "sign" ]	6	0	1	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2022-02-26T18:55:52	oeisdata/seq/A012/A012422.seq	c4fda32cb28376c505cda1eef6e88b0b
A012423	arctan(arctan(x)sin(x))=2/2!x^2-12/4!x^4-50/6!x^6+12936/8!*x^8...	[ "0", "2", "-12", "-50", "12936", "-643142", "-60323780", "22895524678", "-2421315237488", "-864760878344718", "527455288321939204", "-55917569000158790850", "-108932420480580224669416", "83957330220575698201816746" ]	[ "sign" ]	6	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2016-11-28T18:36:41	oeisdata/seq/A012/A012423.seq	fdd25f1e57e7f4a0ac4b5ac5afac210d
A012424	cos(arctan(x)sin(x))=1-12/4!x^4+360/6!x^6-14000/8!x^8...	[ "1", "0", "-12", "360", "-14000", "826560", "-74707776", "9918004096", "-1826276458240", "443565659817984", "-136830226103770112", "52123659256392435712", "-23992831220659002945536", "13113491065080505366691840" ]	[ "sign" ]	6	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2015-05-24T10:05:17	oeisdata/seq/A012/A012424.seq	e4063f875bd0c6ddc2d4f4d2b1a3d98d
A012425	sinh(arctan(x)sin(x))=2/2!x^2-12/4!x^4+310/6!x^6-17304/8!*x^8...	[ "2", "-12", "310", "-17304", "1458538", "-179076260", "30579769246", "-6937516847408", "2018483632983762", "-732877524097108796", "324856264038732166662", "-172652168729948174280904", "108374992202504938057945146" ]	[ "sign" ]	4	0	1	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:49	oeisdata/seq/A012/A012425.seq	b3365027e06bf928ce4ab90183f362c8
A012426	arcsinh(arctan(x)sin(x))=2/2!x^2-12/4!x^4+70/6!x^6+2856/8!*x^8...	[ "2", "-12", "70", "2856", "-164342", "-26727140", "9513652174", "-1509132606128", "-24850989613038", "96289752279508804", "-8229825010792301226", "-30295913573130207257992", "26332910393982197524318746" ]	[ "sign" ]	4	0	1	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:49	oeisdata/seq/A012/A012426.seq	a8ea8e34e0df91a10aea0b1a99da4c5a
A012427	tanh(arctan(x)sin(x))=2/2!x^2-12/4!x^4-50/6!x^6+12936/8!*x^8...	[ "2", "-12", "-50", "12936", "-885062", "19509820", "8446530118", "-2256645131888", "271169972750322", "52894208663673604", "-48060787092036123330", "16320006114052519358744", "-62047368403218100000854" ]	[ "sign" ]	4	0	1	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:49	oeisdata/seq/A012/A012427.seq	9f02cfe377dcb93c0bf0bb1fde5cbf72
A012428	arctanh(arctan(x)sin(x))=2/2!x^2-12/4!x^4+430/6!x^6-27384/8!*x^8...	[ "0", "2", "-12", "430", "-27384", "3086458", "-524689220", "126513823462", "-40981407368048", "17181884789561202", "-9052122654113318396", "5854705311144202022046", "-4561027328402726456335720", "4212695076131749316430016746" ]	[ "sign" ]	7	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2016-11-28T18:38:19	oeisdata/seq/A012/A012428.seq	44a2f4756f03d57856389b692edccb0c
A012429	cosh(arctan(x)sin(x))=1+12/4!x^4-360/6!x^6+17360/8!x^8...	[ "1", "0", "12", "-360", "17360", "-1431360", "176717376", "-30259605376", "6872523424000", "-2001253898164224", "727157103049997312", "-322526390192253356032", "171508583202445765136384", "-107708920891668309118730240" ]	[ "sign" ]	4	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:49	oeisdata/seq/A012/A012429.seq	e348c586f222e2c449f774786be4bf34
A012430	sec(arctan(x)sin(x))=1+12/4!x^4-360/6!x^6+24080/8!x^8...	[ "1", "0", "12", "-360", "24080", "-2640960", "420653376", "-92737380736", "26980142475520", "-10012413760149504", "4615824952212134912", "-2587662789242232604672", "1733488941554235507937280", "-1367558750121199449308119040" ]	[ "sign" ]	4	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:49	oeisdata/seq/A012/A012430.seq	ed2196a81a9aa05d7b9ab46965ce2121
A012431	sech(arctan(x)sin(x)) = 1-12/4!x^4+360/6!x^6-7280/8!x^8...	[ "1", "0", "-12", "360", "-7280", "-383040", "89394624", "-8970625664", "-316692862720", "470941672802304", "-146844936720038912", "18279034160407939072", "9932590980055055503360", "-8395139128320596309032960" ]	[ "sign" ]	8	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2023-05-12T14:54:33	oeisdata/seq/A012/A012431.seq	e6a79e758e3905eb8207c2448c3561b1
A012432	exp(arctan(x)arcsin(x))=1+2/2!x^2+8/4!x^4+158/6!x^6+4104/8!*x^8...	[ "1", "2", "8", "158", "4104", "346602", "24240372", "4851149886", "651838359408", "239431266389586", "52363260776961132", "30711336758113317990", "9908919510460647921960", "8503014202216759714206330", "3792595745728445864618214180", "4484803880283207420946418876430" ]	[ "nonn" ]	6	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2014-08-18T15:42:50	oeisdata/seq/A012/A012432.seq	3e55a24685b58313216b5a00dc861b2e
A012433	sin(arctan(x)arcsin(x))=2/2!x^2-4/4!x^4+38/6!x^6-264/8!*x^8...	[ "2", "-4", "38", "-264", "9162", "6423540", "-875983890", "380802735600", "-91040517107310", "46795149700613100", "-17544576509662829130", "11815590123153714787560", "-6408554682643734028619430", "5614434324236056272171194340" ]	[ "sign" ]	4	0	1	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:49	oeisdata/seq/A012/A012433.seq	f139410dc5afc80496664e93e8ea824f
A012434	arcsin(arctan(x)arcsin(x))=2/2!x^2-4/4!x^4+278/6!x^6-6984/8!*x^8...	[ "2", "-4", "278", "-6984", "1148202", "-99018060", "28635818430", "-5588393370000", "2487224151815250", "-886910985311966100", "563430775878809461350", "-321709990033199535312600", "277763298278504193429092730" ]	[ "sign" ]	6	0	1	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2013-05-04T14:53:42	oeisdata/seq/A012/A012434.seq	3b4a3fdc7d842e75f594c7a06874a5bc
A012435	arctan(arctan(x)arcsin(x))=2/2!x^2-4/4!x^4-82/6!x^6+3096/8!*x^8...	[ "2", "-4", "-82", "3096", "256122", "-30668460", "856747110", "523284711600", "39637940511090", "-50848285138290900", "19464791037179683230", "1825136551296140381640", "99500526939660052179690", "-1613956014788908960338116220", "2918159856709476758087519928150" ]	[ "sign" ]	6	0	1	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2014-11-05T08:12:17	oeisdata/seq/A012/A012435.seq	22b6da0ce0639c7ebc2d3deb2fb98708
A012436	cos(arctan(x)arcsin(x))=1-12/4!x^4+120/6!x^6-7728/8!x^8...	[ "1", "0", "-12", "120", "-7728", "358080", "-54956352", "5983845504", "-1674895273728", "331567748941824", "-147083657045302272", "46138766175213803520", "-29742693904194176593920", "13565163573403491059712000" ]	[ "sign" ]	6	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2019-10-14T13:42:28	oeisdata/seq/A012/A012436.seq	4aeaad81d565cd6983b10b5ad09a6d04
A012437	sinh(arctan(x)arcsin(x))=2/2!x^2-4/4!x^4+278/6!x^6-6984/8!*x^8...	[ "2", "-4", "278", "-6984", "906282", "-72406860", "16769884350", "-2791769139600", "1025112403117650", "-291983305370462100", "156358879820283153510", "-68012449387139352098520", "50073830528033335130526330" ]	[ "sign" ]	4	0	1	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:50	oeisdata/seq/A012/A012437.seq	d4772d098fd4847c67baa10ad9bc6233
A012438	arcsinh(arctan(x)arcsin(x))=2/2!x^2-4/4!x^4+38/6!x^6-264/8!*x^8...	[ "2", "-4", "38", "-264", "251082", "-20187660", "3240768750", "-246050691600", "164895642091410", "-44832184763361300", "26301902902677945270", "-6982668079815620764440", "6485203397909159496161370" ]	[ "sign" ]	7	0	1	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2013-11-21T12:46:01	oeisdata/seq/A012/A012438.seq	3386a9b7c012a0c8d4a5e589cd5faead
A012439	tanh(arctan(x)arcsin(x))=2/2!x^2-4/4!x^4-82/6!x^6+3096/8!*x^8...	[ "2", "-4", "-82", "3096", "14202", "-4057260", "614585190", "65252737200", "9930277245810", "3938676912038700", "2327811184268315550", "661470912900859782600", "625005810716811201651690", "275157523021831158684027780" ]	[ "sign" ]	6	0	1	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2019-04-05T13:20:48	oeisdata/seq/A012/A012439.seq	300fc353698f8f937d7f35cd912874c7
A012440	arctanh(arctan(x)arcsin(x))=2/2!x^2-4/4!x^4+398/6!x^6-10344/8!*x^8...	[ "0", "2", "-4", "398", "-10344", "2050362", "-188329260", "60987377670", "-12776749381200", "6138167322301170", "-2341662552659308500", "1574696831249089102590", "-954442874464228447345080", "862598218425468174866650410" ]	[ "sign" ]	6	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2016-11-28T18:40:17	oeisdata/seq/A012/A012440.seq	4ae51784ca0a88938eb3c54e2768be70
A012441	cosh(arctan(x)arcsin(x))=1+12/4!x^4-120/6!x^6+11088/8!x^8...	[ "1", "0", "12", "-120", "11088", "-559680", "96647232", "-11918734464", "3443607499008", "-785681136728064", "344346566147423232", "-125647543062169835520", "77921368897600000020480", "-41570816325816575416320000" ]	[ "sign" ]	4	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:50	oeisdata/seq/A012/A012441.seq	55cd780b993f4254a756a01c1c8a9521
A012442	sec(arctan(x)arcsin(x))=1+12/4!x^4-120/6!x^6+17808/8!x^8...	[ "1", "0", "12", "-120", "17808", "-962880", "219945792", "-31053369984", "10719320103168", "-2908608708409344", "1441051026777725952", "-637493975166202091520", "433239709928964325478400", "-282573293205848764594176000" ]	[ "sign" ]	6	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2024-08-10T15:49:56	oeisdata/seq/A012/A012442.seq	603d1f889c3f6e6849595b893b4dbbc8
A012443	sech(arctan(x)arcsin(x))=1-12/4!x^4+120/6!x^6-1008/8!x^8...	[ "1", "0", "-12", "120", "-1008", "-45120", "-11491392", "1378925184", "-443544192768", "53698137606144", "-32840379055537152", "7093049054642411520", "-6636093887068155801600", "2065820944848385959936000" ]	[ "sign" ]	7	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2013-11-21T12:46:01	oeisdata/seq/A012/A012443.seq	776b23c285179b5487f05d0b59420c7e
A012444	exp(arctan(x)tan(x))=1+2/2!x^2+12/4!x^4+280/6!x^6+7952/8!*x^8...	[ "1", "2", "12", "280", "7952", "532768", "30306496", "4657640832", "327222722816", "131738463674880", "2341955285781504", "10584761954697844736", "-1750594656814587244544", "2213182839332047713673216" ]	[ "sign" ]	4	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:50	oeisdata/seq/A012/A012444.seq	791f2f6647ee076e3b3665197ae1a636
A012445	sin(arctan(x)tan(x))=2/2!x^2+40/6!x^6-2688/8!x^8-31712/10!*x^10...	[ "2", "0", "40", "-2688", "-31712", "-13038080", "-341144960", "-124075126784", "-16972742475264", "4013224846508032", "-4370688326014457856", "2734360152236817809408", "-2075517087570212545880064", "1712256529842324555250663424", "-1579921804125758497599230672896" ]	[ "sign" ]	6	0	1	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2014-12-20T18:46:56	oeisdata/seq/A012/A012445.seq	392cb7c69cad543b042feca35e8dc9ad
A012446	arcsin(arctan(x)tan(x))=2/2!x^2+280/6!x^6-2688/8!x^8+1016608/10!*x^10...	[ "2", "0", "280", "-2688", "1016608", "-44971520", "22528934272", "-2475890192384", "1731096311210496", "-365422134993502208", "343466758613102303232", "-121096429560806448922624", "146997236520941470929985536" ]	[ "sign" ]	6	0	1	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2013-11-05T10:28:29	oeisdata/seq/A012/A012446.seq	0c68a7f10fecc77ee665c23a318dbe0c
A012447	arctan(arctan(x)tan(x))=2/2!x^2-80/6!x^6-2688/8!x^8+260608/10!*x^10...	[ "0", "2", "0", "-80", "-2688", "260608", "2928640", "-463763456", "-517376835584", "108823739498496", "-2683131538178048", "5868236283429519360", "-6862655376791380688896", "2738386568702639562817536" ]	[ "sign" ]	8	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2016-11-28T18:43:21	oeisdata/seq/A012/A012447.seq	f5c5ba771659ff2350f2deb0245decbb
A012448	cos(arctan(x)tan(x))=1-12/4!x^4-7280/8!x^8+241920/10!x^10...	[ "1", "0", "-12", "0", "-7280", "241920", "-39796416", "5601756160", "-1164660739840", "326680627961856", "-107144725837171712", "45897715016709799936", "-22689657885234118356992", "13649678748377009638277120" ]	[ "sign" ]	4	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:50	oeisdata/seq/A012/A012448.seq	e1cfaae5cc5225d62af26779b3619ab8
