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
A012001	E.g.f.: -tan(log(cos(x))), even powers only.	[ "0", "1", "2", "46", "1112", "55816", "3804272", "372397936", "47682319232", "7841034902656", "1601250315636992", "398250217200414976", "118406090377889303552", "41478295178427681104896", "16904918898000336224294912" ]	[ "nonn" ]	20	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2017-04-12T23:09:22	oeisdata/seq/A012/A012001.seq	82bd045dc2ac483454dc76d20a695d0d
A012002	arctan(log(cos(x)))=-1/2!x^2-2/4!x^4+14/6!x^6+568/8!x^8...	[ "0", "-1", "-2", "14", "568", "2144", "-1061312", "-65851696", "3745115008", "1232648783744", "50799435228928", "-36670923310299136", "-8828746813705828352", "954888000296009790464", "1122466427244127979911168" ]	[ "sign" ]	9	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2019-08-10T10:57:38	oeisdata/seq/A012/A012002.seq	5260280d55edcbe96edfdd65f7044555
A012003	E.g.f. cos(log(cos(x))), even powers only.	[ "1", "0", "-3", "-30", "-483", "-12660", "-492063", "-26407290", "-1854592743", "-162954226920", "-17150991170523", "-2051454240374550", "-254425037609483403", "-24186909676571913180", "3098088521295623020617" ]	[ "sign" ]	13	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2013-11-21T12:46:00	oeisdata/seq/A012/A012003.seq	e38989648258997dfc7c6e71b4d6b84f
A012004	arcsinh(log(cos(x)))=-1/2!x^2-2/4!x^4-1/6!x^6+148/8!x^8-61/10!*x^10...	[ "0", "-1", "-2", "-1", "148", "-61", "-395702", "-28299181", "93652648", "265509939239", "14066899733398", "-8605652824527001", "-2442549938212838852", "25891773268121861099", "210295085697229695516898" ]	[ "sign" ]	9	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2016-03-21T15:33:30	oeisdata/seq/A012/A012004.seq	d5cfbcf9c988e27c5f8786ca17183b06
A012005	tanh(log(cos(x)))=-1/2!x^2-2/4!x^4+14/6!x^6+568/8!x^8...	[ "-1", "-2", "14", "568", "9704", "-229712", "-35581456", "-1790014592", "72312646784", "28603722780928", "3039116082823424", "-154149928667313152", "-135793191600734657536", "-25782484156469234296832" ]	[ "sign" ]	6	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2022-05-12T18:21:03	oeisdata/seq/A012/A012005.seq	1d89a5a84a80af2e5054f69e780c0250
A012006	-arctanh(log(cos(x))) = 1/2!x^2+2/4!x^4+46/6!x^6+1112/8!x^8...	[ "1", "2", "46", "1112", "63376", "4635872", "523749136", "76049858432", "14634264866176", "3496967323112192", "1032537134569578496", "366067157640456292352", "154146217678162805226496", "75874517780279404503590912" ]	[ "nonn" ]	8	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2013-10-25T10:04:15	oeisdata/seq/A012/A012006.seq	f90ad377f00c1f350f02f0975f785f8d
A012007	cosh(log(cos(x))) = 1+3/4!x^4+30/6!x^6+693/8!x^8+25260/10!x^10...	[ "1", "0", "3", "30", "693", "25260", "1351383", "99680490", "9695756073", "1202439837720", "185185594118763", "34674437196568950", "7757267081778543453", "2043536254646561946180", "626129820701814932734143", "220771946624511552276841410", "88759695789769644718332394833" ]	[ "nonn" ]	24	0	3	[ "A012003", "A012007", "A012008", "A012009" ]	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2017-05-22T13:01:56	oeisdata/seq/A012/A012007.seq	2f34fb23064cecfa6c223920333905d7
A012008	sec(log(cos(x)))= 1+3/4!x^4+30/6!x^6+1113/8!x^8+50460/10!x^10...	[ "1", "0", "3", "30", "1113", "50460", "3693723", "359740290", "46791574833", "7721990402520", "1584990509251443", "395230316479830150", "117766463267804780553", "41313542582787780576180", "16856003114804522914769163" ]	[ "nonn" ]	7	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2015-01-02T16:55:18	oeisdata/seq/A012/A012008.seq	02d2bf3a3157f98217181c0d99f1d5d2
A012009	Expansion of e.g.f. sech(log(cos(x))) (even exponents only).	[ "1", "0", "-3", "-30", "-63", "12540", "602877", "6625710", "-1991169183", "-241970036520", "-7540177734243", "2917041754949850", "699983161534169697", "46722975483964508820", "-21334067257986056115363", "-8882421213380429461235610", "-1081286159351846822872767423" ]	[ "sign" ]	24	0	3	[ "A012003", "A012007", "A012008", "A012009" ]	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2024-08-04T06:36:59	oeisdata/seq/A012/A012009.seq	2c6b01e052b909df602a5f15d4372514
A012010	arctan(sin(sin(x))) = x - 4/3!x^3 + 76/5!x^5 - 3592/7!x^7 + 317968/9!x^9 - ....	[ "1", "-4", "76", "-3592", "317968", "-45286528", "9459412288", "-2724254181760", "1034595588065536", "-500961002883890176", "301230818225601928192", "-220218226893098691684352", "192355329482117756948647936" ]	[ "sign" ]	10	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2013-12-16T13:56:20	oeisdata/seq/A012/A012010.seq	bb2c8cccf0307b9c4e6d7ef5f4d45986
A012011	arcsinh(sin(sin(x)))=x-3/3!x^3+41/5!x^5-1515/7!x^7+113489/9!x^9...	[ "1", "-3", "41", "-1515", "113489", "-14321299", "2716798969", "-721988679547", "255890614389921", "-116619928299347491", "66439023428917759945", "-46262911349611152912395", "38656874720522348065089521" ]	[ "sign" ]	14	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2015-02-03T16:47:24	oeisdata/seq/A012/A012011.seq	e208f9a83fe3acf564e7b730e390e02b
A012012	sec(sin(sin(x)))=1+1/2!x^2-3/4!x^4-27/6!x^6+1145/8!x^8...	[ "1", "1", "-3", "-27", "1145", "-8631", "-1770123", "115778861", "4625206001", "-1652588042607", "75500754980077", "36232528294816885", "-8153373987817082007", "-655897923302322394919", "753704651365381460774501" ]	[ "sign" ]	4	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:36	oeisdata/seq/A012/A012012.seq	4063ae8e22d8d2c40efc1e573b261110
A012013	sech(sin(sin(x)))=1-1/2!x^2+13/4!x^4-373/6!x^6+19545/8!x^8...	[ "1", "-1", "13", "-373", "19545", "-1638569", "201324773", "-34084249501", "7606559175089", "-2164004651794513", "764464999664782013", "-328322677491890500805", "168474698667902836871177", "-101798128590699775451705081" ]	[ "sign" ]	6	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2022-07-27T19:09:59	oeisdata/seq/A012/A012013.seq	0fc0ddeae05ee95d69204aad3c916322
A012014	arctan(sin(tan(x)))=x-1/3!x^3+1/5!x^5-169/7!x^7-1823/9!x^9...	[ "1", "-1", "1", "-169", "-1823", "-365905", "-17126303", "-3688466617", "-393996411839", "-109259290725793", "-20477152840654271", "-7401734340295771849", "-2112803982091750971359", "-978357645904185043693297" ]	[ "sign" ]	6	0	4	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2014-06-04T10:14:28	oeisdata/seq/A012/A012014.seq	a2e96acdb642633cdbc93dbe78194ded
A012015	arcsinh(sin(tan(x)))=x-4/5!x^5-192/7!x^7-7600/9!x^9-507136/11!x^11...	[ "1", "0", "-4", "-192", "-7600", "-507136", "-40159040", "-4621348864", "-627047126784", "-113424912867328", "-23612736247718912", "-6196586681702039552", "-1827473399583593672704", "-652336666072894806360064" ]	[ "sign" ]	4	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:36	oeisdata/seq/A012/A012015.seq	61c0bdacf66ea937065750463a685335
A012016	arctanh(sin(tan(x)))=x+3/3!x^3+41/5!x^5+1299/7!x^7+74609/9!x^9...	[ "1", "3", "41", "1299", "74609", "6787811", "898506649", "163241051315", "39007280136801", "11866656488375747", "4479287777805494665", "2054673461380880189779", "1125793481954983195433681", "726247496033154181534638755" ]	[ "nonn" ]	10	0	2	[ "A009329", "A012016" ]	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2018-10-09T15:29:21	oeisdata/seq/A012/A012016.seq	fa553e48b9711d932203e842021b090e
A012017	sec(sin(tan(x)))=1+1/2!x^2+9/4!x^4+153/6!x^6+2993/8!x^8...	[ "1", "1", "9", "153", "2993", "-72111", "-33331719", "-7328604631", "-1581635839519", "-356792088521439", "-81022312424248727", "-15576441107086727111", "22243831754082386577", "3229505766853670411015281" ]	[ "sign" ]	4	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:36	oeisdata/seq/A012/A012017.seq	7c12dd2af9d08ab7d602bbe1d0648c2c
A012018	sech(sin(tan(x)))=1-1/2!x^2+1/4!x^4+47/6!x^6+897/8!x^8...	[ "1", "-1", "1", "47", "897", "26911", "2176769", "269558351", "38463601409", "6445724731199", "1297792574780417", "307585734223517551", "82426762826906376833", "23816926512873022989919", "6844111898535212011277057" ]	[ "sign" ]	4	0	4	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:36	oeisdata/seq/A012/A012018.seq	0ae4e1c86e1dd91bc8c17335720939d9
A012019	E.g.f.: exp(sin(arctan(x))).	[ "1", "1", "1", "-2", "-11", "16", "301", "-104", "-15287", "-20096", "1239481", "4427776", "-146243459", "-954111872", "23567903269", "243390205696", "-4951201340399", "-75389245067264", "1307274054385393", "28248828019830784", "-420773143716828539" ]	[ "sign" ]	20	0	4	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2025-02-28T12:05:29	oeisdata/seq/A012/A012019.seq	4a57335322abd576abc212d2739ccb98
A012020	Expansion of e.g.f.: sin(sin(arctan(x))) (odd powers only).	[ "1", "-4", "76", "-3256", "245008", "-28441216", "4700478784", "-1047088053376", "302112622479616", "-109527844826856448", "48716214653800569856", "-26075068739563056830464", "16529214537740143196901376" ]	[ "sign" ]	19	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2015-10-21T11:25:11	oeisdata/seq/A012/A012020.seq	a4806b0a924fcb9894f249a6c3e9220c
A012021	Expansion of e.g.f.: tan(sin(arctan(x))) (odd powers only).	[ "1", "-1", "1", "167", "-14303", "1383887", "-170123615", "26560717367", "-5162935778879", "1219537456849055", "-340794504958201919", "109077799391707298759", "-38112045733323708444959", "13139859774638771226676847" ]	[ "sign" ]	18	0	4	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2018-01-29T02:56:35	oeisdata/seq/A012/A012021.seq	2141ff331dc7cd67eb56ea4dd3e7a2ee
A012022	Expansion of e.g.f.: arctan(sin(arctan(x))) (odd powers only).	[ "1", "-5", "129", "-7965", "903105", "-163451925", "43259364225", "-15764670046125", "7571150452490625", "-4634731528895593125", "3522824632122301130625", "-3255279003622294051528125", "3593928024032353882700450625" ]	[ "sign" ]	30	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2018-02-03T16:39:48	oeisdata/seq/A012/A012022.seq	9c01d1811d4c018a627e57f881d61ee6
A012023	Expansion of e.g.f. cos(sin(arctan(x))) (even powers).	[ "1", "-1", "13", "-421", "25369", "-2449801", "346065061", "-67243537453", "17192488230961", "-5593309059948049", "2255588021494237501", "-1103994926592923677621", "644587811150505183179593", "-442516027690815793746696601" ]	[ "sign" ]	18	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2018-01-29T02:52:45	oeisdata/seq/A012/A012023.seq	82b7c1bf028efe09c7e290d2437d4885
A012024	E.g.f. sinh(sin(arctan(x))) (odd powers only).	[ "1", "-2", "16", "-104", "-20096", "4427776", "-954111872", "243390205696", "-75389245067264", "28248828019830784", "-12669814369258471424", "6721694045416881553408", "-4170436153219300846567424", "2994608522937575414450814976" ]	[ "sign" ]	17	1	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2025-02-28T12:05:36	oeisdata/seq/A012/A012024.seq	4fd76ade83e76ae3a15436c95d45e40e
A012025	E.g.f. arcsinh(sin(arctan(x))) = arcsinh(x/(1+x^2)^(1/2)) (odd powers only).	[ "1", "-4", "84", "-4320", "418320", "-66225600", "15657364800", "-5187108326400", "2296766568096000", "-1310785979158656000", "937056917610253440000", "-820081468493365478400000", "862301491174096979765760000" ]	[ "sign" ]	19	1	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2013-10-30T16:55:15	oeisdata/seq/A012/A012025.seq	5567df4f4047e876fbc3cd2c12daac5b
