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
A012201	cosh(arctan(arcsin(x)))=1+1/2!x^2-3/4!x^4+69/6!x^6-1159/8!x^8...	[ "1", "1", "-3", "69", "-1159", "115081", "-3250827", "1156388557", "-12628752143", "42394317198097", "2830775181039853", "4335882574518729045", "967557162609958010985", "1031578849176135526526105" ]	[ "sign" ]	6	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2020-08-26T14:48:02	oeisdata/seq/A012/A012201.seq	ab64d2c92bedd5bea6441e4d4a3a6e6c
A012202	sech(arctan(arcsin(x)))=1-1/2!x^2+9/4!x^4-249/6!x^6+11953/8!x^8...	[ "1", "-1", "9", "-249", "11953", "-992401", "115133433", "-19289685193", "4104153335777", "-1154213252748193", "390283459641717353", "-165544701587974757145", "81456402896849322863505", "-48584594120969426596224305" ]	[ "sign" ]	6	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2018-04-08T21:20:56	oeisdata/seq/A012/A012202.seq	78219b33866b03eedbffad857d445e64
A012203	E.g.f.: exp(arctan(arctan(x))) = 1+x+1/2!x^2-3/3!x^3-15/4!x^4+49/5!x^5...	[ "1", "1", "1", "-3", "-15", "49", "609", "-1859", "-48031", "119617", "6247681", "-10283171", "-1214813487", "678311217", "330587407201", "246695568861", "-120086685689663", "-270153706006015", "56186566871496961", "221300400903581245" ]	[ "sign" ]	11	0	4	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2014-08-15T03:18:10	oeisdata/seq/A012/A012203.seq	2b69f18d2595ec472a14a3c37e070d8f
A012204	arcsin(arctan(arctan(x)))=x-3/3!x^3+57/5!x^5-2755/7!x^7+251601/9!x^9...	[ "1", "-3", "57", "-2755", "251601", "-37281923", "8163849353", "-2479580033411", "997801392400929", "-513852593272870403", "329599574990913085529", "-257652341842242812773955", "241116753509976748759134193" ]	[ "sign" ]	6	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2016-11-28T17:43:54	oeisdata/seq/A012/A012204.seq	9d8736241d255df56e6e80c8863dbc0c
A012205	arctan(arctan(arctan(x)))=x-6/3!x^3+192/5!x^5-14704/7!*x^7...	[ "1", "-6", "192", "-14704", "2058624", "-457982720", "148443124736", "-66066559066112", "38672430452342784", "-28812765976119148544", "26627757204719641296896", "-29895731887419723149213696", "40082507396600200285753704448" ]	[ "sign" ]	6	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2016-11-28T17:45:48	oeisdata/seq/A012/A012205.seq	df1f2e8c1034f75a211e77064b55ad6d
A012206	sinh(arctan(arctan(x)))=x-3/3!x^3+49/5!x^5-1859/7!x^7+119617/9!x^9...	[ "1", "-3", "49", "-1859", "119617", "-10283171", "678311217", "246695568861", "-270153706006015", "221300400903581245", "-191103844337252819535", "185242544952868387351165", "-204711474044267911803243455" ]	[ "sign" ]	6	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2016-11-28T17:47:46	oeisdata/seq/A012/A012206.seq	af3242a68b53776487495779c2e1baa9
A012207	arcsinh(arctan(arctan(x)))=x-5/3!x^3+137/5!x^5-9141/7!*x^7...	[ "1", "-5", "137", "-9141", "1130993", "-225155941", "66037540345", "-26862446793685", "14500070037397089", "-10041538909269213637", "8686453887771982767337", "-9185311291945403768547829", "11662015255583014905028727633" ]	[ "sign" ]	6	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2013-07-16T16:02:51	oeisdata/seq/A012/A012207.seq	46b7d49bcef5928d32f2eb17d4e7e5dc