A012449	sinh(arctan(x)tan(x))=2/2!x^2+280/6!x^6-2688/8!x^8+774688/10!*x^10...	[ "2", "0", "280", "-2688", "774688", "-44971520", "12196692352", "-2010939305984", "682495898190336", "-217798427799339008", "100459217814408271872", "-50559840345962764140544", "31791509418375951964839936" ]	[ "sign" ]	4	0	1	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:50	oeisdata/seq/A012/A012449.seq	63b68b57223065c0412bbf4c07f8e48e
A012450	arcsinh(arctan(x)tan(x))=2/2!x^2+40/6!x^6-2688/8!x^8+210208/10!*x^10...	[ "2", "0", "40", "-2688", "210208", "-13038080", "2241915520", "-589026013184", "146361182839296", "-42690102749216768", "18963982821764573184", "-10109322351828827471872", "5702647873782168851521536" ]	[ "sign" ]	6	1	1	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:50	oeisdata/seq/A012/A012450.seq	8e90199d048ca12ec2ba10d5f0bb0f42
A012451	tanh(arctan(x)tan(x))=2/2!x^2-80/6!x^6-2688/8!x^8+18688/10!*x^10...	[ "2", "0", "-80", "-2688", "18688", "2928640", "827766784", "-52425949184", "11263759220736", "-6439993741672448", "1974174235078164480", "-952764420869394006016", "577855093673994995367936", "-371995357739088472730238976" ]	[ "sign" ]	6	0	1	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2015-12-30T12:01:38	oeisdata/seq/A012/A012451.seq	25b51b7d19a3bae494b3f569a3e7d483
A012452	arctanh(arctan(x)tan(x))=2/2!x^2+400/6!x^6-2688/8!x^8...	[ "0", "2", "0", "400", "-2688", "1873408", "-60938240", "49450805248", "-4291105193984", "4345356280528896", "-769792296435580928", "962815994229666349056", "-298377426990773724774400", "452668537171760533299265536" ]	[ "sign" ]	6	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2016-11-28T18:46:16	oeisdata/seq/A012/A012452.seq	575ca3e5524fc81f617bf4959879847d
A012453	cosh(arctan(x)tan(x))=1+12/4!x^4+10640/8!x^8-241920/10!x^10...	[ "1", "0", "12", "0", "10640", "-241920", "75278016", "-7539051520", "2338162028800", "-550757434515456", "220140383085120512", "-89874455859710427136", "48809245689148176896000", "-29578326579043904251166720" ]	[ "sign" ]	4	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:50	oeisdata/seq/A012/A012453.seq	1545b25df227805ca5536f262d9c54df
A012454	sec(arctan(x)tan(x))=1+12/4!x^4+17360/8!x^8-241920/10!x^10...	[ "1", "0", "12", "0", "17360", "-241920", "186158016", "-11413642240", "7726026430720", "-1212323504480256", "892608906281741312", "-274005660019568705536", "234514059257417538031616", "-119571044071522301122641920" ]	[ "sign" ]	6	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2016-01-12T10:58:59	oeisdata/seq/A012/A012454.seq	d4258b714158ff2f77a09388111473d6
A012455	sech(arctan(x)tan(x))=1-12/4!x^4-560/8!x^8+241920/10!x^10...	[ "1", "0", "-12", "0", "-560", "241920", "-8750016", "1727165440", "-426305201920", "91939471712256", "-31563179893517312", "13087008599986241536", "-6237304648085400498176", "3651782585501269235793920" ]	[ "sign" ]	6	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2025-06-06T15:47:02	oeisdata/seq/A012/A012455.seq	51b0ecbd37d704cb82172205b7bb1bf7
A012456	exp((arctan(x))^2)=1+2/2!x^2-4/4!x^4+8/6!x^6+912/8!x^8...	[ "1", "2", "-4", "8", "912", "-99168", "11815872", "-1790856576", "347783278848", "-85244795874816", "25888104843574272", "-9570587679263078400", "4239434238319441121280", "-2218976274384029204766720" ]	[ "sign" ]	6	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2016-04-24T09:30:33	oeisdata/seq/A012/A012456.seq	2e51cab32bfce1425b1817c3d1d46439
A012457	sin(arctan(x)^2)=2/2!x^2-16/4!x^4+248/6!x^6-3456/8!x^8...	[ "2", "-16", "248", "-3456", "-406368", "123982080", "-31807263360", "9173875200000", "-3114459024453120", "1251070155460915200", "-591321674803999426560", "326012628782956574638080", "-207713640106463567695994880" ]	[ "sign" ]	10	0	1	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2016-04-04T23:19:17	oeisdata/seq/A012/A012457.seq	335587e907191c3749a94bc35ca16b0a
A012458	arcsin(arctan(x)^2) = 2/2!x^2 - 16/4!x^4 + 488/6!x^6 - 30336/8!x^8...	[ "2", "-16", "488", "-30336", "3303072", "-556926720", "135234491520", "-44790227865600", "19434264780034560", "-10703464305128755200", "7296385856008015226880", "-6031102564833737842851840", "5942962739028147945628999680" ]	[ "sign" ]	10	0	1	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2013-11-21T12:46:01	oeisdata/seq/A012/A012458.seq	f3e8f15a7905ba1bf5e05810ed9efebe
A012459	Expansion of e.g.f. arctan(arctan(x)*arctan(x)) (even powers only).	[ "0", "2", "-16", "128", "9984", "-1444608", "105185280", "11495516160", "-7997802086400", "2106956324536320", "3592879276032000", "-400446184903952302080", "271017181684548910448640", "-56861458491339484126248960" ]	[ "sign" ]	14	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2018-01-29T02:53:49	oeisdata/seq/A012/A012459.seq	0ac17998b7be1b393748cd807b248d76
A012460	cos(arctan(x)^2)=1-12/4!x^4+480/6!x^6-27888/8!*x^8...	[ "1", "0", "-12", "480", "-27888", "2353920", "-274245312", "41974872576", "-8068087373568", "1860842339721216", "-486190504963034112", "129225947748233994240", "-22917287813817561968640", "-13673939410058068058112000" ]	[ "sign" ]	6	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2016-10-07T17:56:50	oeisdata/seq/A012/A012460.seq	cf37e093e70288f62f92a4e1d00ce66f
A012461	sinh(arctan(x)arctan(x))=2/2!x^2-16/4!x^4+488/6!x^6-30336/8!*x^8...	[ "0", "2", "-16", "488", "-30336", "3061152", "-450481920", "90676698240", "-23889578496000", "7972943138664960", "-3286129765438771200", "1638857583672607549440", "-972524875970827007262720", "677113960144029088030433280" ]	[ "sign" ]	8	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2016-11-28T18:50:11	oeisdata/seq/A012/A012461.seq	03e00adb239e44829a58994c3c80a084
A012462	Arcsinh(arctan(x)^2) = 2/2!x^2 - 16/4!x^4 + 248/6!x^6 - 3456/8!x^8 + ...	[ "0", "2", "-16", "248", "-3456", "-164448", "17537280", "5001348480", "-3047690956800", "999150768960000", "-194340969261158400", "-28292890791044597760", "48811395838790000148480", "-15658656394130132870062080", "-19215487887156327014813859840", "37972554002174500707798919249920" ]	[ "sign" ]	13	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2024-01-09T13:20:30	oeisdata/seq/A012/A012462.seq	0f9744a393be3df15c4bb1e6ee6b0c4e
A012463	tanh(arctan(x)arctan(x))=2/2!x^2-16/4!x^4+128/6!x^6+9984/8!*x^8...	[ "0", "2", "-16", "128", "9984", "-1686528", "211630080", "-21438504960", "-115777536000", "1290343156285440", "-677718502185369600", "262776565415742013440", "-69499554745499013611520", "-9137401716948937432104960" ]	[ "sign" ]	6	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2016-11-28T18:53:27	oeisdata/seq/A012/A012463.seq	2ae07559ea53445af7e3b64111896b60
A012464	arctanh(arctan(x)arctan(x))=2/2!x^2-16/4!x^4+608/6!x^6-43776/8!*x^8...	[ "0", "2", "-16", "608", "-43776", "5490432", "-1043742720", "281302333440", "-101944270848000", "47833801306275840", "-28212954337286553600", "20432760600063600230400", "-17826780360146975037849600", "18441699370235590444905922560" ]	[ "sign" ]	9	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2016-11-28T18:54:28	oeisdata/seq/A012/A012464.seq	a1bb2b74700e47f027d7cc91ad28de6b
A012465	cosh(arctan(x)arctan(x))=1+12/4!x^4-480/6!x^6+31248/8!x^8...	[ "1", "0", "12", "-480", "31248", "-3160320", "462297792", "-92467554816", "24237361774848", "-8058187934539776", "3312017870282345472", "-1648428171351870627840", "976764310209146448384000", "-679332936418413117235200000" ]	[ "sign" ]	8	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2016-11-28T18:55:40	oeisdata/seq/A012/A012465.seq	31a4e02d094ad16148b1b7edae3944c3
A012466	E.g.f. sec(arctan(x)^2) (even powers only).	[ "1", "0", "12", "-480", "37968", "-4773120", "878319552", "-222512349696", "74262725323008", "-31578556041732096", "16666719859336276992", "-10690478515516973015040", "8190555666463900906475520", "-7387658525325188387856384000" ]	[ "sign" ]	10	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2013-01-13T06:14:00	oeisdata/seq/A012/A012466.seq	f8daf7787112f083df7452ed83c888c9
A012467	sech(arctan(x)^2) = 1 - 12/4!x^4 + 480/6!x^6 - 21168/8!*x^8 + ...	[ "1", "0", "-12", "480", "-21168", "741120", "61942848", "-29951061504", "8015861467392", "-1745546459848704", "215844160641143808", "91751419512905687040", "-109687232118939992862720", "71900040403600384794624000" ]	[ "sign" ]	10	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2013-11-21T12:46:01	oeisdata/seq/A012/A012467.seq	a2e8857f694d50f70eb008358277ae68
A012468	Expansion of e.g.f. arcsin(cos(x) * log(x+1)).	[ "0", "1", "-1", "0", "-6", "23", "-135", "1288", "-10164", "106661", "-1257165", "15497152", "-222045450", "3414340811", "-56743257571", "1031328757912", "-19972120728840", "414440475923689", "-9175579196399001", "215060308589382272" ]	[ "sign" ]	11	0	5	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2019-05-10T15:40:01	oeisdata/seq/A012/A012468.seq	b5d66cbc1d2ed7662f62d012d6808610
A012469	Expansion of e.g.f. arctan(cos(x) * log(x+1)).	[ "0", "1", "-1", "-3", "12", "23", "-495", "931", "27552", "-214699", "-1991565", "44340769", "25066668", "-9372982933", "70732779845", "2089607037415", "-43990273165920", "-339320074587383", "22626180254319399", "-95718973807370395" ]	[ "sign" ]	7	0	4	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2018-07-19T17:38:34	oeisdata/seq/A012/A012469.seq	9d1163a3fdd0590a0bec510c0a037300
A012470	arcsinh(cos(x)log(x+1))=x-1/2!x^2-2/3!x^3+6/4!x^4+13/5!*x^5...	[ "0", "1", "-1", "-2", "6", "13", "-225", "530", "8540", "-65579", "-650565", "13899070", "-8281878", "-2388363655", "18379145603", "516826612354", "-11083263907560", "-64702488848279", "5027641615912599", "-24199820388513346" ]	[ "sign" ]	8	0	4	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2013-11-02T08:23:52	oeisdata/seq/A012/A012470.seq	6344fd32f1ac39d25585b2550a6e10a3
A012471	Expansion of e.g.f. arctanh(cos(x)*log(x+1)).	[ "0", "1", "-1", "1", "-12", "43", "-315", "2987", "-24976", "288541", "-3544965", "46607053", "-707823996", "11389328039", "-199011366463", "3776136616951", "-76078523849280", "1640713749767833", "-37603782922082121", "910746316680339641" ]	[ "sign" ]	9	0	5	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2020-08-18T14:20:57	oeisdata/seq/A012/A012471.seq	f8575f363a14b9a60e99d2af2855b881
A012472	Expansion of e.g.f.: sec(cos(x)log(x+1))=1+1/2!x^2-3/3!x^3+4/4!x^4-40/5!*x^5...	[ "1", "0", "1", "-3", "4", "-40", "250", "-1260", "14012", "-133992", "1310660", "-16809980", "215083592", "-2938291200", "45330896832", "-728363224680", "12475447944528", "-230003712851648", "4451144492528080", "-91010462837366448" ]	[ "sign" ]	6	0	4	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2014-12-24T11:51:36	oeisdata/seq/A012/A012472.seq	c63f495d1e680dde295d523ebb4eb392
A012473	sech(cos(x)log(x+1))=1-1/2!x^2+3/3!x^3+6/4!x^4-60/5!*x^5...	[ "1", "0", "-1", "3", "6", "-60", "0", "2310", "-10752", "-84168", "1152240", "2453880", "-154467192", "797768400", "16907851688", "-250017997320", "-1746679208128", "77446551835648", "-318565680255360", "-18241668233387712", "262053618149070080" ]	[ "sign" ]	4	0	4	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:50	oeisdata/seq/A012/A012473.seq	832119f79db74aa0890b37521dbc4eed
A012474	Expansion of arcsin(cos(x)sin(x)) = x - 3/3!x^3 - 15/5!x^5 + 357/7!x^7 + 22305/9!*x^9...	[ "1", "-3", "-15", "357", "22305", "-582483", "-217683375", "-2001865323", "7258418490945", "826442897487837", "-580853295560646735", "-204631967729205027003", "85920364932388858911585", "79053144190920049745846157" ]	[ "sign" ]	7	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2021-07-18T12:12:31	oeisdata/seq/A012/A012474.seq	1507e686ddbea824625ccca505965857