A012026	Expansion of e.g.f. tanh(sin(arctan(x))) = tanh(x/sqrt(1+x^2)) (odd powers only).	[ "1", "-5", "121", "-6677", "651985", "-98741477", "21378584137", "-6259615830197", "2380487154907681", "-1140222272527932869", "671453734616884934041", "-476714184862146843059285", "401522701697360654591942641" ]	[ "sign" ]	19	1	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2018-01-29T02:52:50	oeisdata/seq/A012/A012026.seq	9a67e7eb3c836a22fb81cd94e8dfc584
A012027	E.g.f. cosh(sin(arctan(x))) = cosh(x/sqrt(1+x^2)) (even powers only).	[ "1", "1", "-11", "301", "-15287", "1239481", "-146243459", "23567903269", "-4951201340399", "1307274054385393", "-420773143716828539", "160635990248839962781", "-70764171306270411101351", "34822234810202848704345001" ]	[ "sign" ]	25	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2025-02-28T12:05:43	oeisdata/seq/A012/A012027.seq	8b5c499dfafe34365aed9af3218bad27
A012028	E.g.f. sec(sin(arctan(x))) = 1/cos(x/sqrt(1+x^2)).	[ "1", "1", "-7", "121", "-3823", "186961", "-12464695", "967217161", "-51115216735", "-15922673810399", "12685061907297305", "-7463929930799687399", "4531120544938557395633", "-3032728078954072676445839" ]	[ "sign" ]	9	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-08-06T10:36:36	oeisdata/seq/A012/A012028.seq	811b86ba4904601d299dcbc17f299e28
A012029	E.g.f.: sech(sin(arctan(x))) (even powers only).	[ "1", "-1", "17", "-721", "56993", "-7232161", "1344866225", "-344599447921", "116382225519425", "-50097660050713921", "26773024797675332945", "-17392081348966913859601", "13497082647397365780254177" ]	[ "sign" ]	14	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2013-11-08T09:32:22	oeisdata/seq/A012/A012029.seq	c69e5cd50ad523e47371defedc35f0ac
A012030	arctan(sin(sinh(x))) = x - 2/3!x^3 +16/5!x^5 - 440/7!x^7 + 20224/9!x^9 - ....	[ "1", "-2", "16", "-440", "20224", "-1582976", "178612864", "-27969867008", "5765737517056", "-1516228355846144", "495092243779256320", "-196552136456231321600", "93232152295610535018496", "-52074797114273752377786368" ]	[ "sign" ]	10	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2024-12-04T19:23:26	oeisdata/seq/A012/A012030.seq	ffbe773bc8fae2be8888b6d79d9b2b1e
A012031	arcsinh(sin(sinh(x)))=x-1/3!x^3+1/5!x^5-113/7!x^7+4033/9!x^9...	[ "1", "-1", "1", "-113", "4033", "-307297", "32041153", "-4722808145", "919792817281", "-229762987386049", "71595055755086977", "-27226195625057526833", "12411835138553868048961", "-6681718218812850626513185" ]	[ "sign" ]	8	0	4	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2015-02-03T15:02:32	oeisdata/seq/A012/A012031.seq	6e8e71c5e55050426a2ac815c9b4a406
A012032	sec(sin(sinh(x)))=1+1/2!x^2+5/4!x^4+13/6!x^6-1303/8!x^8...	[ "1", "1", "5", "13", "-1303", "-97351", "-5539667", "-182565627", "23677748561", "8153921374705", "1571128609968341", "190412412110488701", "-16146953133290647751", "-22882305147029329939799" ]	[ "sign" ]	6	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2025-03-18T18:52:18	oeisdata/seq/A012/A012032.seq	3652feb21e0db0604854679b845a433b
A012033	sech(sin(sinh(x)))=1-1/2!x^2+5/4!x^4-13/6!x^6-407/8!x^8...	[ "1", "-1", "5", "-13", "-407", "30151", "-1142483", "19202427", "3747342929", "-722092683505", "76341208430549", "-2313301317273981", "-1769780901329435719", "628518840135423728599", "-125498832189487922441219" ]	[ "sign" ]	4	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:37	oeisdata/seq/A012/A012033.seq	7ee56491e3f9db1b64bef041d0efbdc2
A012034	exp(sin(arcsinh(x))) = 1+x+1/2!x^2-1/3!x^3-7/4!x^4+1/5!x^5...	[ "1", "1", "1", "-1", "-7", "1", "121", "111", "-4271", "-9407", "262801", "957791", "-25257079", "-131065791", "3510517193", "23876150351", "-667413187039", "-5645293077119", "166471455235489", "1689130316350143", "-52750545434135399" ]	[ "sign" ]	9	0	5	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2013-10-30T16:56:07	oeisdata/seq/A012/A012034.seq	f722909d2a7eff182625e4937197df6b
A012035	sin(sin(arcsinh(x))) = x-3/3!x^3+41/5!x^5-1291/7!x^7+73169/9!x^9...	[ "1", "-3", "41", "-1291", "73169", "-6551251", "852920953", "-152425617371", "35839758063521", "-10733139641944739", "3990221478883366601", "-1803635523024068325803", "974372554797510153337201" ]	[ "sign" ]	9	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2013-10-30T16:56:58	oeisdata/seq/A012/A012035.seq	01c11d4ad840821784396eafc24534d9
A012036	tan(sin(arcsinh(x)))=x-4/5!x^5+32/7!x^7+80/9!x^9-34048/11!x^11...	[ "1", "0", "-4", "32", "80", "-34048", "5048512", "-984048128", "246504417536", "-76892124225536", "29350173573487616", "-13506119868179701760", "7388967312556159062016", "-4745632815309786449379328", "3538391474251613805070172160" ]	[ "sign" ]	9	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2015-02-03T05:07:56	oeisdata/seq/A012/A012036.seq	5fa728ac4659956bd1f7c6297d7eb9ad
A012037	arctan(sin(arcsinh(x)))=x-4/3!x^3+84/5!x^5-4320/7!x^7+410640/9!x^9...	[ "1", "-4", "84", "-4320", "410640", "-62424000", "13882209600", "-4250758886400", "1715097849504000", "-881945575315584000", "563062441711086720000", "-436991853893041873920000", "405186856780938968885760000" ]	[ "sign" ]	4	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:37	oeisdata/seq/A012/A012037.seq	32194e4eed1a3fb5f0f1ff0dc30ec0cb
A012038	cos(sin(arcsinh(x)))=1-1/2!x^2+9/4!x^4-201/6!x^6+8753/8!x^8...	[ "1", "-1", "9", "-201", "8753", "-634481", "69292281", "-10655767929", "2197620415201", "-585914236294753", "196238045270790761", "-80691386297887323561", "39976011626025680236049", "-23490521419525456192130001" ]	[ "sign" ]	7	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2013-11-21T12:46:00	oeisdata/seq/A012/A012038.seq	9f01eededc217ee87fa2bba28e7f3091
A012039	sinh(sin(arcsinh(x))) = x-1/3!x^3+1/5!x^5+111/7!x^7-9407/9!x^9...	[ "1", "-1", "1", "111", "-9407", "957791", "-131065791", "23876150351", "-5645293077119", "1689130316350143", "-625455343415905919", "281176376077651011119", "-150982531394396522439999", "95493861079696805301099551" ]	[ "sign" ]	10	0	4	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2023-03-18T16:51:34	oeisdata/seq/A012/A012039.seq	ba99fac998c07729411a07578e4540dc
A012040	arcsinh(sin(arcsinh(x)))=x-3/3!x^3+49/5!x^5-2075/7!x^7+168865/9!x^9...	[ "1", "-3", "49", "-2075", "168865", "-22606675", "4522468625", "-1266169501675", "473063766306625", "-227507081427747875", "136918092950286480625", "-100805803028947763426875", "89129323309512937147750625" ]	[ "sign" ]	10	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2015-02-03T16:47:51	oeisdata/seq/A012/A012040.seq	a5eaf2484e2faadfe4d38ff42f2e369a
A012041	tanh(sin(arcsinh(x)))=x-4/3!x^3+76/5!x^5-3312/7!x^7+255952/9!x^9...	[ "1", "-4", "76", "-3312", "255952", "-30728512", "5281229760", "-1228900532992", "371761489090816", "-141763213277045760", "66504626862819552256", "-37635004127910391803904", "25277676503178610861756416" ]	[ "sign" ]	10	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2015-02-04T07:30:41	oeisdata/seq/A012/A012041.seq	5349f810150aec7177baa603654acb77
A012042	arctanh(sin(arcsinh(x)))=x+4/5!x^5-80/7!x^7+4240/9!x^9-342400/11!x^11...	[ "1", "0", "4", "-80", "4240", "-342400", "41806400", "-7093216000", "1601470624000", "-464003651072000", "167847611351680000", "-74143433704737280000", "39275771932443138560000", "-24575763662119940608000000" ]	[ "sign" ]	10	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2024-03-17T07:58:56	oeisdata/seq/A012/A012042.seq	24a3070c5693e3d153c9d1ff00bed9c3
A012043	cosh(sin(arcsinh(x))) = 1+1/2!x^2-7/4!x^4+121/6!x^6-4271/8!x^8...	[ "1", "1", "-7", "121", "-4271", "262801", "-25257079", "3510517193", "-667413187039", "166471455235489", "-52750545434135399", "20700581434214572441", "-9854557734715140280207", "5594838313934367657655601" ]	[ "sign" ]	11	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2025-04-20T12:53:22	oeisdata/seq/A012/A012043.seq	4cbb4fc983bb8c9715d38ffe80ec3812
A012044	sec(sin(arcsinh(x)))=1+1/2!x^2-3/4!x^4+21/6!x^6-647/8!x^8...	[ "1", "1", "-3", "21", "-647", "45161", "-4655115", "671831421", "-131445679375", "33601481453521", "-10874248371483155", "4345212201159011301", "-2101132542287329737623", "1209250716473417141359161" ]	[ "sign" ]	7	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2013-11-21T12:46:00	oeisdata/seq/A012/A012044.seq	a4b849e5d1f26ae3e154feff5019b184
A012045	sech(sin(arcsinh(x)))=1-1/2!x^2+13/4!x^4-421/6!x^6+25817/8!x^8...	[ "1", "-1", "13", "-421", "25817", "-2565961", "375964645", "-76201822061", "20411701862065", "-6981810963526801", "2968895846823113405", "-1536132530083569544501", "950209903347072336087433", "-692439473656550310042291161" ]	[ "sign" ]	4	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:37	oeisdata/seq/A012/A012045.seq	2abeaee0036ff32ca4e0a2ad2720aaac
A012046	arctan(sin(tanh(x)))=x-5/3!x^3+121/5!x^5-7013/7!x^7+752785/9!x^9...	[ "1", "-5", "121", "-7013", "752785", "-129763589", "32812992265", "-11441858264741", "5261501926546081", "-3084889329990554117", "2246121092328414171673", "-1988316104656824914919653", "2102978545788269109358313521" ]	[ "sign" ]	6	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2023-09-01T15:29:33	oeisdata/seq/A012/A012046.seq	140bf5928dbc8cb2da5ff2f971ec7eed
A012047	arcsinh(sin(tanh(x)))=x-4/3!x^3+76/5!x^5-3536/7!x^7+317392/9!x^9...	[ "1", "-4", "76", "-3536", "317392", "-47590720", "10785422272", "-3441103532288", "1468657322465536", "-807408622401283072", "555453404529224756224", "-467352773254586231115776", "472081158536303158224572416" ]	[ "sign" ]	8	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2015-02-04T04:26:58	oeisdata/seq/A012/A012047.seq	f48d9f2e29a09cbcde4acd29da67af4e
A012048	arctanh(sin(tanh(x)))=x-1/3!x^3+1/5!x^5+55/7!x^7-2207/9!x^9...	[ "1", "-1", "1", "55", "-2207", "79727", "-2834207", "81045991", "1107720001", "-715785186337", "165075476417857", "-44818254949260905", "14626040239803925921", "-5177396773524357363889", "1885895392048206524730145" ]	[ "sign" ]	6	0	4	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2017-03-07T08:59:24	oeisdata/seq/A012/A012048.seq	2661774dc084a828bb8e54120df8d4d2
A012049	sec(sin(tanh(x))) = 1+1/2!x^2-7/4!x^4+73/6!x^6+209/8!x^8...	[ "1", "1", "-7", "73", "209", "-144271", "16935049", "-1681509255", "121927140641", "7429711841377", "-7368737635468135", "2672443484700215337", "-714451608564077085455", "102412390388191040345041", "45342663705298790615837737", "-56227306534265498361644426407" ]	[ "sign" ]	14	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2023-10-27T21:05:57	oeisdata/seq/A012/A012049.seq	86b1aef6089a43de72f0e6edc733a284
A012050	sech(sin(tanh(x)))=1-1/2!x^2+17/4!x^4-673/6!x^6+48481/8!x^8...	[ "1", "-1", "17", "-673", "48481", "-5556929", "930399601", "-214412110305", "65104843008449", "-25194079035190657", "12104203127776694225", "-7069126951831617433377", "4932323527151866597114145", "-4052159085639349626953573441" ]	[ "sign" ]	4	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:39	oeisdata/seq/A012/A012050.seq	a8665e9d05bc24568da1af382e428c2d