A012208	tanh(arctan(arctan(x)))=x-6/3!x^3+184/5!x^5-13136/7!*x^7...	[ "1", "-6", "184", "-13136", "1679488", "-335723264", "96492653568", "-37665610561536", "19158060131778560", "-12304193595906129920", "9734505561510299566080", "-9299736312230986726768640", "10553185490408007072659537920" ]	[ "sign" ]	6	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2014-11-15T17:34:25	oeisdata/seq/A012/A012208.seq	c9019e09c2f62dfbe135dcef77061c2f
A012209	arctanh(arctan(arctan(x)))=x-2/3!x^3+32/5!x^5-1392/7!x^7+118400/9!x^9...	[ "1", "-2", "32", "-1392", "118400", "-16678144", "3517084672", "-1037502889984", "407811782836224", "-205957880207835136", "129921324821854289920", "-100089923129501690626048", "92456928301505596639674368" ]	[ "sign" ]	6	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2016-11-28T17:51:28	oeisdata/seq/A012/A012209.seq	d193edc8b02b85b63f4112dc697f0065
A012210	cosh(arctan(arctan(x)))=1+1/2!x^2-15/4!x^4+609/6!x^6-48031/8!x^8...	[ "1", "1", "-15", "609", "-48031", "6247681", "-1214813487", "330587407201", "-120086685689663", "56186566871496961", "-32929237073496552527", "23637878950680710828385", "-20404361373477159717443295" ]	[ "sign" ]	6	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2016-11-28T17:53:24	oeisdata/seq/A012/A012210.seq	27656fe9d8695d8a23c801a1c0b5eb39
A012211	sech(arctan(arctan(x)))=1-1/2!x^2+21/4!x^4-1149/6!x^6+119305/8!x^8...	[ "1", "-1", "21", "-1149", "119305", "-20082841", "4984310493", "-1711500674389", "776816116717457", "-450301381427975089", "324553968807761095973", "-284661632752853556677805", "298518404617173649259722905" ]	[ "sign" ]	6	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2016-11-28T17:54:34	oeisdata/seq/A012/A012211.seq	5f99add3ead5b640ac87167e327d6f52
A012212	Number of squarefree palindromes over {0, 1, 2} of length 2n+1.	[ "3", "6", "6", "12", "12", "12", "12", "18", "18", "24", "36", "48", "60", "84", "102", "138", "186", "246", "306", "378", "486", "630", "816", "1050", "1350", "1782", "2328", "2988", "3870", "5076", "6624", "8616", "11112", "14454", "18882", "24630", "31944", "41442", "53988", "70422", "91614", "119046", "154896", "201834", "262824", "341688" ]	[ "nonn", "base" ]	16	0	1	[ "A006156", "A012212" ]	null	Jeffrey Shallit	2018-08-27T16:28:41	oeisdata/seq/A012/A012212.seq	cdb404120e7a5698d2571db4a740a14c
A012213	exp(arctan(arcsinh(x)))=1+x+1/2!x^2-2/3!x^3-11/4!x^4+24/5!x^5...	[ "1", "1", "1", "-2", "-11", "24", "349", "-664", "-22007", "28416", "2312601", "-942336", "-365164227", "-260697984", "80916522933", "165900454656", "-23968582079343", "-85943912448000", "9151870592718513", "48584004553543680", "-4378918837383018747" ]	[ "sign" ]	4	0	4	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:44	oeisdata/seq/A012/A012213.seq	2a28f952545ab308273a4f67b482c8ca
A012214	arcsin(arctan(arcsinh(x)))=x-2/3!x^3+32/5!x^5-1280/7!x^7+96896/9!x^9...	[ "1", "-2", "32", "-1280", "96896", "-11867008", "2142673920", "-535571951616", "177110831202304", "-74879716881661952", "39403647907518971904", "-25258353322454300164096", "19376893280575897343623168" ]	[ "sign" ]	4	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:44	oeisdata/seq/A012/A012214.seq	2a259dc180a60da5a28714901c67a9c8