A012475	arctan(cos(x)sin(x))=x-6/3!x^3+120/5!x^5-7056/7!x^7+758400/9!*x^9...	[ "1", "-6", "120", "-7056", "758400", "-130918656", "33173038080", "-11587651270656", "5337660866396160", "-3134856182239789056", "2286367634020679024640", "-2027369655249396662009856", "2147914157998443571728875520" ]	[ "sign" ]	4	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:50	oeisdata/seq/A012/A012475.seq	f5948dfab0d0cf6bd3088c8041ba2e28
A012476	arcsinh(cos(x)sin(x))=x-5/3!x^3+65/5!x^5-3005/7!x^7+278465/9!*x^9...	[ "1", "-5", "65", "-3005", "278465", "-42738005", "9852460865", "-3178878885005", "1367383455547265", "-756164182327284005", "522662665715777337665", "-441523138107985704375005", "447556468280585958726432065" ]	[ "sign" ]	8	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2013-10-31T04:33:27	oeisdata/seq/A012/A012476.seq	fd27da69a1fa33343cdae9c87939693d
A012477	arctanh(cos(x)sin(x))=x-2/3!x^3-40/5!x^5+208/7!x^7+64640/9!*x^9...	[ "1", "-2", "-40", "208", "64640", "986368", "-652487680", "-60911593472", "20973645824000", "6185783347314688", "-1429441147870904320", "-1203534317202507825152", "109702530161745707663360", "415034067689086640359211008" ]	[ "sign" ]	8	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2013-10-24T09:54:57	oeisdata/seq/A012/A012477.seq	4f6aced36205dd03e7c6653f6f09df27
A012478	sec(cos(x)sin(x))=1+1/2!x^2-11/4!x^4-83/6!x^6+10505/8!*x^8...	[ "1", "1", "-11", "-83", "10505", "6009", "-60553539", "2140355557", "1174906248337", "-146823377897103", "-55094515820657147", "17482899642565858461", "4900898798285366105753", "-3664217968514770645784087" ]	[ "sign" ]	6	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2022-11-09T13:30:02	oeisdata/seq/A012/A012478.seq	11e32eee49a248afe161322b6b3041fc
A012479	sech(cos(x)sin(x))=1-1/2!x^2+21/4!x^4-717/6!x^6+46025/8!*x^8...	[ "1", "-1", "21", "-717", "46025", "-4817209", "734055069", "-154121194437", "42674286160913", "-15062120873888497", "6601538801733818277", "-3517682024725193957181", "2239550167783452398617817", "-1678950113256157460626211113" ]	[ "sign" ]	4	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:51	oeisdata/seq/A012/A012479.seq	d525a980ca6d1d65d8aec7068006e0b0
A012480	Expansion of e.g.f.: exp(cos(x)arcsin(x))=1+x+1/2!x^2-1/3!x^3-7/4!x^4-15/5!*x^5...	[ "1", "1", "1", "-1", "-7", "-15", "25", "359", "1297", "3713", "785", "347151", "3237577", "62839153", "476552297", "10196506423", "93536269473", "2397571040897", "25410713978785", "714196911010335", "8498142387238425", "263318643848985457" ]	[ "sign" ]	6	0	5	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2024-07-21T15:09:51	oeisdata/seq/A012/A012480.seq	03f8016dfc8c32e704a1578f7570a4bf
A012481	sin(cos(x)arcsin(x))=x-3/3!x^3+25/5!x^5-371/7!x^7+11985/9!*x^9...	[ "1", "-3", "25", "-371", "11985", "13981", "45127017", "5553908333", "1415759895841", "404022487469117", "148035510590478137", "65626203271548278349", "34895786732343693436145", "21890894044531231133450973" ]	[ "sign" ]	4	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:51	oeisdata/seq/A012/A012481.seq	4f360461728914dd74e36f648953342c
A012482	arcsin(cos(x)arcsin(x))=x-1/3!x^3-7/5!x^5+23/7!x^7+8017/9!*x^9...	[ "1", "-1", "-7", "23", "8017", "747727", "74222601", "10474339367", "2425803672609", "797453256598559", "314897142584114585", "142725117278783779511", "75352861977241143203441", "47181023399211225968222703" ]	[ "sign" ]	4	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:51	oeisdata/seq/A012/A012482.seq	1d3805ee26e5c042c8cf88b9666d36e9
A012483	E.g.f.: tan(cos(x)arcsin(x))=x-20/5!x^5-56/7!x^7+20112/9!x^9...	[ "1", "0", "-20", "-56", "20112", "1097536", "38765376", "9775415168", "3760405592320", "1130444627523584", "374326578677906432", "166462985126115207168", "92968540423042714603520", "59757419067771727772172288" ]	[ "sign" ]	11	1	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-07-20T14:10:09	oeisdata/seq/A012/A012483.seq	b6168667c942bef9e4fcfe09372c9e77
A012484	arctan(cos(x)arcsin(x))=x-4/3!x^3+68/5!x^5-3064/7!x^7+265936/9!*x^9...	[ "1", "-4", "68", "-3064", "265936", "-35730176", "7235106240", "-1984468240000", "725871298851072", "-336136505074527232", "194162507080835314688", "-135973687998348753147904", "113975638131557424617639936" ]	[ "sign" ]	4	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:51	oeisdata/seq/A012/A012484.seq	d5ac59ec2cc1dbbd9500a803b666bf13
A012485	cos(cos(x)arcsin(x))=1-1/2!x^2+9/4!x^4-105/6!x^6+1393/8!*x^8...	[ "1", "-1", "9", "-105", "1393", "-71025", "-898887", "-455252889", "-75822681503", "-21366754787169", "-7036035942040855", "-2891117170991668553", "-1426147181806835610927", "-835104626729810211267025" ]	[ "sign" ]	6	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2022-10-14T11:01:51	oeisdata/seq/A012/A012485.seq	c80a0547f8f7f924705cc28e5ca1082f
A012486	sinh(cos(x)arcsin(x))=x-1/3!x^3-15/5!x^5+359/7!x^7+3713/9!*x^9...	[ "1", "-1", "-15", "359", "3713", "347151", "62839153", "10196506423", "2397571040897", "714196911010335", "263318643848985457", "118248746057101708295", "63495547245752463558145", "40188528694405725339687983" ]	[ "sign" ]	6	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2020-06-02T12:02:08	oeisdata/seq/A012/A012486.seq	d8d6c27f785c3d6c5e8e2ec7ddd72dc5
A012487	arcsinh(cos(x)arcsin(x))=x-3/3!x^3+33/5!x^5-1155/7!x^7+91553/9!*x^9...	[ "1", "-3", "33", "-1155", "91553", "-10478435", "2004751617", "-496122561571", "172663180364481", "-74458608812963395", "41124360344562400097", "-27302583872806500602179", "21988222585362167359370081" ]	[ "sign" ]	4	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:51	oeisdata/seq/A012/A012487.seq	572be38a9b4fe7ee12c6b31884d35ec9
A012488	tanh(cos(x)arcsin(x))=x-4/3!x^3+60/5!x^5-2056/7!x^7+127376/9!*x^9...	[ "1", "-4", "60", "-2056", "127376", "-11253504", "1524986944", "-257629834112", "60842617280768", "-16737691854400512", "6112605714322803712", "-2481449664133693548544", "1299422306103439813611520" ]	[ "sign" ]	6	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2020-06-20T16:34:50	oeisdata/seq/A012/A012488.seq	8f518e4b3cea5d6ed381a45375c3f1d1
A012489	arctanh(cos(x)arcsin(x))=x-12/5!x^5-168/7!x^7+8144/9!x^9...	[ "1", "0", "-12", "-168", "8144", "1384768", "149032128", "16299168896", "2859883876608", "1008997773326336", "466978134769624064", "228641400872390260736", "120327829272472868704256", "72933308761894955432460288" ]	[ "sign" ]	6	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2019-02-10T17:17:40	oeisdata/seq/A012/A012489.seq	2d06e11b3be60311c312c2595574eb77
A012490	cosh(cos(x)arcsin(x))=1+1/2!x^2-7/4!x^4+25/6!x^6+1297/8!*x^8...	[ "1", "1", "-7", "25", "1297", "785", "3237577", "476552297", "93536269473", "25410713978785", "8498142387238425", "3493252199008249913", "1729861042158836509361", "1015648464575702746171825", "697882405841324552721582569" ]	[ "sign" ]	4	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:51	oeisdata/seq/A012/A012490.seq	db1364678f908fad2b0acbe7de1c48bb
A012491	sec(cos(x)arcsin(x))=1+1/2!x^2-3/4!x^4-75/6!x^6+1337/8!*x^8...	[ "1", "1", "-3", "-75", "1337", "144105", "3933237", "118760733", "129911988593", "47180864336337", "13805291952312685", "5130037600431416453", "2642764719782227835049", "1617152674535806453668025" ]	[ "sign" ]	4	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:51	oeisdata/seq/A012/A012491.seq	0ff6a010ff7094b7d7dc4d8b2d92a1fe
A012492	sech(cos(x)arcsin(x))=1-1/2!x^2+13/4!x^4-325/6!x^6+14873/8!*x^8...	[ "1", "-1", "13", "-325", "14873", "-1157705", "123919013", "-19431568013", "3783114987057", "-997881588156817", "307028543021467965", "-122601833964174456533", "54600351690827520350281", "-30810847280896713474456025" ]	[ "sign" ]	4	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:51	oeisdata/seq/A012/A012492.seq	d4f277d8431a7c5c92fcf8a54ee39266
A012493	Take every 5th term of Padovan sequence A000931, beginning with the fifth term.	[ "0", "2", "9", "37", "151", "616", "2513", "10252", "41824", "170625", "696081", "2839729", "11584946", "47261895", "192809420", "786584466", "3208946545", "13091204281", "53406819691", "217878227876", "888855064897", "3626169232672", "14793304131648" ]	[ "nonn", "easy", "changed" ]	22	0	2	null	null	N. J. A. Sloane	2025-07-08T02:46:54	oeisdata/seq/A012/A012493.seq	680314bc6c1c431497081944278fb56c
A012494	Expansion of e.g.f. arctan(sin(x)) (odd powers only).	[ "1", "-3", "45", "-1743", "125625", "-14554683", "2473184805", "-579439207623", "179018972217585", "-70518070842040563", "34495620120141463965", "-20515677772241956573503", "14578232896601243652363945", "-12198268199871431840616166443", "11871344562637111570703016357525" ]	[ "sign", "easy" ]	51	0	2	[ "A000281", "A000364", "A001209", "A002437", "A003704", "A012494", "A013208", "A101923", "A156134" ]	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2018-08-17T02:41:53	oeisdata/seq/A012/A012494.seq	f157efcbfff45ad1b510d49e41b48ed7
A012495	Expansion of e.g.f. arcsinh(sin(x)) (odd powers only).	[ "1", "-2", "20", "-632", "39440", "-4087712", "634237760", "-137605112192", "39776178356480", "-14775064298435072", "6857795892626969600", "-3889298341511511652352", "2646362625886738240901120", "-2127690488032789501903020032" ]	[ "sign" ]	25	0	2	[ "A012495", "A101922" ]	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2023-09-29T13:09:28	oeisdata/seq/A012/A012495.seq	6425787dd51fbdf3d53159c5cdae72b5
A012496	exp(cos(x)arctan(x))=1+x+1/2!x^2-4/3!x^3-19/4!x^4+445/6!*x^6...	[ "1", "1", "1", "-4", "-19", "0", "445", "1304", "-14663", "-109120", "718265", "10816896", "-50970203", "-1441841024", "4876389557", "258762139648", "-548752599567", "-60872480247808", "47436062951281", "18224782774259712", "12631837146241245" ]	[ "sign" ]	7	0	4	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2013-11-21T12:46:01	oeisdata/seq/A012/A012496.seq	4c292cf0d6f78bf5331dfe97db1cc1fc
A012497	sin(cos(x)arctan(x))=x-6/3!x^3+100/5!x^5-4256/7!x^7+302352/9!*x^9...	[ "1", "-6", "100", "-4256", "302352", "-32245664", "4879093440", "-996485811712", "264232448010496", "-88283645811756544", "36292696703112000512", "-18004529956099757727744", "10606618572326341265592320" ]	[ "sign" ]	6	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2025-04-17T15:26:16	oeisdata/seq/A012/A012497.seq	42cef17f9841420fbb3b0fb40567fd89
A012498	arcsin(cos(x)arctan(x))=x-4/3!x^3+8/5!x^5+128/7!x^7+25216/9!*x^9...	[ "1", "-4", "8", "128", "25216", "-3387008", "160621056", "-6497102848", "10675803193344", "-4485074198855680", "823007646284349440", "-188938583696417751040", "280059136770757168726016", "-235157137580491486235983872" ]	[ "sign" ]	6	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2019-11-16T13:25:29	oeisdata/seq/A012/A012498.seq	ca29ebf5c69208a764b44107a446e4d3
A012499	Expansion of e.g.f. tan(cos(x)*arctan(x)) (odd powers only).	[ "1", "-3", "-35", "1729", "-12711", "-5819099", "581423349", "26066838953", "-19485197470415", "2379630157273805", "789057561743200397", "-445703452244142678255", "25928070972710765150345", "80008658408138506870433013", "-41780425117352684596856468827", "-7585811803346771885529485351175", "23110904483392454783722911793216609" ]	[ "sign" ]	11	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2025-03-11T10:56:13	oeisdata/seq/A012/A012499.seq	d0e1336761c36e5af2db92ea9e0a2d26
A012500	arctan(cos(x)arctan(x))=x-7/3!x^3+173/5!x^5-11779/7!x^7...	[ "1", "-7", "173", "-11779", "1474969", "-296068991", "87094091589", "-35308668668155", "18872654969343537", "-12860552599622997751", "10882609077370643446493", "-11195876625633675125480947", "13761866805554489099492092361" ]	[ "sign" ]	7	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2015-10-04T13:06:34	oeisdata/seq/A012/A012500.seq	0bb75ec619e9d01d6cf9b9d43ab7df92