A012051	exp(sin(arctanh(x)))=1+x+1/2!x^2+2/3!x^3+5/4!x^4+16/5!x^5...	[ "1", "1", "1", "2", "5", "16", "61", "216", "937", "-1280", "-34919", "-1141504", "-13257619", "-263392128", "-3269873515", "-64804059904", "-890367567919", "-18858549039104", "-286428853272143", "-6592583427379200", "-109915623105978539" ]	[ "sign" ]	4	0	4	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:39	oeisdata/seq/A012/A012051.seq	ee01f25fecd82cb43467ebf0c002a28f
A012052	sin(sin(arctanh(x)))=x-4/5!x^5-136/7!x^7-7408/9!x^9-644416/11!x^11...	[ "1", "0", "-4", "-136", "-7408", "-644416", "-84562880", "-15811723136", "-4005496370944", "-1317763889887232", "-544096638435718144", "-274416039275290634240", "-165481485047921126273024", "-117299354914466636092850176" ]	[ "sign" ]	6	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2023-07-06T15:01:53	oeisdata/seq/A012/A012052.seq	bc50ed9c270dddb6dccb3e4a28cee994
A012053	tan(sin(arctanh(x)))=x+3/3!x^3+41/5!x^5+1187/7!x^7+54449/9!x^9...	[ "1", "3", "41", "1187", "54449", "3092867", "95391193", "-48911197853", "-28872742806559", "-14158572958744829", "-7331436852140378359", "-4214348760692049240797", "-2723345361371865447323759", "-1980230597926036207884317053" ]	[ "sign" ]	6	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-09-25T17:40:40	oeisdata/seq/A012/A012053.seq	b56de3bd109eafebbdc67dc0c0a3091c
A012054	arctan(sin(arctanh(x)))=x-1/3!x^3+9/5!x^5-225/7!x^7+3345/9!x^9...	[ "1", "-1", "9", "-225", "3345", "-893025", "-36212775", "-20892252225", "-3614048241375", "-1664630362370625", "-584598534985164375", "-327627617091486830625", "-181787523574523506599375", "-131875411531849225343390625" ]	[ "sign" ]	8	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2013-01-23T17:20:34	oeisdata/seq/A012/A012054.seq	524d698e95d92c3375211b43a36cd1c9
A012055	cos(sin(arctanh(x)))=1-1/2!x^2-3/4!x^4-21/6!x^6+185/8!x^8...	[ "1", "-1", "-3", "-21", "185", "67159", "11805621", "2380474563", "591392066161", "181472052075695", "68002767860495981", "30687549807072450459", "16452262725440109947177", "10350119384788050029211399" ]	[ "sign" ]	6	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2017-07-04T12:11:03	oeisdata/seq/A012/A012055.seq	e87e3994287250af0e83dff443b7b00c
A012056	sinh(sin(arctanh(x)))=x+2/3!x^3+16/5!x^5+216/7!x^7-1280/9!x^9...	[ "1", "2", "16", "216", "-1280", "-1141504", "-263392128", "-64804059904", "-18858549039104", "-6592583427379200", "-2757743938862710784", "-1367930584522073079808", "-796483574916192660455424", "-539009967859883250211815424" ]	[ "sign" ]	6	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2018-04-29T17:16:32	oeisdata/seq/A012/A012056.seq	ac5ad828cf515cd632d36af00cd9a23f
A012057	arcsinh(sin(arctanh(x)))=x+4/5!x^5-80/7!x^7-3440/9!x^9-764800/11!x^11...	[ "1", "0", "4", "-80", "-3440", "-764800", "-107953600", "-25833184000", "-6745073504000", "-2368021859840000", "-968030415297920000", "-487629248007416320000", "-285882353240737277440000", "-197729299896592542208000000" ]	[ "sign" ]	7	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2015-02-03T08:27:17	oeisdata/seq/A012/A012057.seq	af07eaf7dd8d4a5165e6cd1b4a5deb89
A012058	tanh(sin(arctanh(x)))=x-1/3!x^3+1/5!x^5-57/7!x^7-3167/9!x^9...	[ "1", "-1", "1", "-57", "-3167", "-362737", "-56653791", "-11948396137", "-3257340575039", "-1115453379837153", "-468755833785218879", "-237209057387611844761", "-142289210803187916748959", "-99838786688751535495417297" ]	[ "sign" ]	4	0	4	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:39	oeisdata/seq/A012/A012058.seq	08d9b73a2d0ef8272d5f52c532267ef2
A012059	arctanh(sin(arctanh(x))) = x + (3/3!)x^3 + (49/5!)x^5 + (1915/7!)x^7 + (136225/9!)x^9 + ...	[ "1", "3", "49", "1915", "136225", "15321875", "2499086225", "557414129675", "162944338818625", "60444849108947875", "27742201644414960625", "15435312024168291246875", "10237075067482444345750625", "7979873933940396519383421875" ]	[ "nonn" ]	10	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2018-08-17T16:20:25	oeisdata/seq/A012/A012059.seq	10484dac4233cd3734df3191ebb51f85
A012060	cosh(sin(arctanh(x)))=1+1/2!x^2+5/4!x^4+61/6!x^6+937/8!x^8...	[ "1", "1", "5", "61", "937", "-34919", "-13257619", "-3269873515", "-890367567919", "-286428853272143", "-109915623105978539", "-50081947723080008339", "-26861824093922170259335", "-16800404374717805427318199" ]	[ "sign" ]	6	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2021-07-09T13:56:47	oeisdata/seq/A012/A012060.seq	38fc3b6c681311c0f29510c38b5436d9
A012061	sec(sin(arctanh(x)))=1+1/2!x^2+9/4!x^4+201/6!x^6+7921/8!x^8...	[ "1", "1", "9", "201", "7921", "447281", "28121145", "230243001", "-940995291295", "-539358796035359", "-280768914546419735", "-156059839698555664599", "-96215805882840361663151", "-66431831409927100446899439" ]	[ "sign" ]	6	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2021-09-24T17:03:46	oeisdata/seq/A012/A012061.seq	c16fe6e87728b48978311b7c514f0d32
A012062	sech(sin(arctanh(x)))=1-1/2!x^2+1/4!x^4-1/6!x^6+449/8!x^8...	[ "1", "-1", "1", "-1", "449", "45119", "6456385", "1205597119", "290952557185", "88525830844799", "33241403103347585", "15120239602445366399", "8199386238595549354561", "5228782379279703730965439", "3875091407041220683147290049" ]	[ "sign" ]	6	0	5	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2013-09-15T13:29:08	oeisdata/seq/A012/A012062.seq	141e9076df1eb94603219544cc993d37
A012063	exp(arcsin(arcsin(x)))=1+x+1/2!x^2+3/3!x^3+9/4!x^4+49/5!x^5...	[ "1", "1", "1", "3", "9", "49", "249", "1963", "14129", "146017", "1362961", "17450227", "200409465", "3064381137", "41812246345", "744091967643", "11765081428705", "239039270010305", "4298599985014945", "98237724213189475", "1980239469431883625" ]	[ "nonn" ]	10	0	4	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2013-11-21T12:46:00	oeisdata/seq/A012/A012063.seq	c5e919a7297b67d8d0ccddc629d4751f
A012064	arcsin(arcsin(arcsin(x)))=x+3/3!x^3+57/5!x^5+2747/7!x^7+249777/9!x^9...	[ "1", "3", "57", "2747", "249777", "36846835", "8040193769", "2437436057131", "981033890934369", "506479242594080227", "326455632550618599065", "257043518901496857566107", "242838347551317678123524113" ]	[ "nonn" ]	6	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2019-03-06T11:23:25	oeisdata/seq/A012/A012064.seq	d4a9922ef915060d34e8e1a2de2e08a1
A012065	Expansion of e.g.f. tan(arcsin(arcsin(x))).	[ "1", "4", "84", "4152", "370128", "51861888", "10494283968", "2894815734912", "1043916757274880", "476720372375608320", "268870416029396075520", "183537887154798761809920", "149132786692921038502318080", "142236877875834944842378444800", "157352707306190456257327051161600" ]	[ "nonn" ]	23	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2025-04-17T01:55:57	oeisdata/seq/A012/A012065.seq	fd8e43f638f701fb9614ca529efb7ceb
A012066	arctan(arcsin(arcsin(x)))=x+12/5!x^5+248/7!x^7+21648/9!*x^9...	[ "1", "0", "12", "248", "21648", "2241088", "390536000", "91111189120", "28811937609984", "11657540060256256", "5912796798580972544", "3665610214092467574784", "2729315998404117133692928", "2402622277659457905178820608" ]	[ "nonn" ]	7	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2013-11-21T12:46:00	oeisdata/seq/A012/A012066.seq	269da2c66d5d008402dc980ea224dcd5
A012067	cos(arcsin(arcsin(x)))=1-1/2!x^2-7/4!x^4-169/6!x^6-8751/8!x^8...	[ "1", "-1", "-7", "-169", "-8751", "-789681", "-110381943", "-22142611737", "-6041067843807", "-2153812782224097", "-972958293249140583", "-543350342541113761545", "-367659108914973687690255", "-296447255926407313341954705" ]	[ "sign" ]	6	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2020-08-21T15:14:13	oeisdata/seq/A012/A012067.seq	41f3640dd14092ad9a35db3aaee79ff8
A012068	sinh(arcsin(arcsin(x)))=x+3/3!x^3+49/5!x^5+1963/7!x^7+146017/9!x^9...	[ "1", "3", "49", "1963", "146017", "17450227", "3064381137", "744091967643", "239039270010305", "98237724213189475", "50300088100727103345", "31409480786365735560715", "23501653583412713065987105", "20761459048626350764508502355" ]	[ "nonn" ]	4	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:39	oeisdata/seq/A012/A012068.seq	a7d17c15d1a4ce8a430d4cb615867e2b
A012069	arcsinh(arcsin(arcsin(x)))=x+1/3!x^3+17/5!x^5+561/7!x^7+39521/9!x^9...	[ "1", "1", "17", "561", "39521", "4429217", "749371633", "176540328017", "55517224330689", "22448523976439873", "11356291769744087761", "7026618486154627990385", "5220988665867670545052193", "4587518335717939527563335649" ]	[ "nonn" ]	6	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-12-06T09:02:35	oeisdata/seq/A012/A012069.seq	1e7a6ee7448435b84b2c7a8108ebabd8
A012070	tanh(arcsin(arcsin(x)))=x+4/5!x^5+136/7!x^7+9424/9!*x^9...	[ "1", "0", "4", "136", "9424", "1075264", "183697344", "43928797056", "14007826346240", "5742582570096640", "2941974233347077120", "1841370038568483235840", "1382314169497713897656320", "1225713884449600233499770880" ]	[ "nonn" ]	6	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2015-02-12T11:37:52	oeisdata/seq/A012/A012070.seq	e29584dba66f5207974d2ac07e66325d
A012071	arctanh(arcsin(arcsin(x)))=x+4/3!x^3+92/5!x^5+5160/7!x^7+532880/9!x^9...	[ "1", "4", "92", "5160", "532880", "87726464", "21073486912", "6956206790528", "3020988238174464", "1670080968001854464", "1145224829994344492032", "953987340413779610175488", "948917210079076407043002368" ]	[ "nonn" ]	6	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2015-02-05T11:44:15	oeisdata/seq/A012/A012071.seq	37470713d191a1b4c531c6ec36a01438
A012072	cosh(arcsin(arcsin(x)))=1+1/2!x^2+9/4!x^4+249/6!x^6+14129/8!x^8...	[ "1", "1", "9", "249", "14129", "1362961", "200409465", "41812246345", "11765081428705", "4298599985014945", "1980239469431883625", "1123437678322006300185", "769950079011855688807185", "627326819278687159338591665" ]	[ "nonn" ]	4	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:39	oeisdata/seq/A012/A012072.seq	81e5b99dd2c5e26f42d70ea7a178d78e
A012073	sec(arcsin(arcsin(x)))=1+1/2!x^2+13/4!x^4+469/6!x^6+32985/8!x^8...	[ "1", "1", "13", "469", "32985", "3818601", "658371429", "158197312701", "50529852678321", "20707179214389201", "10591085815045781949", "6613325759240221954725", "4951199941339632477906825", "4377912560491798717856660025" ]	[ "nonn" ]	4	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:39	oeisdata/seq/A012/A012073.seq	2585eaf7106dc2f28737c0b3c9cac675
A012074	sech(arcsin(arcsin(x)))=1-1/2!x^2-3/4!x^4-69/6!x^6-3335/8!x^8...	[ "1", "-1", "-3", "-69", "-3335", "-289801", "-39612939", "-7845054541", "-2125704833551", "-755532171928081", "-341044077485199379", "-190581499954444336725", "-129146418452087275163415", "-104328785204254369631603225" ]	[ "sign" ]	7	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2013-11-21T12:46:00	oeisdata/seq/A012/A012074.seq	a2610251be67835ed44c90e169e2d04f
A012075	Expansion of e.g.f.: exp(arcsin(tan(x)))=1+x+1/2!x^2+4/3!x^3+13/4!x^4+76/5!x^5...	[ "1", "1", "1", "4", "13", "76", "421", "3424", "26713", "285136", "2871241", "38302144", "473357413", "7603381696", "111506036461", "2097552753664", "35624155784113", "768471264000256", "14838126699784081", "361133162545705984" ]	[ "nonn" ]	6	0	4	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2017-12-12T16:09:22	oeisdata/seq/A012/A012075.seq	4233945b57d03ec17235ffa03e605546