A012215	arctan(arctan(arcsinh(x)))=x-5/3!x^3+137/5!x^5-9029/7!*x^7...	[ "1", "-5", "137", "-9029", "1089713", "-209177605", "58539026361", "-22507046465157", "11386223123252449", "-7334290106238920453", "5861710212500532385641", "-5692596379677558396424645", "6602985113623111671589590673" ]	[ "sign" ]	7	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-10-20T16:04:35	oeisdata/seq/A012/A012215.seq	1af0921aad8008a470140975fc8bbc40
A012216	sinh(arctan(arcsinh(x)))=x-2/3!x^3+24/5!x^5-664/7!x^7+28416/9!x^9...	[ "1", "-2", "24", "-664", "28416", "-942336", "-260697984", "165900454656", "-85943912448000", "48584004553543680", "-31574321393019125760", "23832746038658540666880", "-20858343927838973179822080", "21048655959583804491297914880" ]	[ "sign" ]	8	0	2	[ "A012213", "A012216" ]	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2024-10-04T11:28:17	oeisdata/seq/A012/A012216.seq	35749cc4c86a7981bd1c2b0345170482
A012217	arcsinh(arctan(arcsinh(x)))=x-4/3!x^3+92/5!x^5-5216/7!*x^7...	[ "1", "-4", "92", "-5216", "551504", "-94170176", "23756009664", "-8329952294400", "3882725102061824", "-2324928136769545216", "1740643970081187412992", "-1594058498088175066406912", "1753510369493317462917828608" ]	[ "sign" ]	6	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2013-03-10T15:53:31	oeisdata/seq/A012/A012217.seq	20ea46870a2b12c4d7992f6231f7344d
A012218	tanh(arctan(arcsinh(x)))=x-5/3!x^3+129/5!x^5-7741/7!*x^7...	[ "1", "-5", "129", "-7741", "830529", "-139115349", "33466193409", "-10924199283981", "4643317555286145", "-2490727724722757925", "1645111995753399461505", "-1311624218654589461390685", "1241813393715548870981284545" ]	[ "sign" ]	4	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:44	oeisdata/seq/A012/A012218.seq	ddcec7a6ed6697d5d3a5ae45c6b1a788
A012219	arctanh(arctan(arcsinh(x)))=x-1/3!x^3+17/5!x^5-617/7!x^7+44417/9!x^9...	[ "1", "-1", "17", "-617", "44417", "-5210129", "909126033", "-220910314809", "71341157623169", "-29556627270426145", "15282372258542389905", "-9645984260739983339273", "7298836347461102485422593", "-6521512480584315170326457393" ]	[ "sign" ]	6	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2016-11-28T17:57:52	oeisdata/seq/A012/A012219.seq	1560c4c057bfd8973edb6bc94230e848
A012220	cosh(arctan(arcsinh(x)))=1+1/2!x^2-11/4!x^4+349/6!x^6-22007/8!x^8...	[ "1", "1", "-11", "349", "-22007", "2312601", "-365164227", "80916522933", "-23968582079343", "9151870592718513", "-4378918837383018747", "2566828786036427906445", "-1809533477302236292739175", "1510703360292377534570508105" ]	[ "sign" ]	6	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2020-11-06T16:12:18	oeisdata/seq/A012/A012220.seq	8974768180a4a77c1b566a6883e09054
A012221	sech(arctan(arcsinh(x)))=1-1/2!x^2+17/4!x^4-769/6!x^6+66401/8!x^8...	[ "1", "-1", "17", "-769", "66401", "-9313281", "1927198833", "-551835917697", "208856369686977", "-100945109069282817", "60655475821737151953", "-44346899335054478649345", "38762487400695339770533665" ]	[ "sign" ]	4	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:44	oeisdata/seq/A012/A012221.seq	7713e6a3a53314cc5f23aa80c201080f