A012401

Expansion of e.g.f.: sinh(arctan(x)*log(x+1))=2/2!*x^2-3/3!*x^3-10/5!*x^5+328/6!*x^6...

[ "0", "0", "2", "-3", "0", "-10", "328", "-2184", "5040", "-40104", "1311552", "-15123240", "72848160", "-748098000", "27513786480", "-450798649560", "3381295357440", "-44199243856320", "1837919010900480", "-39019174967975040", "402216681934690560" ]

[ "sign" ]

6

0

3

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2018-02-13T19:34:46

oeisdata/seq/A012/A012401.seq

95480dbc426236f896f880acce6c1ec3

A012402

arcsinh(arctan(x)*log(x+1)) = 2/2!*x^2 - 3/3!*x^3 - 10/5!*x^5 + 88/6!*x^6 - ...

[ "2", "-3", "0", "-10", "88", "336", "-5040", "5256", "202752", "-2094840", "26943840", "-534147120", "7877529840", "-41350410360", "-804692528640", "16885512006720", "-166653340523520", "3621340758072960", "-48704381263560960", "-2035821123825148800", "99959690241598844160", "-1979439236443512264960" ]

[ "sign" ]

9

2

1

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2012-11-27T11:28:39

oeisdata/seq/A012/A012402.seq

5304b392307324b3ed6cfcad5f439546

A012403

E.g.f. tanh(arctan(x)*log(x+1)).

[ "2", "-3", "0", "-10", "-32", "1596", "-10080", "27936", "-260928", "1924560", "33929280", "-686630880", "4846421760", "-42426084960", "778331473920", "-1890071554560", "-216298842931200", "4070252020032000", "-41366803088056320" ]

[ "sign" ]

16

2

1

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2025-06-01T22:21:19

oeisdata/seq/A012/A012403.seq

c444b1e490c154d752afac0804086226

A012404

arctanh(arctan(x)*log(x+1))=2/2!*x^2-3/3!*x^3-10/5!*x^5+448/6!*x^6...

[ "0", "0", "2", "-3", "0", "-10", "448", "-3444", "10080", "-62784", "2682432", "-44090640", "365238720", "-3190206240", "98622664320", "-2518618203360", "38819985684480", "-522802362915840", "13679170866554880", "-437041001210135040" ]

[ "sign" ]

6

0

3

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2016-11-28T18:29:14

oeisdata/seq/A012/A012404.seq

be7c78d0ff63034f780fb1341cd35f9f

A012405

Expansion of e.g.f.: cosh(arctan(x)*log(x+1))=1+12/4!*x^4-60/5!*x^5+90/6!*x^6-420/7!*x^7...

[ "1", "0", "0", "0", "12", "-60", "90", "-420", "15008", "-149184", "572040", "-4263600", "153746472", "-2274880608", "14574976416", "-151922927520", "6077379610368", "-119360435727744", "1090133783570880", "-14675613664063104" ]

[ "sign" ]

6

0

5

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2019-06-22T19:08:17

oeisdata/seq/A012/A012405.seq

b9723e7dd0b930ca8b47019ef1a66e62

A012406

Expansion of e.g.f.: sec(arctan(x)*log(x+1))=1+12/4!*x^4-60/5!*x^5+90/6!*x^6-420/7!*x^7...

[ "1", "0", "0", "0", "12", "-60", "90", "-420", "21728", "-270144", "1479240", "-9807600", "330821832", "-6651092448", "71604108576", "-744095308320", "20714430198528", "-548875353239424", "9233126375705280", "-138948347142163584" ]

[ "sign" ]

6

0

5

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2018-04-07T13:23:08

oeisdata/seq/A012/A012406.seq

a3d93bb7b2085963165f2465eb8a2848

A012407

sech(arctan(x)*log(x+1)) = 1 - 12/4!*x^4 + 60/5!*x^5 - 90/6!*x^6 + 420/7!*x^7...

[ "1", "0", "0", "0", "-12", "60", "-90", "420", "-4928", "-32256", "788760", "-4052400", "12074568", "-397549152", "2860681824", "80960836320", "-1570434928128", "8575093540224", "-83967092441280", "3671889608928384", "-27749577690072192" ]

[ "sign" ]

12

0

5

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2013-10-31T12:17:13

oeisdata/seq/A012/A012407.seq

fa17795061c7c2b9931f68eb5bce7f01

A012408

exp(arctan(x)*exp(x))=1+x+3/2!*x^2+8/3!*x^3+25/4!*x^4+100/5!*x^5...

[ "1", "1", "3", "8", "25", "100", "465", "2186", "10273", "58568", "428193", "2778382", "11360177", "71102044", "1639157169", "15866637762", "-85280723135", "-1590866608240", "41214840121921", "683822331420054", "-11338214469525167" ]

[ "sign" ]

4

0

3

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2012-02-24T12:50:48

oeisdata/seq/A012/A012408.seq

7474e4afa81906e7d8737aa8ce43aa00

A012409

E.g.f. sin(arctan(x)*exp(x)).

[ "0", "1", "2", "0", "-16", "-60", "-40", "336", "-2560", "-20976", "342688", "4002944", "-24866048", "-523996096", "3812202368", "103065059072", "-777384271872", "-26888473739008", "196597142376960", "8734488670474240", "-63053651090673664" ]

[ "sign" ]

16

0

3

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2013-05-17T11:44:21

oeisdata/seq/A012/A012409.seq

cbc1fe61a861046afc6cc1f8a6b0fa75

A012410

Expansion of e.g.f. arcsin(arctan(x) * exp(x)).

[ "0", "1", "2", "2", "8", "88", "560", "3880", "48064", "645376", "8447488", "129332480", "2305269760", "43823270528", "893173681920", "19883237893376", "476731844235264", "12171513901662208", "330755844515020800", "9543303550734733312", "291053885585803034624", "9354941906907855192064" ]

[ "nonn" ]

11

0

3

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2018-07-19T02:57:21

oeisdata/seq/A012/A012410.seq

5f925690f8fec1884fd54a056c1727d8

A012411

arctan(arctan(x)*exp(x)) = x + 2/2!*x^2 - 1/3!*x^3 - 28/4!*x^4 - 107/5!*x^5 + ...

[ "0", "1", "2", "-1", "-28", "-107", "470", "10243", "51592", "-677879", "-15870422", "-76105753", "2647708780", "62662672733", "171362144382", "-21259413359701", "-489069754224624", "774485831879569", "300884931182492754" ]

[ "sign" ]

9

0

3

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2018-01-15T15:26:01

oeisdata/seq/A012/A012411.seq

7862fece688dfd13af676d1927c26327

A012412

cos(arctan(x)*exp(x))=1-1/2!*x^2-6/3!*x^3-15/4!*x^4+20/5!*x^5...

[ "1", "0", "-1", "-6", "-15", "20", "255", "70", "-3423", "46728", "501375", "-3625358", "-60112239", "420430556", "9211149311", "-79037179650", "-2033765765567", "18361020368016", "572833991092479", "-5418169914165654", "-201869115241158607" ]

[ "sign" ]

4

0

4

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2012-02-24T12:50:49

oeisdata/seq/A012/A012412.seq

7285fe1cb0ff48a489a3f96426d0b5ed

A012413

sinh(arctan(x)*exp(x)) = x + 2/2!*x^2 + 2/3!*x^3 + 8/4!*x^4 + 80/5!*x^5 +...