A012076	arcsin(arcsin(tan(x)))=x+4/3!x^3+84/5!x^5+4488/7!x^7+458448/9!x^9...	[ "1", "4", "84", "4488", "458448", "76530048", "18958160064", "6533187385728", "2990371546714368", "1755799654033628160", "1286962755283219153920", "1152156355072706267179008", "1237421224352190570236497920" ]	[ "nonn" ]	4	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:39	oeisdata/seq/A012/A012076.seq	30aad21aee22d02544d49bf8e79fcfb0
A012077	tan(arcsin(tan(x))) = x+5/3!x^3+121/5!x^5+6845/7!x^7+698161/9!x^9...	[ "1", "5", "121", "6845", "698161", "111973685", "25947503401", "8200346492525", "3389281372287841", "1774459993676715365", "1147649139272698443481", "898537335398420151634205", "837511978485668107020082321" ]	[ "nonn" ]	26	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2017-05-13T23:58:22	oeisdata/seq/A012/A012077.seq	ec244aef4bbb85f5c12a38b601eeb968
A012078	arctan(arcsin(tan(x)))=x+1/3!x^3+9/5!x^5+393/7!x^7+33009/9!x^9...	[ "1", "1", "9", "393", "33009", "4410033", "872617017", "240500373753", "88094910348129", "41401437242599905", "24287046275803547625", "17396048031084882189033", "14941352753081733849348945", "15157924050230673397966293393" ]	[ "nonn" ]	6	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2021-05-07T17:02:40	oeisdata/seq/A012/A012078.seq	7a6042c1b42a2fdea7107fc916c12767
A012079	cos(arcsin(tan(x)))=1-1/2!x^2-11/4!x^4-301/6!x^6-16631/8!x^8...	[ "1", "-1", "-11", "-301", "-16631", "-1620601", "-250557251", "-56629836901", "-17602836565871", "-7193368568377201", "-3735581618747946491", "-2401310609311293289501", "-1871136400199563216523111" ]	[ "sign" ]	17	0	3	[ "A012079", "A012253" ]	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2024-10-31T22:34:58	oeisdata/seq/A012/A012079.seq	97e28c318b6a9e54535ecf02912bb7f1
A012080	E.g.f.: sinh(arcsin(tan(x)))=x+4/3!x^3+76/5!x^5+3424/7!x^7+285136/9!x^9...	[ "1", "4", "76", "3424", "285136", "38302144", "7603381696", "2097552753664", "768471264000256", "361133162545705984", "211820037816772258816", "151696192774576615727104", "130270853179191716758245376" ]	[ "nonn" ]	6	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-05-24T12:23:06	oeisdata/seq/A012/A012080.seq	73fd9245cc79612089ac24cf00c8cd99
A012081	arcsinh(arcsin(tan(x)))=x+2/3!x^3+24/5!x^5+888/7!x^7+68352/9!x^9...	[ "1", "2", "24", "888", "68352", "8853888", "1724221056", "470304668928", "171029448056832", "79950698284462080", "46709069479002931200", "33347332565041919950848", "28565775294718770340331520", "28915860353300526164581613568" ]	[ "nonn" ]	4	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:40	oeisdata/seq/A012/A012081.seq	a40713bb2b9a2a0d066804c9b2368d31
A012082	tanh(arcsin(tan(x)))=x+1/3!x^3+1/5!x^5+1/7!x^7+7681/9!x^9...	[ "1", "1", "1", "1", "7681", "1689601", "390274561", "113644876801", "42729427952641", "20428848924057601", "12142755781873873921", "8789483754515321088001", "7614001483915573936550401", "7778864404689826961021184001" ]	[ "nonn" ]	4	0	5	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:40	oeisdata/seq/A012/A012082.seq	ac62ad9acbf915adc5faebf7c87c6ea2
A012083	arctanh(arcsin(tan(x)))=x+5/3!x^3+129/5!x^5+8133/7!x^7+949281/9!x^9...	[ "1", "5", "129", "8133", "949281", "177127653", "48290752353", "18102997908453", "8931245615625921", "5609823664317348165", "4370983985597526359745", "4137308650120582099800453", "4676183786000402886175691745" ]	[ "nonn" ]	8	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2015-02-05T11:49:32	oeisdata/seq/A012/A012083.seq	d403a418e8b2644f8b3b1aae646e040a
A012084	cosh(arcsin(tan(x)))=1+1/2!x^2+13/4!x^4+421/6!x^6+26713/8!x^8...	[ "1", "1", "13", "421", "26713", "2871241", "473357413", "111506036461", "35624155784113", "14838126699784081", "7813931867856058813", "5076900281143623362101", "3989607021222775392853513", "3730016905780866035656178521" ]	[ "nonn" ]	4	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:40	oeisdata/seq/A012/A012084.seq	8a976112836ce405145b0e14322a0332
A012085	Even coefficients in expansion of e.g.f. cos(x)/sqrt(cos(2*x)).	[ "1", "1", "17", "721", "58337", "7734241", "1526099057", "419784870961", "153563504618177", "72104198836466881", "42270463533824671697", "30262124466958766778001", "25981973075048213029395617", "26350476755161831091778460321" ]	[ "nonn" ]	20	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2023-10-02T13:48:30	oeisdata/seq/A012/A012085.seq	0e5b22dc0922693a46777e449939560e
A012086	sech(arcsin(tan(x)))=1-1/2!x^2-7/4!x^4-121/6!x^6-5167/8!x^8...	[ "1", "-1", "-7", "-121", "-5167", "-487441", "-78804727", "-18558463561", "-5919443326687", "-2457116797560481", "-1289150916753299047", "-834798631079038210201", "-654139310316332313889807", "-610085118687493622960844721" ]	[ "sign" ]	6	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2023-09-17T15:25:41	oeisdata/seq/A012/A012086.seq	5720c0363c97873f7e622befe4eee231
A012087	Expansion of e.g.f.: exp(arcsin(arctan(x)))=1+x+1/2!x^2-3/4!x^4+4/5!x^5+69/6!x^6...	[ "1", "1", "1", "0", "-3", "4", "69", "-32", "-2503", "1936", "177481", "-67328", "-18539595", "4140096", "2813939725", "353591808", "-573509386895", "-262064131840", "152349815266705", "130347373404160", "-50966873710838675", "-65058714844462080" ]	[ "sign" ]	6	0	5	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2018-05-27T10:56:54	oeisdata/seq/A012/A012087.seq	c53d1e1f741d7f97d564f3e57c451485
A012088	arcsin(arcsin(arctan(x)))=x+12/5!x^5-88/7!x^7+13968/9!*x^9...	[ "1", "0", "12", "-88", "13968", "-597440", "132709184", "-15685157504", "5014687029504", "-1181425359497216", "528315488687774720", "-207409825492284028928", "125603683629593633394688", "-73594034552724198387236864" ]	[ "sign" ]	6	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2021-06-30T18:24:52	oeisdata/seq/A012/A012088.seq	ac3b4993d6880865b3710fda09b870ea
A012089	tan(arcsin(arctan(x)))=x+1/3!x^3+9/5!x^5+57/7!x^7+5169/9!x^9...	[ "1", "1", "9", "57", "5169", "-93807", "31981689", "-3857766903", "1058896281825", "-286891166986335", "108826313005021545", "-47766338018402914215", "25721485923005221938705", "-16179153687877979599066575" ]	[ "sign" ]	12	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2024-11-17T16:10:46	oeisdata/seq/A012/A012089.seq	f0b95401404e9daab3f9b3c197f34596
A012090	arctan(arcsin(arctan(x))) = x - 3/3!x^3 + 57/5!x^5 - 2587/7!x^7 + 217137/9!x^9 - ...	[ "1", "-3", "57", "-2587", "217137", "-29025587", "5664605801", "-1519556355275", "536514935904609", "-241225069255390307", "134580033555427233689", "-91237165395466088195963", "73877505225687035803070353", "-70425423338543411535873624467", "78071169657855750497737512497097" ]	[ "sign" ]	8	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2018-01-15T15:01:25	oeisdata/seq/A012/A012090.seq	f23e25166ab9ec0a83fd671a6d542381
A012091	cos(arcsin(arctan(x)))=1-1/2!x^2+5/4!x^4-109/6!x^6+4521/8!x^8...	[ "1", "-1", "5", "-109", "4521", "-330681", "36468717", "-5721101541", "1205289090513", "-328897528901361", "112769846051251797", "-47472161654530776285", "24068680135210975714425", "-14466929567049590650593705" ]	[ "sign" ]	14	0	3	[ "A012091", "A012254" ]	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2024-10-31T22:28:48	oeisdata/seq/A012/A012091.seq	f3dd980a7eb89518dde9b7dfd50c582b
A012092	sinh(arcsin(arctan(x)))=x+4/5!x^5-32/7!x^7+1936/9!x^9-67328/11!x^11...	[ "1", "0", "4", "-32", "1936", "-67328", "4140096", "353591808", "-262064131840", "130347373404160", "-65058714844462080", "36397620373403361280", "-23130160076947953643520", "16791590408623398030868480" ]	[ "sign" ]	6	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2016-03-12T14:34:37	oeisdata/seq/A012/A012092.seq	9dc107b735c9789be5e79d0908605b3e
A012093	arcsinh(arcsin(arctan(x)))=x-2/3!x^3+32/5!x^5-1224/7!x^7+89984/9!x^9...	[ "1", "-2", "32", "-1224", "89984", "-10705408", "1889967232", "-464238999808", "151661217091584", "-63641246944645120", "33381024310383640576", "-21408234533329528127488", "16485197581627921671815168" ]	[ "sign" ]	6	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2025-06-02T14:22:50	oeisdata/seq/A012/A012093.seq	150561134c4e06dbb61dcf402f2dfe4b
A012094	E.g.f.: tanh(arcsin(arctan(x))), odd powers only.	[ "1", "-3", "49", "-1859", "127297", "-13662371", "2114110257", "-445110767139", "122308548673025", "-42491524107649475", "18204849127687565745", "-9427087716053634833795", "5803356448065850202170945", "-4188507975000626549209008995", "3502566426777342320289454951345" ]	[ "sign" ]	23	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2018-02-15T15:38:36	oeisdata/seq/A012/A012094.seq	9a4c93dc142c5f98220ec791be78cff5
A012095	arctanh(arcsin(arctan(x))) = x + 1/3!x^3 + 17/5!x^5 + 225/7!x^7 + 19745/9!x^9 + ...	[ "1", "1", "17", "225", "19745", "613889", "165999025", "6543673313", "5318503266369", "97941778159361", "473023280425720657", "-24807619116269601823", "96456947558141320688993", "-18191159887705677530042623", "39579539155416746718880624881", "-15661645517509146973335115013919" ]	[ "sign" ]	8	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2018-01-15T15:03:26	oeisdata/seq/A012/A012095.seq	d8b33038971d9810403c9673558b042e
A012096	cosh(arcsin(arctan(x)))=1+1/2!x^2-3/4!x^4+69/6!x^6-2503/8!x^8...	[ "1", "1", "-3", "69", "-2503", "177481", "-18539595", "2813939725", "-573509386895", "152349815266705", "-50966873710838675", "20993994712780457685", "-10435138367654204994135", "6159973489221376775016665" ]	[ "sign" ]	4	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:40	oeisdata/seq/A012/A012096.seq	18dcb0c0b0ff109ed950456c8c2b11c4
A012097	sec(arcsin(arctan(x)))=1+1/2!x^2+1/4!x^4+49/6!x^6-447/8!x^8...	[ "1", "1", "1", "49", "-447", "78561", "-5655231", "1014069393", "-187639949439", "51144433721793", "-16631972691697791", "6837287119716744945", "-3357388632038371909695", "1969419543279480607781025" ]	[ "sign" ]	6	0	4	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2019-11-28T15:06:59	oeisdata/seq/A012/A012097.seq	7eee9a8d9ce5227ef7e21722ad84f436
A012098	sech(arcsin(arctan(x)))=1-1/2!x^2+9/4!x^4-249/6!x^6+13297/8!x^8...	[ "1", "-1", "9", "-249", "13297", "-1175761", "154625721", "-28328562313", "6890453792609", "-2147692998841633", "834418870682339561", "-395288520944694504345", "224249503561141591847505", "-150078278389547160573482225" ]	[ "sign" ]	6	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2019-10-26T16:45:55	oeisdata/seq/A012/A012098.seq	ef8d63473e7fbd0ceb18cc5a2f02eccb
A012099	Expansion of e.g.f.: exp(arcsin(sinh(x)))=1+x+1/2!x^2+3/3!x^3+9/4!x^4+41/5!x^5...	[ "1", "1", "1", "3", "9", "41", "201", "1403", "9649", "90641", "809201", "9578803", "105268089", "1504717241", "19650225401", "329275068203", "4982657935329", "95780865239841", "1648151554792801", "35749976635509603", "689411371817131369" ]	[ "nonn" ]	8	0	4	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2024-04-21T10:46:46	oeisdata/seq/A012/A012099.seq	27ebbfd5624eeee4b2d6e07f05bb80eb
A012100	arcsin(arcsin(sinh(x)))=x+3/3!x^3+49/5!x^5+2187/7!x^7+186337/9!x^9...	[ "1", "3", "49", "2187", "186337", "25929907", "5355694161", "1539910627387", "588565856592577", "288782211525088995", "176996414128700874865", "132567145102215208555627", "119162444909413724755024545" ]	[ "nonn" ]	4	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:40	oeisdata/seq/A012/A012100.seq	4bc6756d5d8f45eda866b4c12b8e9b1a