A012222	Expansion of e.g.f.: exp(arctan(tanh(x)))=1+x+1/2!x^2-3/3!x^3-15/4!x^4+41/5!x^5...	[ "1", "1", "1", "-3", "-15", "41", "561", "-1243", "-40415", "58001", "4825121", "-1956083", "-866056815", "-740509639", "218527875281", "509169335477", "-73838559553215", "-295854887910879", "32207514779999041", "189240977761969437" ]	[ "sign" ]	6	0	4	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2025-03-17T16:51:25	oeisdata/seq/A012/A012222.seq	eaab5e2ff339193600db62ac21bd5cd2
A012223	arcsin(arctan(tanh(x)))=x-3/3!x^3+49/5!x^5-2139/7!x^7+181921/9!x^9...	[ "1", "-3", "49", "-2139", "181921", "-25347539", "5231635473", "-1498270773419", "568381637171521", "-275844413823596835", "166680279670474243825", "-122705715387723016322939", "108112687783657068510670305" ]	[ "sign" ]	4	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:44	oeisdata/seq/A012/A012223.seq	aef087936bb2242e8b257a1a910298b7
A012224	arctan(arctan(tanh(x)))=x-6/3!x^3+184/5!x^5-13584/7!*x^7...	[ "1", "-6", "184", "-13584", "1840768", "-397140224", "124961670144", "-54024939321344", "30732245464219648", "-22258174840910315520", "20000813079319781048320", "-21837489688957057049821184", "28476242253811580631861166080" ]	[ "sign" ]	6	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2016-11-28T17:59:41	oeisdata/seq/A012/A012224.seq	d7da58d350eea39afddedbfa4eaa286a
A012225	sinh(arctan(tanh(x)))=x-3/3!x^3+41/5!x^5-1243/7!x^7+58001/9!x^9...	[ "1", "-3", "41", "-1243", "58001", "-1956083", "-740509639", "509169335477", "-295854887910879", "189240977761969437", "-139751997081117953719", "120179815628074668521797", "-120043777513489781645646159" ]	[ "sign" ]	4	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-02-24T12:50:44	oeisdata/seq/A012/A012225.seq	6d697e362d1200f8ee39c26e68f69a9d
A012226	arcsinh(arctan(tanh(x)))=x-5/3!x^3+129/5!x^5-8189/7!*x^7...	[ "1", "-5", "129", "-8189", "972609", "-186825429", "53036534017", "-20924521480269", "10970414196349569", "-7386311927549483045", "6216439933812148586625", "-6398271924540885631183389", "7909256594572491509610323905" ]	[ "sign" ]	6	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2019-08-24T10:22:13	oeisdata/seq/A012/A012226.seq	a9598866e4664ca55163d1c2e1b00514
A012227	tanh(arctan(tanh(x)))=x-6/3!x^3+176/5!x^5-12016/7!*x^7...	[ "1", "-6", "176", "-12016", "1469696", "-280971776", "77198422016", "-28793654081536", "13988424620507136", "-8578076577450295296", "6478101995566379565056", "-5906079803365219349037056", "6394716233788355978540875776" ]	[ "sign" ]	7	0	2	[ "A012227", "A101921" ]	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2018-12-08T19:37:13	oeisdata/seq/A012/A012227.seq	c5594dca78995cb16fcb1136d6a74c7f
A012228	arctanh(arctan(tanh(x)))=x-2/3!x^3+24/5!x^5-944/7!x^7+77952/9!x^9...	[ "1", "-2", "24", "-944", "77952", "-10623744", "2145104896", "-602082207744", "224357319278592", "-107165894175948800", "63836869263529082880", "-46390243522547859062784", "40392288941602607862906880" ]	[ "sign" ]	6	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2016-11-28T18:01:33	oeisdata/seq/A012/A012228.seq	b80c16bcb5ff2dfe0b91e3decb006baf
A012229	cosh(arctan(tanh(x)))=1+1/2!x^2-15/4!x^4+561/6!x^6-40415/8!x^8...	[ "1", "1", "-15", "561", "-40415", "4825121", "-866056815", "218527875281", "-73838559553215", "32207514779999041", "-17624680185473393615", "11826144583278421964401", "-9549876975469294700602015", "9137286945784401729622059361" ]	[ "sign" ]	6	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2019-03-11T17:56:59	oeisdata/seq/A012/A012229.seq	00685236bc6b2b9f37983e31ef7f864a