[ "0", "1", "2", "2", "8", "80", "320", "16", "1920", "99776", "416128", "-5760896", "-13486592", "1070744064", "3323114496", "-195141029888", "-464796680192", "51108813787136", "107290616242176", "-16422323853352960", "-25773434486882304" ]

[ "sign" ]

13

0

3

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2013-11-21T12:46:01

oeisdata/seq/A012/A012413.seq

f888a5ab20302d313c1974f62f0ccc31

A012414

Expansion of e.g.f. arcsinh(arctan(x) * exp(x)).

[ "0", "1", "2", "0", "-16", "-52", "200", "3752", "18496", "-190384", "-4797152", "-28063552", "661457920", "17348360768", "74504846208", "-4999196993152", "-124352680593408", "-83620707815168", "65968266617811456", "1541961961341134848" ]

[ "sign" ]

9

0

3

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2018-07-19T03:05:05

oeisdata/seq/A012/A012414.seq

e07c2f69c63773ce9b0d68d66f99393a

A012415

Expansion of e.g.f. tanh(arctan(x) * exp(x)).

[ "0", "1", "2", "-1", "-28", "-115", "230", "7051", "43080", "-172327", "-6067382", "-47080361", "309697324", "12289126629", "114505019694", "-1105109602973", "-48948382516592", "-522517588252495", "7065091754607762", "338212264324430255" ]

[ "sign" ]

17

0

3

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2024-08-04T04:14:47

oeisdata/seq/A012/A012415.seq

88d073192beee015183886ba4499e006

A012416

arctanh(arctan(x)*exp(x))=x+2/2!*x^2+3/3!*x^3+20/4!*x^4+173/5!*x^5...

[ "0", "1", "2", "3", "20", "173", "1190", "11039", "140968", "1855481", "26494858", "441706331", "8105309500", "159190672613", "3403623626286", "78823813121975", "1949180731782480", "51354602068725361", "1439864769232356882" ]

[ "nonn" ]

12

0

3

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2016-11-28T18:32:17

oeisdata/seq/A012/A012416.seq

5563f33cd6d873ba3343413f1b681f99

A012417

cosh(arctan(x)*exp(x))=1+1/2!*x^2+6/3!*x^3+17/4!*x^4+20/5!*x^5...

[ "1", "0", "1", "6", "17", "20", "145", "2170", "8353", "-41208", "12065", "8539278", "24846769", "-999642020", "-1683957327", "211007667650", "379515957057", "-52699680395376", "-66075776120255", "17106146184773014", "14435220017357137" ]

[ "sign" ]

6

0

4

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2012-12-15T12:33:12

oeisdata/seq/A012/A012417.seq

88dc4da9b921039b9ac2f36ee4ba31e6

A012418

Expansion of e.g.f.: sec(arctan(x)*exp(x))=1+1/2!*x^2+6/3!*x^3+21/4!*x^4+100/5!*x^5...

[ "1", "0", "1", "6", "21", "100", "1005", "9170", "73353", "794952", "11042745", "144625118", "1936131549", "31475441452", "562265168101", "9960214270890", "187956163443857", "3970728871687824", "88040662078595313", "1994667867977462454" ]

[ "nonn" ]

6

0

4

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2016-03-19T16:17:11

oeisdata/seq/A012/A012418.seq

0a956ded4a065c6ca16c75e4cbc094b0

A012419

Expansion of e.g.f.: sech(arctan(x)*exp(x))=1-1/2!*x^2-6/3!*x^3-11/4!*x^4+100/5!*x^5...

[ "1", "0", "-1", "-6", "-11", "100", "995", "2030", "-45943", "-568632", "-1189145", "54818082", "845395901", "1936128428", "-142744278261", "-2685086733290", "-6197620433007", "713212265955216", "15393015776009807", "26780979282600266" ]

[ "sign" ]

6

0

4

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2016-03-06T11:01:09

oeisdata/seq/A012/A012419.seq

2bb616018fd455135820e31300a1b857

A012420

exp(arctan(x)*sin(x))=1+2/2!*x^2-50/6!*x^6+56/8!*x^8+27178/10!*x^10...

[ "1", "2", "0", "-50", "56", "27178", "-2358884", "320163870", "-64993423408", "17229734819538", "-5720421047111484", "2329873846478810630", "-1143585527502409144520", "666071310836628939214906", "-454305678798485051002579924" ]

[ "sign" ]

6

0

2

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2016-06-19T10:06:12

oeisdata/seq/A012/A012420.seq

b2bfb325f0719a631441feec245a1301

A012421

sin(arctan(x)*sin(x))=2/2!*x^2-12/4!*x^4+70/6!*x^6+2856/8!*x^8...

[ "2", "-12", "70", "2856", "-406262", "53106460", "-8809933106", "1910193704272", "-531575014780398", "185190064964692804", "-78983931548861495466", "40480351020220065079928", "-24547642682771502545050854" ]

[ "sign" ]

4

0

1

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2012-02-24T12:50:49

oeisdata/seq/A012/A012421.seq

731e70642448b6fda6262c98bd132dfd

A012422

arcsin(arctan(x)*sin(x))=2/2!*x^2-12/4!*x^4+310/6!*x^6-17304/8!*x^8...

[ "2", "-12", "310", "-17304", "1700458", "-258909860", "56652535966", "-16866155567408", "6564236008307922", "-3237559423419911996", "1974150395798812732422", "-1458519974560491245318344", "1283942399735883713487058746" ]

[ "sign" ]

6

0

1

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2022-02-26T18:55:52

oeisdata/seq/A012/A012422.seq

c4fda32cb28376c505cda1eef6e88b0b

A012423

arctan(arctan(x)*sin(x))=2/2!*x^2-12/4!*x^4-50/6!*x^6+12936/8!*x^8...

[ "0", "2", "-12", "-50", "12936", "-643142", "-60323780", "22895524678", "-2421315237488", "-864760878344718", "527455288321939204", "-55917569000158790850", "-108932420480580224669416", "83957330220575698201816746" ]

[ "sign" ]

6

0

2

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2016-11-28T18:36:41

oeisdata/seq/A012/A012423.seq

fdd25f1e57e7f4a0ac4b5ac5afac210d

A012424

cos(arctan(x)*sin(x))=1-12/4!*x^4+360/6!*x^6-14000/8!*x^8...

[ "1", "0", "-12", "360", "-14000", "826560", "-74707776", "9918004096", "-1826276458240", "443565659817984", "-136830226103770112", "52123659256392435712", "-23992831220659002945536", "13113491065080505366691840" ]

[ "sign" ]

6

0

3

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2015-05-24T10:05:17

oeisdata/seq/A012/A012424.seq

e4063f875bd0c6ddc2d4f4d2b1a3d98d

A012425

sinh(arctan(x)*sin(x))=2/2!*x^2-12/4!*x^4+310/6!*x^6-17304/8!*x^8...

[ "2", "-12", "310", "-17304", "1458538", "-179076260", "30579769246", "-6937516847408", "2018483632983762", "-732877524097108796", "324856264038732166662", "-172652168729948174280904", "108374992202504938057945146" ]

[ "sign" ]

4

0

1

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2012-02-24T12:50:49

oeisdata/seq/A012/A012425.seq

b3365027e06bf928ce4ab90183f362c8

A012426

arcsinh(arctan(x)*sin(x))=2/2!*x^2-12/4!*x^4+70/6!*x^6+2856/8!*x^8...

[ "2", "-12", "70", "2856", "-164342", "-26727140", "9513652174", "-1509132606128", "-24850989613038", "96289752279508804", "-8229825010792301226", "-30295913573130207257992", "26332910393982197524318746" ]

[ "sign" ]

4

0

1

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2012-02-24T12:50:49

oeisdata/seq/A012/A012426.seq

a8ea8e34e0df91a10aea0b1a99da4c5a

A012427

tanh(arctan(x)*sin(x))=2/2!*x^2-12/4!*x^4-50/6!*x^6+12936/8!*x^8...

[ "2", "-12", "-50", "12936", "-885062", "19509820", "8446530118", "-2256645131888", "271169972750322", "52894208663673604", "-48060787092036123330", "16320006114052519358744", "-62047368403218100000854" ]

[ "sign" ]

4

0

1

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2012-02-24T12:50:49

oeisdata/seq/A012/A012427.seq

9f02cfe377dcb93c0bf0bb1fde5cbf72

A012428

arctanh(arctan(x)*sin(x))=2/2!*x^2-12/4!*x^4+430/6!*x^6-27384/8!*x^8...

[ "0", "2", "-12", "430", "-27384", "3086458", "-524689220", "126513823462", "-40981407368048", "17181884789561202", "-9052122654113318396", "5854705311144202022046", "-4561027328402726456335720", "4212695076131749316430016746" ]

[ "sign" ]

7

0

2

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2016-11-28T18:38:19

oeisdata/seq/A012/A012428.seq

44a2f4756f03d57856389b692edccb0c

A012429

cosh(arctan(x)*sin(x))=1+12/4!*x^4-360/6!*x^6+17360/8!*x^8...

[ "1", "0", "12", "-360", "17360", "-1431360", "176717376", "-30259605376", "6872523424000", "-2001253898164224", "727157103049997312", "-322526390192253356032", "171508583202445765136384", "-107708920891668309118730240" ]

[ "sign" ]

4

0

3

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2012-02-24T12:50:49

oeisdata/seq/A012/A012429.seq

e348c586f222e2c449f774786be4bf34

A012430

sec(arctan(x)*sin(x))=1+12/4!*x^4-360/6!*x^6+24080/8!*x^8...

[ "1", "0", "12", "-360", "24080", "-2640960", "420653376", "-92737380736", "26980142475520", "-10012413760149504", "4615824952212134912", "-2587662789242232604672", "1733488941554235507937280", "-1367558750121199449308119040" ]

[ "sign" ]

4

0

3

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2012-02-24T12:50:49

oeisdata/seq/A012/A012430.seq

ed2196a81a9aa05d7b9ab46965ce2121

A012431

sech(arctan(x)*sin(x)) = 1-12/4!*x^4+360/6!*x^6-7280/8!*x^8...

[ "1", "0", "-12", "360", "-7280", "-383040", "89394624", "-8970625664", "-316692862720", "470941672802304", "-146844936720038912", "18279034160407939072", "9932590980055055503360", "-8395139128320596309032960" ]

[ "sign" ]

8

0

3

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2023-05-12T14:54:33

oeisdata/seq/A012/A012431.seq

e6a79e758e3905eb8207c2448c3561b1

A012432

exp(arctan(x)*arcsin(x))=1+2/2!*x^2+8/4!*x^4+158/6!*x^6+4104/8!*x^8...

[ "1", "2", "8", "158", "4104", "346602", "24240372", "4851149886", "651838359408", "239431266389586", "52363260776961132", "30711336758113317990", "9908919510460647921960", "8503014202216759714206330", "3792595745728445864618214180", "4484803880283207420946418876430" ]

[ "nonn" ]

6

0

2

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2014-08-18T15:42:50

oeisdata/seq/A012/A012432.seq

3e55a24685b58313216b5a00dc861b2e

A012433

sin(arctan(x)*arcsin(x))=2/2!*x^2-4/4!*x^4+38/6!*x^6-264/8!*x^8...

[ "2", "-4", "38", "-264", "9162", "6423540", "-875983890", "380802735600", "-91040517107310", "46795149700613100", "-17544576509662829130", "11815590123153714787560", "-6408554682643734028619430", "5614434324236056272171194340" ]

[ "sign" ]

4

0

1

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2012-02-24T12:50:49

oeisdata/seq/A012/A012433.seq

f139410dc5afc80496664e93e8ea824f

A012434

arcsin(arctan(x)*arcsin(x))=2/2!*x^2-4/4!*x^4+278/6!*x^6-6984/8!*x^8...

[ "2", "-4", "278", "-6984", "1148202", "-99018060", "28635818430", "-5588393370000", "2487224151815250", "-886910985311966100", "563430775878809461350", "-321709990033199535312600", "277763298278504193429092730" ]

[ "sign" ]

6

0

1

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2013-05-04T14:53:42

oeisdata/seq/A012/A012434.seq

3b4a3fdc7d842e75f594c7a06874a5bc

A012435

arctan(arctan(x)*arcsin(x))=2/2!*x^2-4/4!*x^4-82/6!*x^6+3096/8!*x^8...