A012001

E.g.f.: -tan(log(cos(x))), even powers only.

[ "0", "1", "2", "46", "1112", "55816", "3804272", "372397936", "47682319232", "7841034902656", "1601250315636992", "398250217200414976", "118406090377889303552", "41478295178427681104896", "16904918898000336224294912" ]

[ "nonn" ]

20

0

3

null

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

2017-04-12T23:09:22

oeisdata/seq/A012/A012001.seq

82bd045dc2ac483454dc76d20a695d0d

A012002

arctan(log(cos(x)))=-1/2!*x^2-2/4!*x^4+14/6!*x^6+568/8!*x^8...

[ "0", "-1", "-2", "14", "568", "2144", "-1061312", "-65851696", "3745115008", "1232648783744", "50799435228928", "-36670923310299136", "-8828746813705828352", "954888000296009790464", "1122466427244127979911168" ]

[ "sign" ]

9

0

3

null

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

2019-08-10T10:57:38

oeisdata/seq/A012/A012002.seq

5260280d55edcbe96edfdd65f7044555

A012003

E.g.f. cos(log(cos(x))), even powers only.

[ "1", "0", "-3", "-30", "-483", "-12660", "-492063", "-26407290", "-1854592743", "-162954226920", "-17150991170523", "-2051454240374550", "-254425037609483403", "-24186909676571913180", "3098088521295623020617" ]

[ "sign" ]

13

0

3

null

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

2013-11-21T12:46:00

oeisdata/seq/A012/A012003.seq

e38989648258997dfc7c6e71b4d6b84f

A012004

arcsinh(log(cos(x)))=-1/2!*x^2-2/4!*x^4-1/6!*x^6+148/8!*x^8-61/10!*x^10...

[ "0", "-1", "-2", "-1", "148", "-61", "-395702", "-28299181", "93652648", "265509939239", "14066899733398", "-8605652824527001", "-2442549938212838852", "25891773268121861099", "210295085697229695516898" ]

[ "sign" ]

9

0

3

null

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

2016-03-21T15:33:30

oeisdata/seq/A012/A012004.seq

d5cfbcf9c988e27c5f8786ca17183b06

A012005

tanh(log(cos(x)))=-1/2!*x^2-2/4!*x^4+14/6!*x^6+568/8!*x^8...

[ "-1", "-2", "14", "568", "9704", "-229712", "-35581456", "-1790014592", "72312646784", "28603722780928", "3039116082823424", "-154149928667313152", "-135793191600734657536", "-25782484156469234296832" ]

[ "sign" ]

6

0

2

null

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

2022-05-12T18:21:03

oeisdata/seq/A012/A012005.seq

1d89a5a84a80af2e5054f69e780c0250

A012006

-arctanh(log(cos(x))) = 1/2!*x^2+2/4!*x^4+46/6!*x^6+1112/8!*x^8...

[ "1", "2", "46", "1112", "63376", "4635872", "523749136", "76049858432", "14634264866176", "3496967323112192", "1032537134569578496", "366067157640456292352", "154146217678162805226496", "75874517780279404503590912" ]

[ "nonn" ]

8

0

2

null

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

2013-10-25T10:04:15

oeisdata/seq/A012/A012006.seq

f90ad377f00c1f350f02f0975f785f8d

A012007

cosh(log(cos(x))) = 1+3/4!*x^4+30/6!*x^6+693/8!*x^8+25260/10!*x^10...

[ "1", "0", "3", "30", "693", "25260", "1351383", "99680490", "9695756073", "1202439837720", "185185594118763", "34674437196568950", "7757267081778543453", "2043536254646561946180", "626129820701814932734143", "220771946624511552276841410", "88759695789769644718332394833" ]

[ "nonn" ]

24

0

3

[ "A012003", "A012007", "A012008", "A012009" ]

null

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

2017-05-22T13:01:56

oeisdata/seq/A012/A012007.seq

2f34fb23064cecfa6c223920333905d7

A012008

sec(log(cos(x)))= 1+3/4!*x^4+30/6!*x^6+1113/8!*x^8+50460/10!*x^10...

[ "1", "0", "3", "30", "1113", "50460", "3693723", "359740290", "46791574833", "7721990402520", "1584990509251443", "395230316479830150", "117766463267804780553", "41313542582787780576180", "16856003114804522914769163" ]

[ "nonn" ]

7

0

3

null

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

2015-01-02T16:55:18

oeisdata/seq/A012/A012008.seq

02d2bf3a3157f98217181c0d99f1d5d2

A012009

Expansion of e.g.f. sech(log(cos(x))) (even exponents only).

[ "1", "0", "-3", "-30", "-63", "12540", "602877", "6625710", "-1991169183", "-241970036520", "-7540177734243", "2917041754949850", "699983161534169697", "46722975483964508820", "-21334067257986056115363", "-8882421213380429461235610", "-1081286159351846822872767423" ]

[ "sign" ]

24

0

3

[ "A012003", "A012007", "A012008", "A012009" ]

null

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

2024-08-04T06:36:59

oeisdata/seq/A012/A012009.seq

2c6b01e052b909df602a5f15d4372514

A012010

arctan(sin(sin(x))) = x - 4/3!*x^3 + 76/5!*x^5 - 3592/7!*x^7 + 317968/9!*x^9 - ....

[ "1", "-4", "76", "-3592", "317968", "-45286528", "9459412288", "-2724254181760", "1034595588065536", "-500961002883890176", "301230818225601928192", "-220218226893098691684352", "192355329482117756948647936" ]

[ "sign" ]

10

0

2

null

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

2013-12-16T13:56:20

oeisdata/seq/A012/A012010.seq

bb2c8cccf0307b9c4e6d7ef5f4d45986

A012011

arcsinh(sin(sin(x)))=x-3/3!*x^3+41/5!*x^5-1515/7!*x^7+113489/9!*x^9...

[ "1", "-3", "41", "-1515", "113489", "-14321299", "2716798969", "-721988679547", "255890614389921", "-116619928299347491", "66439023428917759945", "-46262911349611152912395", "38656874720522348065089521" ]

[ "sign" ]

14

0

2

null

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

2015-02-03T16:47:24

oeisdata/seq/A012/A012011.seq

e208f9a83fe3acf564e7b730e390e02b

A012012

sec(sin(sin(x)))=1+1/2!*x^2-3/4!*x^4-27/6!*x^6+1145/8!*x^8...

[ "1", "1", "-3", "-27", "1145", "-8631", "-1770123", "115778861", "4625206001", "-1652588042607", "75500754980077", "36232528294816885", "-8153373987817082007", "-655897923302322394919", "753704651365381460774501" ]

[ "sign" ]

4

0

3

null

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

2012-02-24T12:50:36

oeisdata/seq/A012/A012012.seq

4063ae8e22d8d2c40efc1e573b261110

A012013

sech(sin(sin(x)))=1-1/2!*x^2+13/4!*x^4-373/6!*x^6+19545/8!*x^8...

[ "1", "-1", "13", "-373", "19545", "-1638569", "201324773", "-34084249501", "7606559175089", "-2164004651794513", "764464999664782013", "-328322677491890500805", "168474698667902836871177", "-101798128590699775451705081" ]

[ "sign" ]

6

0

3

null

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

2022-07-27T19:09:59

oeisdata/seq/A012/A012013.seq

0fc0ddeae05ee95d69204aad3c916322

A012014

arctan(sin(tan(x)))=x-1/3!*x^3+1/5!*x^5-169/7!*x^7-1823/9!*x^9...

[ "1", "-1", "1", "-169", "-1823", "-365905", "-17126303", "-3688466617", "-393996411839", "-109259290725793", "-20477152840654271", "-7401734340295771849", "-2112803982091750971359", "-978357645904185043693297" ]

[ "sign" ]

6

0

4

null

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

2014-06-04T10:14:28

oeisdata/seq/A012/A012014.seq

a2e96acdb642633cdbc93dbe78194ded

A012015

arcsinh(sin(tan(x)))=x-4/5!*x^5-192/7!*x^7-7600/9!*x^9-507136/11!*x^11...

[ "1", "0", "-4", "-192", "-7600", "-507136", "-40159040", "-4621348864", "-627047126784", "-113424912867328", "-23612736247718912", "-6196586681702039552", "-1827473399583593672704", "-652336666072894806360064" ]

[ "sign" ]

4

0

3

null

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

2012-02-24T12:50:36

oeisdata/seq/A012/A012015.seq

61c0bdacf66ea937065750463a685335

A012016

arctanh(sin(tan(x)))=x+3/3!*x^3+41/5!*x^5+1299/7!*x^7+74609/9!*x^9...

[ "1", "3", "41", "1299", "74609", "6787811", "898506649", "163241051315", "39007280136801", "11866656488375747", "4479287777805494665", "2054673461380880189779", "1125793481954983195433681", "726247496033154181534638755" ]

[ "nonn" ]

10

0

2

[ "A009329", "A012016" ]

null

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

2018-10-09T15:29:21

oeisdata/seq/A012/A012016.seq

fa553e48b9711d932203e842021b090e

A012017

sec(sin(tan(x)))=1+1/2!*x^2+9/4!*x^4+153/6!*x^6+2993/8!*x^8...

[ "1", "1", "9", "153", "2993", "-72111", "-33331719", "-7328604631", "-1581635839519", "-356792088521439", "-81022312424248727", "-15576441107086727111", "22243831754082386577", "3229505766853670411015281" ]

[ "sign" ]

4

0

3

null

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

2012-02-24T12:50:36

oeisdata/seq/A012/A012017.seq

7c12dd2af9d08ab7d602bbe1d0648c2c

A012018

sech(sin(tan(x)))=1-1/2!*x^2+1/4!*x^4+47/6!*x^6+897/8!*x^8...

[ "1", "-1", "1", "47", "897", "26911", "2176769", "269558351", "38463601409", "6445724731199", "1297792574780417", "307585734223517551", "82426762826906376833", "23816926512873022989919", "6844111898535212011277057" ]

[ "sign" ]

4

0

4

null

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

2012-02-24T12:50:36

oeisdata/seq/A012/A012018.seq

0ae4e1c86e1dd91bc8c17335720939d9

A012019

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

[ "1", "1", "1", "-2", "-11", "16", "301", "-104", "-15287", "-20096", "1239481", "4427776", "-146243459", "-954111872", "23567903269", "243390205696", "-4951201340399", "-75389245067264", "1307274054385393", "28248828019830784", "-420773143716828539" ]

[ "sign" ]

20

0

4

null

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

2025-02-28T12:05:29

oeisdata/seq/A012/A012019.seq

4a57335322abd576abc212d2739ccb98

A012020

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

[ "1", "-4", "76", "-3256", "245008", "-28441216", "4700478784", "-1047088053376", "302112622479616", "-109527844826856448", "48716214653800569856", "-26075068739563056830464", "16529214537740143196901376" ]

[ "sign" ]

19

0

2

null

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

2015-10-21T11:25:11

oeisdata/seq/A012/A012020.seq

a4806b0a924fcb9894f249a6c3e9220c

A012021

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

[ "1", "-1", "1", "167", "-14303", "1383887", "-170123615", "26560717367", "-5162935778879", "1219537456849055", "-340794504958201919", "109077799391707298759", "-38112045733323708444959", "13139859774638771226676847" ]

[ "sign" ]

18

0

4

null

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

2018-01-29T02:56:35

oeisdata/seq/A012/A012021.seq

2141ff331dc7cd67eb56ea4dd3e7a2ee

A012022

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

[ "1", "-5", "129", "-7965", "903105", "-163451925", "43259364225", "-15764670046125", "7571150452490625", "-4634731528895593125", "3522824632122301130625", "-3255279003622294051528125", "3593928024032353882700450625" ]

[ "sign" ]

30

0

2

null

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

2018-02-03T16:39:48

oeisdata/seq/A012/A012022.seq

9c01d1811d4c018a627e57f881d61ee6

A012023

Expansion of e.g.f. cos(sin(arctan(x))) (even powers).

[ "1", "-1", "13", "-421", "25369", "-2449801", "346065061", "-67243537453", "17192488230961", "-5593309059948049", "2255588021494237501", "-1103994926592923677621", "644587811150505183179593", "-442516027690815793746696601" ]

[ "sign" ]

18

0

3

null

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

2018-01-29T02:52:45

oeisdata/seq/A012/A012023.seq

82b7c1bf028efe09c7e290d2437d4885

A012024

E.g.f. sinh(sin(arctan(x))) (odd powers only).

[ "1", "-2", "16", "-104", "-20096", "4427776", "-954111872", "243390205696", "-75389245067264", "28248828019830784", "-12669814369258471424", "6721694045416881553408", "-4170436153219300846567424", "2994608522937575414450814976" ]

[ "sign" ]

17

1

2

null

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

2025-02-28T12:05:36

oeisdata/seq/A012/A012024.seq

4fd76ade83e76ae3a15436c95d45e40e

A012025

E.g.f. arcsinh(sin(arctan(x))) = arcsinh(x/(1+x^2)^(1/2)) (odd powers only).

[ "1", "-4", "84", "-4320", "418320", "-66225600", "15657364800", "-5187108326400", "2296766568096000", "-1310785979158656000", "937056917610253440000", "-820081468493365478400000", "862301491174096979765760000" ]

[ "sign" ]

19

1

2

null

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

2013-10-30T16:55:15

oeisdata/seq/A012/A012025.seq

5567df4f4047e876fbc3cd2c12daac5b

A012026

Expansion of e.g.f. tanh(sin(arctan(x))) = tanh(x/sqrt(1+x^2)) (odd powers only).

[ "1", "-5", "121", "-6677", "651985", "-98741477", "21378584137", "-6259615830197", "2380487154907681", "-1140222272527932869", "671453734616884934041", "-476714184862146843059285", "401522701697360654591942641" ]

[ "sign" ]

19

1

2

null

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

2018-01-29T02:52:50

oeisdata/seq/A012/A012026.seq

9a67e7eb3c836a22fb81cd94e8dfc584

A012027

E.g.f. cosh(sin(arctan(x))) = cosh(x/sqrt(1+x^2)) (even powers only).

[ "1", "1", "-11", "301", "-15287", "1239481", "-146243459", "23567903269", "-4951201340399", "1307274054385393", "-420773143716828539", "160635990248839962781", "-70764171306270411101351", "34822234810202848704345001" ]

[ "sign" ]

25

0

3

null

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

2025-02-28T12:05:43

oeisdata/seq/A012/A012027.seq

8b5c499dfafe34365aed9af3218bad27

A012028

E.g.f. sec(sin(arctan(x))) = 1/cos(x/sqrt(1+x^2)).

[ "1", "1", "-7", "121", "-3823", "186961", "-12464695", "967217161", "-51115216735", "-15922673810399", "12685061907297305", "-7463929930799687399", "4531120544938557395633", "-3032728078954072676445839" ]

[ "sign" ]

9

0

3

null

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

2012-08-06T10:36:36

oeisdata/seq/A012/A012028.seq

811b86ba4904601d299dcbc17f299e28

A012029

E.g.f.: sech(sin(arctan(x))) (even powers only).

[ "1", "-1", "17", "-721", "56993", "-7232161", "1344866225", "-344599447921", "116382225519425", "-50097660050713921", "26773024797675332945", "-17392081348966913859601", "13497082647397365780254177" ]

[ "sign" ]

14

0

3

null

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

2013-11-08T09:32:22

oeisdata/seq/A012/A012029.seq

c69e5cd50ad523e47371defedc35f0ac

A012030

arctan(sin(sinh(x))) = x - 2/3!*x^3 +16/5!*x^5 - 440/7!*x^7 + 20224/9!*x^9 - ....

[ "1", "-2", "16", "-440", "20224", "-1582976", "178612864", "-27969867008", "5765737517056", "-1516228355846144", "495092243779256320", "-196552136456231321600", "93232152295610535018496", "-52074797114273752377786368" ]

[ "sign" ]

10

0

2

null

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

2024-12-04T19:23:26

oeisdata/seq/A012/A012030.seq

ffbe773bc8fae2be8888b6d79d9b2b1e

A012031

arcsinh(sin(sinh(x)))=x-1/3!*x^3+1/5!*x^5-113/7!*x^7+4033/9!*x^9...

[ "1", "-1", "1", "-113", "4033", "-307297", "32041153", "-4722808145", "919792817281", "-229762987386049", "71595055755086977", "-27226195625057526833", "12411835138553868048961", "-6681718218812850626513185" ]

[ "sign" ]

8

0

4

null

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

2015-02-03T15:02:32

oeisdata/seq/A012/A012031.seq

6e8e71c5e55050426a2ac815c9b4a406

A012032

sec(sin(sinh(x)))=1+1/2!*x^2+5/4!*x^4+13/6!*x^6-1303/8!*x^8...

[ "1", "1", "5", "13", "-1303", "-97351", "-5539667", "-182565627", "23677748561", "8153921374705", "1571128609968341", "190412412110488701", "-16146953133290647751", "-22882305147029329939799" ]

[ "sign" ]

6

0

3

null

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

2025-03-18T18:52:18

oeisdata/seq/A012/A012032.seq

3652feb21e0db0604854679b845a433b

A012033

sech(sin(sinh(x)))=1-1/2!*x^2+5/4!*x^4-13/6!*x^6-407/8!*x^8...

[ "1", "-1", "5", "-13", "-407", "30151", "-1142483", "19202427", "3747342929", "-722092683505", "76341208430549", "-2313301317273981", "-1769780901329435719", "628518840135423728599", "-125498832189487922441219" ]

[ "sign" ]

4

0

3

null

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

2012-02-24T12:50:37

oeisdata/seq/A012/A012033.seq

7ee56491e3f9db1b64bef041d0efbdc2

A012034

exp(sin(arcsinh(x))) = 1+x+1/2!*x^2-1/3!*x^3-7/4!*x^4+1/5!*x^5...

[ "1", "1", "1", "-1", "-7", "1", "121", "111", "-4271", "-9407", "262801", "957791", "-25257079", "-131065791", "3510517193", "23876150351", "-667413187039", "-5645293077119", "166471455235489", "1689130316350143", "-52750545434135399" ]

[ "sign" ]

9

0

5

null

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

2013-10-30T16:56:07

oeisdata/seq/A012/A012034.seq

f722909d2a7eff182625e4937197df6b

A012035

sin(sin(arcsinh(x))) = x-3/3!*x^3+41/5!*x^5-1291/7!*x^7+73169/9!*x^9...

[ "1", "-3", "41", "-1291", "73169", "-6551251", "852920953", "-152425617371", "35839758063521", "-10733139641944739", "3990221478883366601", "-1803635523024068325803", "974372554797510153337201" ]

[ "sign" ]

9

0

2

null

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

2013-10-30T16:56:58

oeisdata/seq/A012/A012035.seq

01c11d4ad840821784396eafc24534d9

A012036

tan(sin(arcsinh(x)))=x-4/5!*x^5+32/7!*x^7+80/9!*x^9-34048/11!*x^11...

[ "1", "0", "-4", "32", "80", "-34048", "5048512", "-984048128", "246504417536", "-76892124225536", "29350173573487616", "-13506119868179701760", "7388967312556159062016", "-4745632815309786449379328", "3538391474251613805070172160" ]

[ "sign" ]

9

0

3

null

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

2015-02-03T05:07:56

oeisdata/seq/A012/A012036.seq

5fa728ac4659956bd1f7c6297d7eb9ad

A012037

arctan(sin(arcsinh(x)))=x-4/3!*x^3+84/5!*x^5-4320/7!*x^7+410640/9!*x^9...

[ "1", "-4", "84", "-4320", "410640", "-62424000", "13882209600", "-4250758886400", "1715097849504000", "-881945575315584000", "563062441711086720000", "-436991853893041873920000", "405186856780938968885760000" ]

[ "sign" ]

4

0

2

null

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

2012-02-24T12:50:37

oeisdata/seq/A012/A012037.seq

32194e4eed1a3fb5f0f1ff0dc30ec0cb

A012038

cos(sin(arcsinh(x)))=1-1/2!*x^2+9/4!*x^4-201/6!*x^6+8753/8!*x^8...

[ "1", "-1", "9", "-201", "8753", "-634481", "69292281", "-10655767929", "2197620415201", "-585914236294753", "196238045270790761", "-80691386297887323561", "39976011626025680236049", "-23490521419525456192130001" ]

[ "sign" ]

7

0

3

null

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

2013-11-21T12:46:00

oeisdata/seq/A012/A012038.seq

9f01eededc217ee87fa2bba28e7f3091

A012039

sinh(sin(arcsinh(x))) = x-1/3!*x^3+1/5!*x^5+111/7!*x^7-9407/9!*x^9...

[ "1", "-1", "1", "111", "-9407", "957791", "-131065791", "23876150351", "-5645293077119", "1689130316350143", "-625455343415905919", "281176376077651011119", "-150982531394396522439999", "95493861079696805301099551" ]

[ "sign" ]

10

0

4

null

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

2023-03-18T16:51:34

oeisdata/seq/A012/A012039.seq

ba99fac998c07729411a07578e4540dc

A012040

arcsinh(sin(arcsinh(x)))=x-3/3!*x^3+49/5!*x^5-2075/7!*x^7+168865/9!*x^9...

[ "1", "-3", "49", "-2075", "168865", "-22606675", "4522468625", "-1266169501675", "473063766306625", "-227507081427747875", "136918092950286480625", "-100805803028947763426875", "89129323309512937147750625" ]

[ "sign" ]

10

0

2

null

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

2015-02-03T16:47:51

oeisdata/seq/A012/A012040.seq

a5eaf2484e2faadfe4d38ff42f2e369a

A012041

tanh(sin(arcsinh(x)))=x-4/3!*x^3+76/5!*x^5-3312/7!*x^7+255952/9!*x^9...

[ "1", "-4", "76", "-3312", "255952", "-30728512", "5281229760", "-1228900532992", "371761489090816", "-141763213277045760", "66504626862819552256", "-37635004127910391803904", "25277676503178610861756416" ]

[ "sign" ]

10

0

2

null

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

2015-02-04T07:30:41

oeisdata/seq/A012/A012041.seq

5349f810150aec7177baa603654acb77

A012042

arctanh(sin(arcsinh(x)))=x+4/5!*x^5-80/7!*x^7+4240/9!*x^9-342400/11!*x^11...

[ "1", "0", "4", "-80", "4240", "-342400", "41806400", "-7093216000", "1601470624000", "-464003651072000", "167847611351680000", "-74143433704737280000", "39275771932443138560000", "-24575763662119940608000000" ]

[ "sign" ]

10

0

3

null

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

2024-03-17T07:58:56

oeisdata/seq/A012/A012042.seq

24a3070c5693e3d153c9d1ff00bed9c3

A012043

cosh(sin(arcsinh(x))) = 1+1/2!*x^2-7/4!*x^4+121/6!*x^6-4271/8!*x^8...

[ "1", "1", "-7", "121", "-4271", "262801", "-25257079", "3510517193", "-667413187039", "166471455235489", "-52750545434135399", "20700581434214572441", "-9854557734715140280207", "5594838313934367657655601" ]

[ "sign" ]

11

0

3

null

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

2025-04-20T12:53:22

oeisdata/seq/A012/A012043.seq

4cbb4fc983bb8c9715d38ffe80ec3812

A012044

sec(sin(arcsinh(x)))=1+1/2!*x^2-3/4!*x^4+21/6!*x^6-647/8!*x^8...

[ "1", "1", "-3", "21", "-647", "45161", "-4655115", "671831421", "-131445679375", "33601481453521", "-10874248371483155", "4345212201159011301", "-2101132542287329737623", "1209250716473417141359161" ]

[ "sign" ]

7

0

3

null

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

2013-11-21T12:46:00

oeisdata/seq/A012/A012044.seq

a4b849e5d1f26ae3e154feff5019b184

A012045

sech(sin(arcsinh(x)))=1-1/2!*x^2+13/4!*x^4-421/6!*x^6+25817/8!*x^8...

[ "1", "-1", "13", "-421", "25817", "-2565961", "375964645", "-76201822061", "20411701862065", "-6981810963526801", "2968895846823113405", "-1536132530083569544501", "950209903347072336087433", "-692439473656550310042291161" ]

[ "sign" ]

4

0

3

null

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

2012-02-24T12:50:37

oeisdata/seq/A012/A012045.seq

2abeaee0036ff32ca4e0a2ad2720aaac

A012046

arctan(sin(tanh(x)))=x-5/3!*x^3+121/5!*x^5-7013/7!*x^7+752785/9!*x^9...

[ "1", "-5", "121", "-7013", "752785", "-129763589", "32812992265", "-11441858264741", "5261501926546081", "-3084889329990554117", "2246121092328414171673", "-1988316104656824914919653", "2102978545788269109358313521" ]

[ "sign" ]

6

0

2

null

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

2023-09-01T15:29:33

oeisdata/seq/A012/A012046.seq

140bf5928dbc8cb2da5ff2f971ec7eed

A012047

arcsinh(sin(tanh(x)))=x-4/3!*x^3+76/5!*x^5-3536/7!*x^7+317392/9!*x^9...

[ "1", "-4", "76", "-3536", "317392", "-47590720", "10785422272", "-3441103532288", "1468657322465536", "-807408622401283072", "555453404529224756224", "-467352773254586231115776", "472081158536303158224572416" ]

[ "sign" ]

8

0

2

null

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

2015-02-04T04:26:58

oeisdata/seq/A012/A012047.seq

f48d9f2e29a09cbcde4acd29da67af4e

A012048

arctanh(sin(tanh(x)))=x-1/3!*x^3+1/5!*x^5+55/7!*x^7-2207/9!*x^9...

[ "1", "-1", "1", "55", "-2207", "79727", "-2834207", "81045991", "1107720001", "-715785186337", "165075476417857", "-44818254949260905", "14626040239803925921", "-5177396773524357363889", "1885895392048206524730145" ]

[ "sign" ]

6

0

4

null

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

2017-03-07T08:59:24

oeisdata/seq/A012/A012048.seq

2661774dc084a828bb8e54120df8d4d2

A012049

sec(sin(tanh(x))) = 1+1/2!*x^2-7/4!*x^4+73/6!*x^6+209/8!*x^8...

[ "1", "1", "-7", "73", "209", "-144271", "16935049", "-1681509255", "121927140641", "7429711841377", "-7368737635468135", "2672443484700215337", "-714451608564077085455", "102412390388191040345041", "45342663705298790615837737", "-56227306534265498361644426407" ]

[ "sign" ]

14

0

3

null

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

2023-10-27T21:05:57

oeisdata/seq/A012/A012049.seq

86b1aef6089a43de72f0e6edc733a284

A012050

sech(sin(tanh(x)))=1-1/2!*x^2+17/4!*x^4-673/6!*x^6+48481/8!*x^8...

[ "1", "-1", "17", "-673", "48481", "-5556929", "930399601", "-214412110305", "65104843008449", "-25194079035190657", "12104203127776694225", "-7069126951831617433377", "4932323527151866597114145", "-4052159085639349626953573441" ]

[ "sign" ]

4

0

3

null

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

2012-02-24T12:50:39

oeisdata/seq/A012/A012050.seq

a8665e9d05bc24568da1af382e428c2d

A012051

exp(sin(arctanh(x)))=1+x+1/2!*x^2+2/3!*x^3+5/4!*x^4+16/5!*x^5...

[ "1", "1", "1", "2", "5", "16", "61", "216", "937", "-1280", "-34919", "-1141504", "-13257619", "-263392128", "-3269873515", "-64804059904", "-890367567919", "-18858549039104", "-286428853272143", "-6592583427379200", "-109915623105978539" ]

[ "sign" ]

4

0

4

null

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

2012-02-24T12:50:39

oeisdata/seq/A012/A012051.seq

ee01f25fecd82cb43467ebf0c002a28f

A012052

sin(sin(arctanh(x)))=x-4/5!*x^5-136/7!*x^7-7408/9!*x^9-644416/11!*x^11...

[ "1", "0", "-4", "-136", "-7408", "-644416", "-84562880", "-15811723136", "-4005496370944", "-1317763889887232", "-544096638435718144", "-274416039275290634240", "-165481485047921126273024", "-117299354914466636092850176" ]

[ "sign" ]

6

0

3

null

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

2023-07-06T15:01:53

oeisdata/seq/A012/A012052.seq

bc50ed9c270dddb6dccb3e4a28cee994

A012053

tan(sin(arctanh(x)))=x+3/3!*x^3+41/5!*x^5+1187/7!*x^7+54449/9!*x^9...