[ "2", "-4", "-82", "3096", "256122", "-30668460", "856747110", "523284711600", "39637940511090", "-50848285138290900", "19464791037179683230", "1825136551296140381640", "99500526939660052179690", "-1613956014788908960338116220", "2918159856709476758087519928150" ]

[ "sign" ]

6

0

1

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2014-11-05T08:12:17

oeisdata/seq/A012/A012435.seq

22b6da0ce0639c7ebc2d3deb2fb98708

A012436

cos(arctan(x)*arcsin(x))=1-12/4!*x^4+120/6!*x^6-7728/8!*x^8...

[ "1", "0", "-12", "120", "-7728", "358080", "-54956352", "5983845504", "-1674895273728", "331567748941824", "-147083657045302272", "46138766175213803520", "-29742693904194176593920", "13565163573403491059712000" ]

[ "sign" ]

6

0

3

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2019-10-14T13:42:28

oeisdata/seq/A012/A012436.seq

4aeaad81d565cd6983b10b5ad09a6d04

A012437

sinh(arctan(x)*arcsin(x))=2/2!*x^2-4/4!*x^4+278/6!*x^6-6984/8!*x^8...

[ "2", "-4", "278", "-6984", "906282", "-72406860", "16769884350", "-2791769139600", "1025112403117650", "-291983305370462100", "156358879820283153510", "-68012449387139352098520", "50073830528033335130526330" ]

[ "sign" ]

4

0

1

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2012-02-24T12:50:50

oeisdata/seq/A012/A012437.seq

d4772d098fd4847c67baa10ad9bc6233

A012438

arcsinh(arctan(x)*arcsin(x))=2/2!*x^2-4/4!*x^4+38/6!*x^6-264/8!*x^8...

[ "2", "-4", "38", "-264", "251082", "-20187660", "3240768750", "-246050691600", "164895642091410", "-44832184763361300", "26301902902677945270", "-6982668079815620764440", "6485203397909159496161370" ]

[ "sign" ]

7

0

1

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2013-11-21T12:46:01

oeisdata/seq/A012/A012438.seq

3386a9b7c012a0c8d4a5e589cd5faead

A012439

tanh(arctan(x)*arcsin(x))=2/2!*x^2-4/4!*x^4-82/6!*x^6+3096/8!*x^8...

[ "2", "-4", "-82", "3096", "14202", "-4057260", "614585190", "65252737200", "9930277245810", "3938676912038700", "2327811184268315550", "661470912900859782600", "625005810716811201651690", "275157523021831158684027780" ]

[ "sign" ]

6

0

1

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2019-04-05T13:20:48

oeisdata/seq/A012/A012439.seq

300fc353698f8f937d7f35cd912874c7

A012440

arctanh(arctan(x)*arcsin(x))=2/2!*x^2-4/4!*x^4+398/6!*x^6-10344/8!*x^8...

[ "0", "2", "-4", "398", "-10344", "2050362", "-188329260", "60987377670", "-12776749381200", "6138167322301170", "-2341662552659308500", "1574696831249089102590", "-954442874464228447345080", "862598218425468174866650410" ]

[ "sign" ]

6

0

2

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2016-11-28T18:40:17

oeisdata/seq/A012/A012440.seq

4ae51784ca0a88938eb3c54e2768be70

A012441

cosh(arctan(x)*arcsin(x))=1+12/4!*x^4-120/6!*x^6+11088/8!*x^8...

[ "1", "0", "12", "-120", "11088", "-559680", "96647232", "-11918734464", "3443607499008", "-785681136728064", "344346566147423232", "-125647543062169835520", "77921368897600000020480", "-41570816325816575416320000" ]

[ "sign" ]

4

0

3

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2012-02-24T12:50:50

oeisdata/seq/A012/A012441.seq

55cd780b993f4254a756a01c1c8a9521

A012442

sec(arctan(x)*arcsin(x))=1+12/4!*x^4-120/6!*x^6+17808/8!*x^8...

[ "1", "0", "12", "-120", "17808", "-962880", "219945792", "-31053369984", "10719320103168", "-2908608708409344", "1441051026777725952", "-637493975166202091520", "433239709928964325478400", "-282573293205848764594176000" ]

[ "sign" ]

6

0

3

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2024-08-10T15:49:56

oeisdata/seq/A012/A012442.seq

603d1f889c3f6e6849595b893b4dbbc8

A012443

sech(arctan(x)*arcsin(x))=1-12/4!*x^4+120/6!*x^6-1008/8!*x^8...

[ "1", "0", "-12", "120", "-1008", "-45120", "-11491392", "1378925184", "-443544192768", "53698137606144", "-32840379055537152", "7093049054642411520", "-6636093887068155801600", "2065820944848385959936000" ]

[ "sign" ]

7

0

3

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2013-11-21T12:46:01

oeisdata/seq/A012/A012443.seq

776b23c285179b5487f05d0b59420c7e

A012444

exp(arctan(x)*tan(x))=1+2/2!*x^2+12/4!*x^4+280/6!*x^6+7952/8!*x^8...

[ "1", "2", "12", "280", "7952", "532768", "30306496", "4657640832", "327222722816", "131738463674880", "2341955285781504", "10584761954697844736", "-1750594656814587244544", "2213182839332047713673216" ]

[ "sign" ]

4

0

2

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2012-02-24T12:50:50

oeisdata/seq/A012/A012444.seq

791f2f6647ee076e3b3665197ae1a636

A012445

sin(arctan(x)*tan(x))=2/2!*x^2+40/6!*x^6-2688/8!*x^8-31712/10!*x^10...

[ "2", "0", "40", "-2688", "-31712", "-13038080", "-341144960", "-124075126784", "-16972742475264", "4013224846508032", "-4370688326014457856", "2734360152236817809408", "-2075517087570212545880064", "1712256529842324555250663424", "-1579921804125758497599230672896" ]

[ "sign" ]

6

0

1

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2014-12-20T18:46:56

oeisdata/seq/A012/A012445.seq

392cb7c69cad543b042feca35e8dc9ad

A012446

arcsin(arctan(x)*tan(x))=2/2!*x^2+280/6!*x^6-2688/8!*x^8+1016608/10!*x^10...

[ "2", "0", "280", "-2688", "1016608", "-44971520", "22528934272", "-2475890192384", "1731096311210496", "-365422134993502208", "343466758613102303232", "-121096429560806448922624", "146997236520941470929985536" ]

[ "sign" ]

6

0

1

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2013-11-05T10:28:29

oeisdata/seq/A012/A012446.seq

0c68a7f10fecc77ee665c23a318dbe0c

A012447

arctan(arctan(x)*tan(x))=2/2!*x^2-80/6!*x^6-2688/8!*x^8+260608/10!*x^10...

[ "0", "2", "0", "-80", "-2688", "260608", "2928640", "-463763456", "-517376835584", "108823739498496", "-2683131538178048", "5868236283429519360", "-6862655376791380688896", "2738386568702639562817536" ]

[ "sign" ]

8

0

2

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2016-11-28T18:43:21

oeisdata/seq/A012/A012447.seq

f5c5ba771659ff2350f2deb0245decbb

A012448

cos(arctan(x)*tan(x))=1-12/4!*x^4-7280/8!*x^8+241920/10!*x^10...

[ "1", "0", "-12", "0", "-7280", "241920", "-39796416", "5601756160", "-1164660739840", "326680627961856", "-107144725837171712", "45897715016709799936", "-22689657885234118356992", "13649678748377009638277120" ]

[ "sign" ]

4

0

3

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2012-02-24T12:50:50

oeisdata/seq/A012/A012448.seq

e1cfaae5cc5225d62af26779b3619ab8

A012449

sinh(arctan(x)*tan(x))=2/2!*x^2+280/6!*x^6-2688/8!*x^8+774688/10!*x^10...

[ "2", "0", "280", "-2688", "774688", "-44971520", "12196692352", "-2010939305984", "682495898190336", "-217798427799339008", "100459217814408271872", "-50559840345962764140544", "31791509418375951964839936" ]

[ "sign" ]

4

0

1

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2012-02-24T12:50:50

oeisdata/seq/A012/A012449.seq

63b68b57223065c0412bbf4c07f8e48e

A012450

arcsinh(arctan(x)*tan(x))=2/2!*x^2+40/6!*x^6-2688/8!*x^8+210208/10!*x^10...

[ "2", "0", "40", "-2688", "210208", "-13038080", "2241915520", "-589026013184", "146361182839296", "-42690102749216768", "18963982821764573184", "-10109322351828827471872", "5702647873782168851521536" ]

[ "sign" ]

6

1

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2012-02-24T12:50:50

oeisdata/seq/A012/A012450.seq

8e90199d048ca12ec2ba10d5f0bb0f42

A012451

tanh(arctan(x)*tan(x))=2/2!*x^2-80/6!*x^6-2688/8!*x^8+18688/10!*x^10...

[ "2", "0", "-80", "-2688", "18688", "2928640", "827766784", "-52425949184", "11263759220736", "-6439993741672448", "1974174235078164480", "-952764420869394006016", "577855093673994995367936", "-371995357739088472730238976" ]

[ "sign" ]

6

0

1

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2015-12-30T12:01:38

oeisdata/seq/A012/A012451.seq

25b51b7d19a3bae494b3f569a3e7d483

A012452

arctanh(arctan(x)*tan(x))=2/2!*x^2+400/6!*x^6-2688/8!*x^8...

[ "0", "2", "0", "400", "-2688", "1873408", "-60938240", "49450805248", "-4291105193984", "4345356280528896", "-769792296435580928", "962815994229666349056", "-298377426990773724774400", "452668537171760533299265536" ]

[ "sign" ]

6

0

2

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2016-11-28T18:46:16

oeisdata/seq/A012/A012452.seq

575ca3e5524fc81f617bf4959879847d

A012453

cosh(arctan(x)*tan(x))=1+12/4!*x^4+10640/8!*x^8-241920/10!*x^10...

[ "1", "0", "12", "0", "10640", "-241920", "75278016", "-7539051520", "2338162028800", "-550757434515456", "220140383085120512", "-89874455859710427136", "48809245689148176896000", "-29578326579043904251166720" ]

[ "sign" ]

4

0

3

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2012-02-24T12:50:50

oeisdata/seq/A012/A012453.seq

1545b25df227805ca5536f262d9c54df

A012454

sec(arctan(x)*tan(x))=1+12/4!*x^4+17360/8!*x^8-241920/10!*x^10...

[ "1", "0", "12", "0", "17360", "-241920", "186158016", "-11413642240", "7726026430720", "-1212323504480256", "892608906281741312", "-274005660019568705536", "234514059257417538031616", "-119571044071522301122641920" ]

[ "sign" ]

6

0

3

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2016-01-12T10:58:59

oeisdata/seq/A012/A012454.seq

d4258b714158ff2f77a09388111473d6

A012455

sech(arctan(x)*tan(x))=1-12/4!*x^4-560/8!*x^8+241920/10!*x^10...

[ "1", "0", "-12", "0", "-560", "241920", "-8750016", "1727165440", "-426305201920", "91939471712256", "-31563179893517312", "13087008599986241536", "-6237304648085400498176", "3651782585501269235793920" ]

[ "sign" ]

6

0

3

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2025-06-06T15:47:02

oeisdata/seq/A012/A012455.seq

51b0ecbd37d704cb82172205b7bb1bf7

A012456

exp((arctan(x))^2)=1+2/2!*x^2-4/4!*x^4+8/6!*x^6+912/8!*x^8...

[ "1", "2", "-4", "8", "912", "-99168", "11815872", "-1790856576", "347783278848", "-85244795874816", "25888104843574272", "-9570587679263078400", "4239434238319441121280", "-2218976274384029204766720" ]

[ "sign" ]

6

0

2

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2016-04-24T09:30:33

oeisdata/seq/A012/A012456.seq

2e51cab32bfce1425b1817c3d1d46439

A012457

sin(arctan(x)^2)=2/2!*x^2-16/4!*x^4+248/6!*x^6-3456/8!*x^8...