[ "1", "3", "41", "1187", "54449", "3092867", "95391193", "-48911197853", "-28872742806559", "-14158572958744829", "-7331436852140378359", "-4214348760692049240797", "-2723345361371865447323759", "-1980230597926036207884317053" ]

[ "sign" ]

6

0

2

null

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

2012-09-25T17:40:40

oeisdata/seq/A012/A012053.seq

b56de3bd109eafebbdc67dc0c0a3091c

A012054

arctan(sin(arctanh(x)))=x-1/3!*x^3+9/5!*x^5-225/7!*x^7+3345/9!*x^9...

[ "1", "-1", "9", "-225", "3345", "-893025", "-36212775", "-20892252225", "-3614048241375", "-1664630362370625", "-584598534985164375", "-327627617091486830625", "-181787523574523506599375", "-131875411531849225343390625" ]

[ "sign" ]

8

0

3

null

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

2013-01-23T17:20:34

oeisdata/seq/A012/A012054.seq

524d698e95d92c3375211b43a36cd1c9

A012055

cos(sin(arctanh(x)))=1-1/2!*x^2-3/4!*x^4-21/6!*x^6+185/8!*x^8...

[ "1", "-1", "-3", "-21", "185", "67159", "11805621", "2380474563", "591392066161", "181472052075695", "68002767860495981", "30687549807072450459", "16452262725440109947177", "10350119384788050029211399" ]

[ "sign" ]

6

0

3

null

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

2017-07-04T12:11:03

oeisdata/seq/A012/A012055.seq

e87e3994287250af0e83dff443b7b00c

A012056

sinh(sin(arctanh(x)))=x+2/3!*x^3+16/5!*x^5+216/7!*x^7-1280/9!*x^9...

[ "1", "2", "16", "216", "-1280", "-1141504", "-263392128", "-64804059904", "-18858549039104", "-6592583427379200", "-2757743938862710784", "-1367930584522073079808", "-796483574916192660455424", "-539009967859883250211815424" ]

[ "sign" ]

6

0

2

null

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

2018-04-29T17:16:32

oeisdata/seq/A012/A012056.seq

ac5ad828cf515cd632d36af00cd9a23f

A012057

arcsinh(sin(arctanh(x)))=x+4/5!*x^5-80/7!*x^7-3440/9!*x^9-764800/11!*x^11...

[ "1", "0", "4", "-80", "-3440", "-764800", "-107953600", "-25833184000", "-6745073504000", "-2368021859840000", "-968030415297920000", "-487629248007416320000", "-285882353240737277440000", "-197729299896592542208000000" ]

[ "sign" ]

7

0

3

null

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

2015-02-03T08:27:17

oeisdata/seq/A012/A012057.seq

af07eaf7dd8d4a5165e6cd1b4a5deb89

A012058

tanh(sin(arctanh(x)))=x-1/3!*x^3+1/5!*x^5-57/7!*x^7-3167/9!*x^9...

[ "1", "-1", "1", "-57", "-3167", "-362737", "-56653791", "-11948396137", "-3257340575039", "-1115453379837153", "-468755833785218879", "-237209057387611844761", "-142289210803187916748959", "-99838786688751535495417297" ]

[ "sign" ]

4

0

4

null

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

2012-02-24T12:50:39

oeisdata/seq/A012/A012058.seq

08d9b73a2d0ef8272d5f52c532267ef2

A012059

arctanh(sin(arctanh(x))) = x + (3/3!)*x^3 + (49/5!)*x^5 + (1915/7!)*x^7 + (136225/9!)*x^9 + ...

[ "1", "3", "49", "1915", "136225", "15321875", "2499086225", "557414129675", "162944338818625", "60444849108947875", "27742201644414960625", "15435312024168291246875", "10237075067482444345750625", "7979873933940396519383421875" ]

[ "nonn" ]

10

0

2

null

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

2018-08-17T16:20:25

oeisdata/seq/A012/A012059.seq

10484dac4233cd3734df3191ebb51f85

A012060

cosh(sin(arctanh(x)))=1+1/2!*x^2+5/4!*x^4+61/6!*x^6+937/8!*x^8...

[ "1", "1", "5", "61", "937", "-34919", "-13257619", "-3269873515", "-890367567919", "-286428853272143", "-109915623105978539", "-50081947723080008339", "-26861824093922170259335", "-16800404374717805427318199" ]

[ "sign" ]

6

0

3

null

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

2021-07-09T13:56:47

oeisdata/seq/A012/A012060.seq

38fc3b6c681311c0f29510c38b5436d9

A012061

sec(sin(arctanh(x)))=1+1/2!*x^2+9/4!*x^4+201/6!*x^6+7921/8!*x^8...

[ "1", "1", "9", "201", "7921", "447281", "28121145", "230243001", "-940995291295", "-539358796035359", "-280768914546419735", "-156059839698555664599", "-96215805882840361663151", "-66431831409927100446899439" ]

[ "sign" ]

6

0

3

null

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

2021-09-24T17:03:46

oeisdata/seq/A012/A012061.seq

c16fe6e87728b48978311b7c514f0d32

A012062

sech(sin(arctanh(x)))=1-1/2!*x^2+1/4!*x^4-1/6!*x^6+449/8!*x^8...

[ "1", "-1", "1", "-1", "449", "45119", "6456385", "1205597119", "290952557185", "88525830844799", "33241403103347585", "15120239602445366399", "8199386238595549354561", "5228782379279703730965439", "3875091407041220683147290049" ]

[ "sign" ]

6

0

5

null

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

2013-09-15T13:29:08

oeisdata/seq/A012/A012062.seq

141e9076df1eb94603219544cc993d37

A012063

exp(arcsin(arcsin(x)))=1+x+1/2!*x^2+3/3!*x^3+9/4!*x^4+49/5!*x^5...

[ "1", "1", "1", "3", "9", "49", "249", "1963", "14129", "146017", "1362961", "17450227", "200409465", "3064381137", "41812246345", "744091967643", "11765081428705", "239039270010305", "4298599985014945", "98237724213189475", "1980239469431883625" ]

[ "nonn" ]

10

0

4

null

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

2013-11-21T12:46:00

oeisdata/seq/A012/A012063.seq

c5e919a7297b67d8d0ccddc629d4751f

A012064

arcsin(arcsin(arcsin(x)))=x+3/3!*x^3+57/5!*x^5+2747/7!*x^7+249777/9!*x^9...

[ "1", "3", "57", "2747", "249777", "36846835", "8040193769", "2437436057131", "981033890934369", "506479242594080227", "326455632550618599065", "257043518901496857566107", "242838347551317678123524113" ]

[ "nonn" ]

6

0

2

null

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

2019-03-06T11:23:25

oeisdata/seq/A012/A012064.seq

d4a9922ef915060d34e8e1a2de2e08a1

A012065

Expansion of e.g.f. tan(arcsin(arcsin(x))).

[ "1", "4", "84", "4152", "370128", "51861888", "10494283968", "2894815734912", "1043916757274880", "476720372375608320", "268870416029396075520", "183537887154798761809920", "149132786692921038502318080", "142236877875834944842378444800", "157352707306190456257327051161600" ]

[ "nonn" ]

23

0

2

null

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

2025-04-17T01:55:57

oeisdata/seq/A012/A012065.seq

fd8e43f638f701fb9614ca529efb7ceb

A012066

arctan(arcsin(arcsin(x)))=x+12/5!*x^5+248/7!*x^7+21648/9!*x^9...

[ "1", "0", "12", "248", "21648", "2241088", "390536000", "91111189120", "28811937609984", "11657540060256256", "5912796798580972544", "3665610214092467574784", "2729315998404117133692928", "2402622277659457905178820608" ]

[ "nonn" ]

7

0

3

null

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

2013-11-21T12:46:00

oeisdata/seq/A012/A012066.seq

269da2c66d5d008402dc980ea224dcd5

A012067

cos(arcsin(arcsin(x)))=1-1/2!*x^2-7/4!*x^4-169/6!*x^6-8751/8!*x^8...

[ "1", "-1", "-7", "-169", "-8751", "-789681", "-110381943", "-22142611737", "-6041067843807", "-2153812782224097", "-972958293249140583", "-543350342541113761545", "-367659108914973687690255", "-296447255926407313341954705" ]

[ "sign" ]

6

0

3

null

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

2020-08-21T15:14:13

oeisdata/seq/A012/A012067.seq

41f3640dd14092ad9a35db3aaee79ff8

A012068

sinh(arcsin(arcsin(x)))=x+3/3!*x^3+49/5!*x^5+1963/7!*x^7+146017/9!*x^9...

[ "1", "3", "49", "1963", "146017", "17450227", "3064381137", "744091967643", "239039270010305", "98237724213189475", "50300088100727103345", "31409480786365735560715", "23501653583412713065987105", "20761459048626350764508502355" ]

[ "nonn" ]

4

0

2

null

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

2012-02-24T12:50:39

oeisdata/seq/A012/A012068.seq

a7d17c15d1a4ce8a430d4cb615867e2b

A012069

arcsinh(arcsin(arcsin(x)))=x+1/3!*x^3+17/5!*x^5+561/7!*x^7+39521/9!*x^9...

[ "1", "1", "17", "561", "39521", "4429217", "749371633", "176540328017", "55517224330689", "22448523976439873", "11356291769744087761", "7026618486154627990385", "5220988665867670545052193", "4587518335717939527563335649" ]

[ "nonn" ]

6

0

3

null

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

2012-12-06T09:02:35

oeisdata/seq/A012/A012069.seq

1e7a6ee7448435b84b2c7a8108ebabd8

A012070

tanh(arcsin(arcsin(x)))=x+4/5!*x^5+136/7!*x^7+9424/9!*x^9...

[ "1", "0", "4", "136", "9424", "1075264", "183697344", "43928797056", "14007826346240", "5742582570096640", "2941974233347077120", "1841370038568483235840", "1382314169497713897656320", "1225713884449600233499770880" ]

[ "nonn" ]

6

0

3

null

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

2015-02-12T11:37:52

oeisdata/seq/A012/A012070.seq

e29584dba66f5207974d2ac07e66325d

A012071

arctanh(arcsin(arcsin(x)))=x+4/3!*x^3+92/5!*x^5+5160/7!*x^7+532880/9!*x^9...

[ "1", "4", "92", "5160", "532880", "87726464", "21073486912", "6956206790528", "3020988238174464", "1670080968001854464", "1145224829994344492032", "953987340413779610175488", "948917210079076407043002368" ]

[ "nonn" ]

6

0

2

null

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

2015-02-05T11:44:15

oeisdata/seq/A012/A012071.seq

37470713d191a1b4c531c6ec36a01438

A012072

cosh(arcsin(arcsin(x)))=1+1/2!*x^2+9/4!*x^4+249/6!*x^6+14129/8!*x^8...

[ "1", "1", "9", "249", "14129", "1362961", "200409465", "41812246345", "11765081428705", "4298599985014945", "1980239469431883625", "1123437678322006300185", "769950079011855688807185", "627326819278687159338591665" ]

[ "nonn" ]

4

0

3

null

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

2012-02-24T12:50:39

oeisdata/seq/A012/A012072.seq

81e5b99dd2c5e26f42d70ea7a178d78e

A012073

sec(arcsin(arcsin(x)))=1+1/2!*x^2+13/4!*x^4+469/6!*x^6+32985/8!*x^8...

[ "1", "1", "13", "469", "32985", "3818601", "658371429", "158197312701", "50529852678321", "20707179214389201", "10591085815045781949", "6613325759240221954725", "4951199941339632477906825", "4377912560491798717856660025" ]

[ "nonn" ]

4

0

3

null

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

2012-02-24T12:50:39

oeisdata/seq/A012/A012073.seq

2585eaf7106dc2f28737c0b3c9cac675

A012074

sech(arcsin(arcsin(x)))=1-1/2!*x^2-3/4!*x^4-69/6!*x^6-3335/8!*x^8...

[ "1", "-1", "-3", "-69", "-3335", "-289801", "-39612939", "-7845054541", "-2125704833551", "-755532171928081", "-341044077485199379", "-190581499954444336725", "-129146418452087275163415", "-104328785204254369631603225" ]

[ "sign" ]

7

0

3

null

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

2013-11-21T12:46:00

oeisdata/seq/A012/A012074.seq

a2610251be67835ed44c90e169e2d04f

A012075

Expansion of e.g.f.: exp(arcsin(tan(x)))=1+x+1/2!*x^2+4/3!*x^3+13/4!*x^4+76/5!*x^5...

[ "1", "1", "1", "4", "13", "76", "421", "3424", "26713", "285136", "2871241", "38302144", "473357413", "7603381696", "111506036461", "2097552753664", "35624155784113", "768471264000256", "14838126699784081", "361133162545705984" ]

[ "nonn" ]

6

0

4

null

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

2017-12-12T16:09:22

oeisdata/seq/A012/A012075.seq

4233945b57d03ec17235ffa03e605546

A012076

arcsin(arcsin(tan(x)))=x+4/3!*x^3+84/5!*x^5+4488/7!*x^7+458448/9!*x^9...

[ "1", "4", "84", "4488", "458448", "76530048", "18958160064", "6533187385728", "2990371546714368", "1755799654033628160", "1286962755283219153920", "1152156355072706267179008", "1237421224352190570236497920" ]

[ "nonn" ]

4

0

2

null

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

2012-02-24T12:50:39

oeisdata/seq/A012/A012076.seq

30aad21aee22d02544d49bf8e79fcfb0

A012077

tan(arcsin(tan(x))) = x+5/3!*x^3+121/5!*x^5+6845/7!*x^7+698161/9!*x^9...