[ "2", "-16", "248", "-3456", "-406368", "123982080", "-31807263360", "9173875200000", "-3114459024453120", "1251070155460915200", "-591321674803999426560", "326012628782956574638080", "-207713640106463567695994880" ]

[ "sign" ]

10

0

1

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2016-04-04T23:19:17

oeisdata/seq/A012/A012457.seq

335587e907191c3749a94bc35ca16b0a

A012458

arcsin(arctan(x)^2) = 2/2!*x^2 - 16/4!*x^4 + 488/6!*x^6 - 30336/8!*x^8...

[ "2", "-16", "488", "-30336", "3303072", "-556926720", "135234491520", "-44790227865600", "19434264780034560", "-10703464305128755200", "7296385856008015226880", "-6031102564833737842851840", "5942962739028147945628999680" ]

[ "sign" ]

10

0

1

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2013-11-21T12:46:01

oeisdata/seq/A012/A012458.seq

f3e8f15a7905ba1bf5e05810ed9efebe

A012459

Expansion of e.g.f. arctan(arctan(x)*arctan(x)) (even powers only).

[ "0", "2", "-16", "128", "9984", "-1444608", "105185280", "11495516160", "-7997802086400", "2106956324536320", "3592879276032000", "-400446184903952302080", "271017181684548910448640", "-56861458491339484126248960" ]

[ "sign" ]

14

0

2

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2018-01-29T02:53:49

oeisdata/seq/A012/A012459.seq

0ac17998b7be1b393748cd807b248d76

A012460

cos(arctan(x)^2)=1-12/4!*x^4+480/6!*x^6-27888/8!*x^8...

[ "1", "0", "-12", "480", "-27888", "2353920", "-274245312", "41974872576", "-8068087373568", "1860842339721216", "-486190504963034112", "129225947748233994240", "-22917287813817561968640", "-13673939410058068058112000" ]

[ "sign" ]

6

0

3

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2016-10-07T17:56:50

oeisdata/seq/A012/A012460.seq

cf37e093e70288f62f92a4e1d00ce66f

A012461

sinh(arctan(x)*arctan(x))=2/2!*x^2-16/4!*x^4+488/6!*x^6-30336/8!*x^8...

[ "0", "2", "-16", "488", "-30336", "3061152", "-450481920", "90676698240", "-23889578496000", "7972943138664960", "-3286129765438771200", "1638857583672607549440", "-972524875970827007262720", "677113960144029088030433280" ]

[ "sign" ]

8

0

2

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2016-11-28T18:50:11

oeisdata/seq/A012/A012461.seq

03e00adb239e44829a58994c3c80a084

A012462

Arcsinh(arctan(x)^2) = 2/2!*x^2 - 16/4!*x^4 + 248/6!*x^6 - 3456/8!*x^8 + ...

[ "0", "2", "-16", "248", "-3456", "-164448", "17537280", "5001348480", "-3047690956800", "999150768960000", "-194340969261158400", "-28292890791044597760", "48811395838790000148480", "-15658656394130132870062080", "-19215487887156327014813859840", "37972554002174500707798919249920" ]

[ "sign" ]

13

0

2

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2024-01-09T13:20:30

oeisdata/seq/A012/A012462.seq

0f9744a393be3df15c4bb1e6ee6b0c4e

A012463

tanh(arctan(x)*arctan(x))=2/2!*x^2-16/4!*x^4+128/6!*x^6+9984/8!*x^8...

[ "0", "2", "-16", "128", "9984", "-1686528", "211630080", "-21438504960", "-115777536000", "1290343156285440", "-677718502185369600", "262776565415742013440", "-69499554745499013611520", "-9137401716948937432104960" ]

[ "sign" ]

6

0

2

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2016-11-28T18:53:27

oeisdata/seq/A012/A012463.seq

2ae07559ea53445af7e3b64111896b60

A012464

arctanh(arctan(x)*arctan(x))=2/2!*x^2-16/4!*x^4+608/6!*x^6-43776/8!*x^8...

[ "0", "2", "-16", "608", "-43776", "5490432", "-1043742720", "281302333440", "-101944270848000", "47833801306275840", "-28212954337286553600", "20432760600063600230400", "-17826780360146975037849600", "18441699370235590444905922560" ]

[ "sign" ]

9

0

2

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2016-11-28T18:54:28

oeisdata/seq/A012/A012464.seq

a1bb2b74700e47f027d7cc91ad28de6b

A012465

cosh(arctan(x)*arctan(x))=1+12/4!*x^4-480/6!*x^6+31248/8!*x^8...

[ "1", "0", "12", "-480", "31248", "-3160320", "462297792", "-92467554816", "24237361774848", "-8058187934539776", "3312017870282345472", "-1648428171351870627840", "976764310209146448384000", "-679332936418413117235200000" ]

[ "sign" ]

8

0

3

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2016-11-28T18:55:40

oeisdata/seq/A012/A012465.seq

31a4e02d094ad16148b1b7edae3944c3

A012466

E.g.f. sec(arctan(x)^2) (even powers only).

[ "1", "0", "12", "-480", "37968", "-4773120", "878319552", "-222512349696", "74262725323008", "-31578556041732096", "16666719859336276992", "-10690478515516973015040", "8190555666463900906475520", "-7387658525325188387856384000" ]

[ "sign" ]

10

0

3

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2013-01-13T06:14:00

oeisdata/seq/A012/A012466.seq

f8daf7787112f083df7452ed83c888c9

A012467

sech(arctan(x)^2) = 1 - 12/4!*x^4 + 480/6!*x^6 - 21168/8!*x^8 + ...

[ "1", "0", "-12", "480", "-21168", "741120", "61942848", "-29951061504", "8015861467392", "-1745546459848704", "215844160641143808", "91751419512905687040", "-109687232118939992862720", "71900040403600384794624000" ]

[ "sign" ]

10

0

3

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2013-11-21T12:46:01

oeisdata/seq/A012/A012467.seq

a2e8857f694d50f70eb008358277ae68

A012468

Expansion of e.g.f. arcsin(cos(x) * log(x+1)).

[ "0", "1", "-1", "0", "-6", "23", "-135", "1288", "-10164", "106661", "-1257165", "15497152", "-222045450", "3414340811", "-56743257571", "1031328757912", "-19972120728840", "414440475923689", "-9175579196399001", "215060308589382272" ]

[ "sign" ]

11

0

5

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2019-05-10T15:40:01

oeisdata/seq/A012/A012468.seq

b5d66cbc1d2ed7662f62d012d6808610

A012469

Expansion of e.g.f. arctan(cos(x) * log(x+1)).

[ "0", "1", "-1", "-3", "12", "23", "-495", "931", "27552", "-214699", "-1991565", "44340769", "25066668", "-9372982933", "70732779845", "2089607037415", "-43990273165920", "-339320074587383", "22626180254319399", "-95718973807370395" ]

[ "sign" ]

7

0

4

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2018-07-19T17:38:34

oeisdata/seq/A012/A012469.seq

9d1163a3fdd0590a0bec510c0a037300

A012470

arcsinh(cos(x)*log(x+1))=x-1/2!*x^2-2/3!*x^3+6/4!*x^4+13/5!*x^5...

[ "0", "1", "-1", "-2", "6", "13", "-225", "530", "8540", "-65579", "-650565", "13899070", "-8281878", "-2388363655", "18379145603", "516826612354", "-11083263907560", "-64702488848279", "5027641615912599", "-24199820388513346" ]

[ "sign" ]

8

0

4

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2013-11-02T08:23:52

oeisdata/seq/A012/A012470.seq

6344fd32f1ac39d25585b2550a6e10a3

A012471

Expansion of e.g.f. arctanh(cos(x)*log(x+1)).

[ "0", "1", "-1", "1", "-12", "43", "-315", "2987", "-24976", "288541", "-3544965", "46607053", "-707823996", "11389328039", "-199011366463", "3776136616951", "-76078523849280", "1640713749767833", "-37603782922082121", "910746316680339641" ]

[ "sign" ]

9

0

5

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2020-08-18T14:20:57

oeisdata/seq/A012/A012471.seq

f8575f363a14b9a60e99d2af2855b881

A012472

Expansion of e.g.f.: sec(cos(x)*log(x+1))=1+1/2!*x^2-3/3!*x^3+4/4!*x^4-40/5!*x^5...

[ "1", "0", "1", "-3", "4", "-40", "250", "-1260", "14012", "-133992", "1310660", "-16809980", "215083592", "-2938291200", "45330896832", "-728363224680", "12475447944528", "-230003712851648", "4451144492528080", "-91010462837366448" ]

[ "sign" ]

6

0

4

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2014-12-24T11:51:36

oeisdata/seq/A012/A012472.seq

c63f495d1e680dde295d523ebb4eb392

A012473

sech(cos(x)*log(x+1))=1-1/2!*x^2+3/3!*x^3+6/4!*x^4-60/5!*x^5...

[ "1", "0", "-1", "3", "6", "-60", "0", "2310", "-10752", "-84168", "1152240", "2453880", "-154467192", "797768400", "16907851688", "-250017997320", "-1746679208128", "77446551835648", "-318565680255360", "-18241668233387712", "262053618149070080" ]

[ "sign" ]

4

0

4

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2012-02-24T12:50:50

oeisdata/seq/A012/A012473.seq

832119f79db74aa0890b37521dbc4eed

A012474

Expansion of arcsin(cos(x)*sin(x)) = x - 3/3!*x^3 - 15/5!*x^5 + 357/7!*x^7 + 22305/9!*x^9...

[ "1", "-3", "-15", "357", "22305", "-582483", "-217683375", "-2001865323", "7258418490945", "826442897487837", "-580853295560646735", "-204631967729205027003", "85920364932388858911585", "79053144190920049745846157" ]

[ "sign" ]

7

0

2

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2021-07-18T12:12:31

oeisdata/seq/A012/A012474.seq

1507e686ddbea824625ccca505965857

A012475

arctan(cos(x)*sin(x))=x-6/3!*x^3+120/5!*x^5-7056/7!*x^7+758400/9!*x^9...

[ "1", "-6", "120", "-7056", "758400", "-130918656", "33173038080", "-11587651270656", "5337660866396160", "-3134856182239789056", "2286367634020679024640", "-2027369655249396662009856", "2147914157998443571728875520" ]

[ "sign" ]

4

0

2

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2012-02-24T12:50:50

oeisdata/seq/A012/A012475.seq

f5948dfab0d0cf6bd3088c8041ba2e28

A012476

arcsinh(cos(x)*sin(x))=x-5/3!*x^3+65/5!*x^5-3005/7!*x^7+278465/9!*x^9...

[ "1", "-5", "65", "-3005", "278465", "-42738005", "9852460865", "-3178878885005", "1367383455547265", "-756164182327284005", "522662665715777337665", "-441523138107985704375005", "447556468280585958726432065" ]

[ "sign" ]

8

0

2

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2013-10-31T04:33:27

oeisdata/seq/A012/A012476.seq

fd27da69a1fa33343cdae9c87939693d

A012477

arctanh(cos(x)*sin(x))=x-2/3!*x^3-40/5!*x^5+208/7!*x^7+64640/9!*x^9...

[ "1", "-2", "-40", "208", "64640", "986368", "-652487680", "-60911593472", "20973645824000", "6185783347314688", "-1429441147870904320", "-1203534317202507825152", "109702530161745707663360", "415034067689086640359211008" ]

[ "sign" ]

8

0

2

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2013-10-24T09:54:57

oeisdata/seq/A012/A012477.seq

4f6aced36205dd03e7c6653f6f09df27

A012478

sec(cos(x)*sin(x))=1+1/2!*x^2-11/4!*x^4-83/6!*x^6+10505/8!*x^8...

[ "1", "1", "-11", "-83", "10505", "6009", "-60553539", "2140355557", "1174906248337", "-146823377897103", "-55094515820657147", "17482899642565858461", "4900898798285366105753", "-3664217968514770645784087" ]

[ "sign" ]

6

0

3

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2022-11-09T13:30:02

oeisdata/seq/A012/A012478.seq

11e32eee49a248afe161322b6b3041fc

A012479

sech(cos(x)*sin(x))=1-1/2!*x^2+21/4!*x^4-717/6!*x^6+46025/8!*x^8...