[ "1", "5", "121", "6845", "698161", "111973685", "25947503401", "8200346492525", "3389281372287841", "1774459993676715365", "1147649139272698443481", "898537335398420151634205", "837511978485668107020082321" ]

[ "nonn" ]

26

0

2

null

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

2017-05-13T23:58:22

oeisdata/seq/A012/A012077.seq

ec244aef4bbb85f5c12a38b601eeb968

A012078

arctan(arcsin(tan(x)))=x+1/3!*x^3+9/5!*x^5+393/7!*x^7+33009/9!*x^9...

[ "1", "1", "9", "393", "33009", "4410033", "872617017", "240500373753", "88094910348129", "41401437242599905", "24287046275803547625", "17396048031084882189033", "14941352753081733849348945", "15157924050230673397966293393" ]

[ "nonn" ]

6

0

3

null

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

2021-05-07T17:02:40

oeisdata/seq/A012/A012078.seq

7a6042c1b42a2fdea7107fc916c12767

A012079

cos(arcsin(tan(x)))=1-1/2!*x^2-11/4!*x^4-301/6!*x^6-16631/8!*x^8...

[ "1", "-1", "-11", "-301", "-16631", "-1620601", "-250557251", "-56629836901", "-17602836565871", "-7193368568377201", "-3735581618747946491", "-2401310609311293289501", "-1871136400199563216523111" ]

[ "sign" ]

17

0

3

[ "A012079", "A012253" ]

null

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

2024-10-31T22:34:58

oeisdata/seq/A012/A012079.seq

97e28c318b6a9e54535ecf02912bb7f1

A012080

E.g.f.: sinh(arcsin(tan(x)))=x+4/3!*x^3+76/5!*x^5+3424/7!*x^7+285136/9!*x^9...

[ "1", "4", "76", "3424", "285136", "38302144", "7603381696", "2097552753664", "768471264000256", "361133162545705984", "211820037816772258816", "151696192774576615727104", "130270853179191716758245376" ]

[ "nonn" ]

6

0

2

null

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

2012-05-24T12:23:06

oeisdata/seq/A012/A012080.seq

73fd9245cc79612089ac24cf00c8cd99

A012081

arcsinh(arcsin(tan(x)))=x+2/3!*x^3+24/5!*x^5+888/7!*x^7+68352/9!*x^9...

[ "1", "2", "24", "888", "68352", "8853888", "1724221056", "470304668928", "171029448056832", "79950698284462080", "46709069479002931200", "33347332565041919950848", "28565775294718770340331520", "28915860353300526164581613568" ]

[ "nonn" ]

4

0

2

null

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

2012-02-24T12:50:40

oeisdata/seq/A012/A012081.seq

a40713bb2b9a2a0d066804c9b2368d31

A012082

tanh(arcsin(tan(x)))=x+1/3!*x^3+1/5!*x^5+1/7!*x^7+7681/9!*x^9...

[ "1", "1", "1", "1", "7681", "1689601", "390274561", "113644876801", "42729427952641", "20428848924057601", "12142755781873873921", "8789483754515321088001", "7614001483915573936550401", "7778864404689826961021184001" ]

[ "nonn" ]

4

0

5

null

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

2012-02-24T12:50:40

oeisdata/seq/A012/A012082.seq

ac62ad9acbf915adc5faebf7c87c6ea2

A012083

arctanh(arcsin(tan(x)))=x+5/3!*x^3+129/5!*x^5+8133/7!*x^7+949281/9!*x^9...

[ "1", "5", "129", "8133", "949281", "177127653", "48290752353", "18102997908453", "8931245615625921", "5609823664317348165", "4370983985597526359745", "4137308650120582099800453", "4676183786000402886175691745" ]

[ "nonn" ]

8

0

2

null

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

2015-02-05T11:49:32

oeisdata/seq/A012/A012083.seq

d403a418e8b2644f8b3b1aae646e040a

A012084

cosh(arcsin(tan(x)))=1+1/2!*x^2+13/4!*x^4+421/6!*x^6+26713/8!*x^8...

[ "1", "1", "13", "421", "26713", "2871241", "473357413", "111506036461", "35624155784113", "14838126699784081", "7813931867856058813", "5076900281143623362101", "3989607021222775392853513", "3730016905780866035656178521" ]

[ "nonn" ]

4

0

3

null

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

2012-02-24T12:50:40

oeisdata/seq/A012/A012084.seq

8a976112836ce405145b0e14322a0332

A012085

Even coefficients in expansion of e.g.f. cos(x)/sqrt(cos(2*x)).

[ "1", "1", "17", "721", "58337", "7734241", "1526099057", "419784870961", "153563504618177", "72104198836466881", "42270463533824671697", "30262124466958766778001", "25981973075048213029395617", "26350476755161831091778460321" ]

[ "nonn" ]

20

0

3

null

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

2023-10-02T13:48:30

oeisdata/seq/A012/A012085.seq

0e5b22dc0922693a46777e449939560e

A012086

sech(arcsin(tan(x)))=1-1/2!*x^2-7/4!*x^4-121/6!*x^6-5167/8!*x^8...

[ "1", "-1", "-7", "-121", "-5167", "-487441", "-78804727", "-18558463561", "-5919443326687", "-2457116797560481", "-1289150916753299047", "-834798631079038210201", "-654139310316332313889807", "-610085118687493622960844721" ]

[ "sign" ]

6

0

3

null

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

2023-09-17T15:25:41

oeisdata/seq/A012/A012086.seq

5720c0363c97873f7e622befe4eee231

A012087

Expansion of e.g.f.: exp(arcsin(arctan(x)))=1+x+1/2!*x^2-3/4!*x^4+4/5!*x^5+69/6!*x^6...

[ "1", "1", "1", "0", "-3", "4", "69", "-32", "-2503", "1936", "177481", "-67328", "-18539595", "4140096", "2813939725", "353591808", "-573509386895", "-262064131840", "152349815266705", "130347373404160", "-50966873710838675", "-65058714844462080" ]

[ "sign" ]

6

0

5

null

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

2018-05-27T10:56:54

oeisdata/seq/A012/A012087.seq

c53d1e1f741d7f97d564f3e57c451485

A012088

arcsin(arcsin(arctan(x)))=x+12/5!*x^5-88/7!*x^7+13968/9!*x^9...

[ "1", "0", "12", "-88", "13968", "-597440", "132709184", "-15685157504", "5014687029504", "-1181425359497216", "528315488687774720", "-207409825492284028928", "125603683629593633394688", "-73594034552724198387236864" ]

[ "sign" ]

6

0

3

null

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

2021-06-30T18:24:52

oeisdata/seq/A012/A012088.seq

ac3b4993d6880865b3710fda09b870ea

A012089

tan(arcsin(arctan(x)))=x+1/3!*x^3+9/5!*x^5+57/7!*x^7+5169/9!*x^9...

[ "1", "1", "9", "57", "5169", "-93807", "31981689", "-3857766903", "1058896281825", "-286891166986335", "108826313005021545", "-47766338018402914215", "25721485923005221938705", "-16179153687877979599066575" ]

[ "sign" ]

12

0

3

null

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

2024-11-17T16:10:46

oeisdata/seq/A012/A012089.seq

f0b95401404e9daab3f9b3c197f34596

A012090

arctan(arcsin(arctan(x))) = x - 3/3!*x^3 + 57/5!*x^5 - 2587/7!*x^7 + 217137/9!*x^9 - ...

[ "1", "-3", "57", "-2587", "217137", "-29025587", "5664605801", "-1519556355275", "536514935904609", "-241225069255390307", "134580033555427233689", "-91237165395466088195963", "73877505225687035803070353", "-70425423338543411535873624467", "78071169657855750497737512497097" ]

[ "sign" ]

8

0

2

null

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

2018-01-15T15:01:25

oeisdata/seq/A012/A012090.seq

f23e25166ab9ec0a83fd671a6d542381

A012091

cos(arcsin(arctan(x)))=1-1/2!*x^2+5/4!*x^4-109/6!*x^6+4521/8!*x^8...

[ "1", "-1", "5", "-109", "4521", "-330681", "36468717", "-5721101541", "1205289090513", "-328897528901361", "112769846051251797", "-47472161654530776285", "24068680135210975714425", "-14466929567049590650593705" ]

[ "sign" ]

14

0

3

[ "A012091", "A012254" ]

null

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

2024-10-31T22:28:48

oeisdata/seq/A012/A012091.seq

f3dd980a7eb89518dde9b7dfd50c582b

A012092

sinh(arcsin(arctan(x)))=x+4/5!*x^5-32/7!*x^7+1936/9!*x^9-67328/11!*x^11...

[ "1", "0", "4", "-32", "1936", "-67328", "4140096", "353591808", "-262064131840", "130347373404160", "-65058714844462080", "36397620373403361280", "-23130160076947953643520", "16791590408623398030868480" ]

[ "sign" ]

6

0

3

null

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

2016-03-12T14:34:37

oeisdata/seq/A012/A012092.seq

9dc107b735c9789be5e79d0908605b3e

A012093

arcsinh(arcsin(arctan(x)))=x-2/3!*x^3+32/5!*x^5-1224/7!*x^7+89984/9!*x^9...

[ "1", "-2", "32", "-1224", "89984", "-10705408", "1889967232", "-464238999808", "151661217091584", "-63641246944645120", "33381024310383640576", "-21408234533329528127488", "16485197581627921671815168" ]

[ "sign" ]

6

0

2

null

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

2025-06-02T14:22:50

oeisdata/seq/A012/A012093.seq

150561134c4e06dbb61dcf402f2dfe4b

A012094

E.g.f.: tanh(arcsin(arctan(x))), odd powers only.

[ "1", "-3", "49", "-1859", "127297", "-13662371", "2114110257", "-445110767139", "122308548673025", "-42491524107649475", "18204849127687565745", "-9427087716053634833795", "5803356448065850202170945", "-4188507975000626549209008995", "3502566426777342320289454951345" ]

[ "sign" ]

23

0

2

null

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

2018-02-15T15:38:36

oeisdata/seq/A012/A012094.seq

9a4c93dc142c5f98220ec791be78cff5

A012095

arctanh(arcsin(arctan(x))) = x + 1/3!*x^3 + 17/5!*x^5 + 225/7!*x^7 + 19745/9!*x^9 + ...

[ "1", "1", "17", "225", "19745", "613889", "165999025", "6543673313", "5318503266369", "97941778159361", "473023280425720657", "-24807619116269601823", "96456947558141320688993", "-18191159887705677530042623", "39579539155416746718880624881", "-15661645517509146973335115013919" ]

[ "sign" ]

8

0

3

null

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

2018-01-15T15:03:26

oeisdata/seq/A012/A012095.seq

d8b33038971d9810403c9673558b042e

A012096

cosh(arcsin(arctan(x)))=1+1/2!*x^2-3/4!*x^4+69/6!*x^6-2503/8!*x^8...

[ "1", "1", "-3", "69", "-2503", "177481", "-18539595", "2813939725", "-573509386895", "152349815266705", "-50966873710838675", "20993994712780457685", "-10435138367654204994135", "6159973489221376775016665" ]

[ "sign" ]

4

0

3

null

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

2012-02-24T12:50:40

oeisdata/seq/A012/A012096.seq

18dcb0c0b0ff109ed950456c8c2b11c4

A012097

sec(arcsin(arctan(x)))=1+1/2!*x^2+1/4!*x^4+49/6!*x^6-447/8!*x^8...

[ "1", "1", "1", "49", "-447", "78561", "-5655231", "1014069393", "-187639949439", "51144433721793", "-16631972691697791", "6837287119716744945", "-3357388632038371909695", "1969419543279480607781025" ]

[ "sign" ]

6

0

4

null

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

2019-11-28T15:06:59

oeisdata/seq/A012/A012097.seq

7eee9a8d9ce5227ef7e21722ad84f436

A012098

sech(arcsin(arctan(x)))=1-1/2!*x^2+9/4!*x^4-249/6!*x^6+13297/8!*x^8...

[ "1", "-1", "9", "-249", "13297", "-1175761", "154625721", "-28328562313", "6890453792609", "-2147692998841633", "834418870682339561", "-395288520944694504345", "224249503561141591847505", "-150078278389547160573482225" ]

[ "sign" ]

6

0

3

null

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

2019-10-26T16:45:55

oeisdata/seq/A012/A012098.seq

ef8d63473e7fbd0ceb18cc5a2f02eccb

A012099

Expansion of e.g.f.: exp(arcsin(sinh(x)))=1+x+1/2!*x^2+3/3!*x^3+9/4!*x^4+41/5!*x^5...

[ "1", "1", "1", "3", "9", "41", "201", "1403", "9649", "90641", "809201", "9578803", "105268089", "1504717241", "19650225401", "329275068203", "4982657935329", "95780865239841", "1648151554792801", "35749976635509603", "689411371817131369" ]

[ "nonn" ]

8

0

4

null

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

2024-04-21T10:46:46

oeisdata/seq/A012/A012099.seq

27ebbfd5624eeee4b2d6e07f05bb80eb

A012100

arcsin(arcsin(sinh(x)))=x+3/3!*x^3+49/5!*x^5+2187/7!*x^7+186337/9!*x^9...

[ "1", "3", "49", "2187", "186337", "25929907", "5355694161", "1539910627387", "588565856592577", "288782211525088995", "176996414128700874865", "132567145102215208555627", "119162444909413724755024545" ]

[ "nonn" ]

4

0

2

null

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

2012-02-24T12:50:40

oeisdata/seq/A012/A012100.seq

4bc6756d5d8f45eda866b4c12b8e9b1a