[ "1", "-1", "21", "-717", "46025", "-4817209", "734055069", "-154121194437", "42674286160913", "-15062120873888497", "6601538801733818277", "-3517682024725193957181", "2239550167783452398617817", "-1678950113256157460626211113" ]

[ "sign" ]

4

0

3

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2012-02-24T12:50:51

oeisdata/seq/A012/A012479.seq

d525a980ca6d1d65d8aec7068006e0b0

A012480

Expansion of e.g.f.: exp(cos(x)*arcsin(x))=1+x+1/2!*x^2-1/3!*x^3-7/4!*x^4-15/5!*x^5...

[ "1", "1", "1", "-1", "-7", "-15", "25", "359", "1297", "3713", "785", "347151", "3237577", "62839153", "476552297", "10196506423", "93536269473", "2397571040897", "25410713978785", "714196911010335", "8498142387238425", "263318643848985457" ]

[ "sign" ]

6

0

5

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2024-07-21T15:09:51

oeisdata/seq/A012/A012480.seq

03f8016dfc8c32e704a1578f7570a4bf

A012481

sin(cos(x)*arcsin(x))=x-3/3!*x^3+25/5!*x^5-371/7!*x^7+11985/9!*x^9...

[ "1", "-3", "25", "-371", "11985", "13981", "45127017", "5553908333", "1415759895841", "404022487469117", "148035510590478137", "65626203271548278349", "34895786732343693436145", "21890894044531231133450973" ]

[ "sign" ]

4

0

2

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2012-02-24T12:50:51

oeisdata/seq/A012/A012481.seq

4f360461728914dd74e36f648953342c

A012482

arcsin(cos(x)*arcsin(x))=x-1/3!*x^3-7/5!*x^5+23/7!*x^7+8017/9!*x^9...

[ "1", "-1", "-7", "23", "8017", "747727", "74222601", "10474339367", "2425803672609", "797453256598559", "314897142584114585", "142725117278783779511", "75352861977241143203441", "47181023399211225968222703" ]

[ "sign" ]

4

0

3

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2012-02-24T12:50:51

oeisdata/seq/A012/A012482.seq

1d3805ee26e5c042c8cf88b9666d36e9

A012483

E.g.f.: tan(cos(x)*arcsin(x))=x-20/5!*x^5-56/7!*x^7+20112/9!*x^9...

[ "1", "0", "-20", "-56", "20112", "1097536", "38765376", "9775415168", "3760405592320", "1130444627523584", "374326578677906432", "166462985126115207168", "92968540423042714603520", "59757419067771727772172288" ]

[ "sign" ]

11

1

3

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2012-07-20T14:10:09

oeisdata/seq/A012/A012483.seq

b6168667c942bef9e4fcfe09372c9e77

A012484

arctan(cos(x)*arcsin(x))=x-4/3!*x^3+68/5!*x^5-3064/7!*x^7+265936/9!*x^9...

[ "1", "-4", "68", "-3064", "265936", "-35730176", "7235106240", "-1984468240000", "725871298851072", "-336136505074527232", "194162507080835314688", "-135973687998348753147904", "113975638131557424617639936" ]

[ "sign" ]

4

0

2

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2012-02-24T12:50:51

oeisdata/seq/A012/A012484.seq

d5ac59ec2cc1dbbd9500a803b666bf13

A012485

cos(cos(x)*arcsin(x))=1-1/2!*x^2+9/4!*x^4-105/6!*x^6+1393/8!*x^8...

[ "1", "-1", "9", "-105", "1393", "-71025", "-898887", "-455252889", "-75822681503", "-21366754787169", "-7036035942040855", "-2891117170991668553", "-1426147181806835610927", "-835104626729810211267025" ]

[ "sign" ]

6

0

3

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2022-10-14T11:01:51

oeisdata/seq/A012/A012485.seq

c80a0547f8f7f924705cc28e5ca1082f

A012486

sinh(cos(x)*arcsin(x))=x-1/3!*x^3-15/5!*x^5+359/7!*x^7+3713/9!*x^9...

[ "1", "-1", "-15", "359", "3713", "347151", "62839153", "10196506423", "2397571040897", "714196911010335", "263318643848985457", "118248746057101708295", "63495547245752463558145", "40188528694405725339687983" ]

[ "sign" ]

6

0

3

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2020-06-02T12:02:08

oeisdata/seq/A012/A012486.seq

d8d6c27f785c3d6c5e8e2ec7ddd72dc5

A012487

arcsinh(cos(x)*arcsin(x))=x-3/3!*x^3+33/5!*x^5-1155/7!*x^7+91553/9!*x^9...

[ "1", "-3", "33", "-1155", "91553", "-10478435", "2004751617", "-496122561571", "172663180364481", "-74458608812963395", "41124360344562400097", "-27302583872806500602179", "21988222585362167359370081" ]

[ "sign" ]

4

0

2

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2012-02-24T12:50:51

oeisdata/seq/A012/A012487.seq

572be38a9b4fe7ee12c6b31884d35ec9

A012488

tanh(cos(x)*arcsin(x))=x-4/3!*x^3+60/5!*x^5-2056/7!*x^7+127376/9!*x^9...

[ "1", "-4", "60", "-2056", "127376", "-11253504", "1524986944", "-257629834112", "60842617280768", "-16737691854400512", "6112605714322803712", "-2481449664133693548544", "1299422306103439813611520" ]

[ "sign" ]

6

0

2

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2020-06-20T16:34:50

oeisdata/seq/A012/A012488.seq

8f518e4b3cea5d6ed381a45375c3f1d1

A012489

arctanh(cos(x)*arcsin(x))=x-12/5!*x^5-168/7!*x^7+8144/9!*x^9...

[ "1", "0", "-12", "-168", "8144", "1384768", "149032128", "16299168896", "2859883876608", "1008997773326336", "466978134769624064", "228641400872390260736", "120327829272472868704256", "72933308761894955432460288" ]

[ "sign" ]

6

0

3

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2019-02-10T17:17:40

oeisdata/seq/A012/A012489.seq

2d06e11b3be60311c312c2595574eb77

A012490

cosh(cos(x)*arcsin(x))=1+1/2!*x^2-7/4!*x^4+25/6!*x^6+1297/8!*x^8...

[ "1", "1", "-7", "25", "1297", "785", "3237577", "476552297", "93536269473", "25410713978785", "8498142387238425", "3493252199008249913", "1729861042158836509361", "1015648464575702746171825", "697882405841324552721582569" ]

[ "sign" ]

4

0

3

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2012-02-24T12:50:51

oeisdata/seq/A012/A012490.seq

db1364678f908fad2b0acbe7de1c48bb

A012491

sec(cos(x)*arcsin(x))=1+1/2!*x^2-3/4!*x^4-75/6!*x^6+1337/8!*x^8...

[ "1", "1", "-3", "-75", "1337", "144105", "3933237", "118760733", "129911988593", "47180864336337", "13805291952312685", "5130037600431416453", "2642764719782227835049", "1617152674535806453668025" ]

[ "sign" ]

4

0

3

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2012-02-24T12:50:51

oeisdata/seq/A012/A012491.seq

0ff6a010ff7094b7d7dc4d8b2d92a1fe

A012492

sech(cos(x)*arcsin(x))=1-1/2!*x^2+13/4!*x^4-325/6!*x^6+14873/8!*x^8...

[ "1", "-1", "13", "-325", "14873", "-1157705", "123919013", "-19431568013", "3783114987057", "-997881588156817", "307028543021467965", "-122601833964174456533", "54600351690827520350281", "-30810847280896713474456025" ]

[ "sign" ]

4

0

3

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2012-02-24T12:50:51

oeisdata/seq/A012/A012492.seq

d4f277d8431a7c5c92fcf8a54ee39266

A012493

Take every 5th term of Padovan sequence A000931, beginning with the fifth term.

[ "0", "2", "9", "37", "151", "616", "2513", "10252", "41824", "170625", "696081", "2839729", "11584946", "47261895", "192809420", "786584466", "3208946545", "13091204281", "53406819691", "217878227876", "888855064897", "3626169232672", "14793304131648" ]

[ "nonn", "easy", "changed" ]

22

0

2

null

N. J. A. Sloane

2025-07-08T02:46:54

oeisdata/seq/A012/A012493.seq

680314bc6c1c431497081944278fb56c

A012494

Expansion of e.g.f. arctan(sin(x)) (odd powers only).

[ "1", "-3", "45", "-1743", "125625", "-14554683", "2473184805", "-579439207623", "179018972217585", "-70518070842040563", "34495620120141463965", "-20515677772241956573503", "14578232896601243652363945", "-12198268199871431840616166443", "11871344562637111570703016357525" ]

[ "sign", "easy" ]

51

0

2

[ "A000281", "A000364", "A001209", "A002437", "A003704", "A012494", "A013208", "A101923", "A156134" ]

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2018-08-17T02:41:53

oeisdata/seq/A012/A012494.seq

f157efcbfff45ad1b510d49e41b48ed7

A012495

Expansion of e.g.f. arcsinh(sin(x)) (odd powers only).

[ "1", "-2", "20", "-632", "39440", "-4087712", "634237760", "-137605112192", "39776178356480", "-14775064298435072", "6857795892626969600", "-3889298341511511652352", "2646362625886738240901120", "-2127690488032789501903020032" ]

[ "sign" ]

25

0

2

[ "A012495", "A101922" ]

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2023-09-29T13:09:28

oeisdata/seq/A012/A012495.seq

6425787dd51fbdf3d53159c5cdae72b5

A012496

exp(cos(x)*arctan(x))=1+x+1/2!*x^2-4/3!*x^3-19/4!*x^4+445/6!*x^6...

[ "1", "1", "1", "-4", "-19", "0", "445", "1304", "-14663", "-109120", "718265", "10816896", "-50970203", "-1441841024", "4876389557", "258762139648", "-548752599567", "-60872480247808", "47436062951281", "18224782774259712", "12631837146241245" ]

[ "sign" ]

7

0

4

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2013-11-21T12:46:01

oeisdata/seq/A012/A012496.seq

4c292cf0d6f78bf5331dfe97db1cc1fc

A012497

sin(cos(x)*arctan(x))=x-6/3!*x^3+100/5!*x^5-4256/7!*x^7+302352/9!*x^9...

[ "1", "-6", "100", "-4256", "302352", "-32245664", "4879093440", "-996485811712", "264232448010496", "-88283645811756544", "36292696703112000512", "-18004529956099757727744", "10606618572326341265592320" ]

[ "sign" ]

6

0

2

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2025-04-17T15:26:16

oeisdata/seq/A012/A012497.seq

42cef17f9841420fbb3b0fb40567fd89

A012498

arcsin(cos(x)*arctan(x))=x-4/3!*x^3+8/5!*x^5+128/7!*x^7+25216/9!*x^9...

[ "1", "-4", "8", "128", "25216", "-3387008", "160621056", "-6497102848", "10675803193344", "-4485074198855680", "823007646284349440", "-188938583696417751040", "280059136770757168726016", "-235157137580491486235983872" ]

[ "sign" ]

6

0

2

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2019-11-16T13:25:29

oeisdata/seq/A012/A012498.seq

ca29ebf5c69208a764b44107a446e4d3

A012499

Expansion of e.g.f. tan(cos(x)*arctan(x)) (odd powers only).

[ "1", "-3", "-35", "1729", "-12711", "-5819099", "581423349", "26066838953", "-19485197470415", "2379630157273805", "789057561743200397", "-445703452244142678255", "25928070972710765150345", "80008658408138506870433013", "-41780425117352684596856468827", "-7585811803346771885529485351175", "23110904483392454783722911793216609" ]

[ "sign" ]

11

0

2

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2025-03-11T10:56:13

oeisdata/seq/A012/A012499.seq

d0e1336761c36e5af2db92ea9e0a2d26

A012500

arctan(cos(x)*arctan(x))=x-7/3!*x^3+173/5!*x^5-11779/7!*x^7...

[ "1", "-7", "173", "-11779", "1474969", "-296068991", "87094091589", "-35308668668155", "18872654969343537", "-12860552599622997751", "10882609077370643446493", "-11195876625633675125480947", "13761866805554489099492092361" ]

[ "sign" ]

7

0

2

null

Patrick Demichel (patrick.demichel(AT)hp.com)

2015-10-04T13:06:34

oeisdata/seq/A012/A012500.seq

0bb75ec619e9d01d6cf9b9d43ab7df92