A012230	sech(arctan(tanh(x)))=1-1/2!x^2+21/4!x^4-1101/6!x^6+109001/8!x^8...	[ "1", "-1", "21", "-1101", "109001", "-17491001", "4139085981", "-1355308485701", "586612833746961", "-324261948714025201", "222851423174495787941", "-186365710421614910029501", "186332939048243649892744921" ]	[ "sign" ]	6	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2017-10-01T12:13:39	oeisdata/seq/A012/A012230.seq	233ea5d7be34e07ba9ad8a2775f0d0d1
A012231	exp(arctan(arctanh(x)))=1+x+1/2!x^2+1/3!x^3+1/4!x^4+9/5!x^5...	[ "1", "1", "1", "1", "1", "9", "49", "281", "1345", "13233", "105441", "1179729", "10336833", "144386553", "1580651409", "25501409961", "316289380737", "5869292202465", "83559601907649", "1744083324947745", "27709107620492673", "643531258862953065" ]	[ "nonn" ]	6	0	6	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2016-11-28T18:05:20	oeisdata/seq/A012/A012231.seq	80b6c879fd51a72100290a4ba86bcdaa
A012232	arcsin(arctan(arctanh(x)))=x+1/3!x^3+17/5!x^5+505/7!x^7+32321/9!x^9...	[ "1", "1", "17", "505", "32321", "3196337", "474305361", "96903709929", "26267702181889", "9102885308254561", "3930753230143374609", "2069316409758628885721", "1305070038882436410153793", "971558826878073011961325841" ]	[ "nonn" ]	6	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2016-11-28T18:07:01	oeisdata/seq/A012/A012232.seq	c4b9bf19cf311773e8d7d304f02094c4
A012233	arctan(arctan(arctanh(x)))=x-2/3!x^3+32/5!x^5-944/7!x^7+64640/9!x^9...	[ "1", "-2", "32", "-944", "64640", "-5881600", "919673856", "-172830523392", "48225099218944", "-15466881283850240", "6745794347282989056", "-3302151520495305490432", "2072514460288282576027648", "-1438958551527596730993344512" ]	[ "sign" ]	6	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2016-11-28T18:08:29	oeisdata/seq/A012/A012233.seq	5ca0782b1fe02733a59bc27ea3506514
A012234	sinh(arctan(arctanh(x)))=x+1/3!x^3+9/5!x^5+281/7!x^7+13233/9!x^9...	[ "1", "1", "9", "281", "13233", "1179729", "144386553", "25501409961", "5869292202465", "1744083324947745", "643531258862953065", "289976769842011018425", "156375721502624955046545", "99525811638120512862203505" ]	[ "nonn" ]	6	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2016-11-28T18:09:35	oeisdata/seq/A012/A012234.seq	822c53fe7ba4724dfa44c072cda4f287
A012235	E.g.f.: arcsinh(arctan(arctanh(x)))=x-1/3!x^3+17/5!x^5-281/7!x^7+24257/9!x^9...	[ "1", "-1", "17", "-281", "24257", "-1331441", "275798481", "-33388170825", "12274116245249", "-2689107736315873", "1507045832586910737", "-530866838718138680441", "415346005609060387325633", "-217242204344672574488013521" ]	[ "sign" ]	8	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2016-11-28T18:10:58	oeisdata/seq/A012/A012235.seq	b9a090d588955d7ddc41f46a22c04983
A012236	tanh(arctan(arctanh(x)))=x-2/3!x^3+24/5!x^5-496/7!x^7+24192/9!x^9...	[ "1", "-2", "24", "-496", "24192", "-1246464", "150408192", "-12132673536", "3380973895680", "-253363927449600", "217523969745223680", "4682388187242823680", "35388810383588767825920", "8821171867345211810119680" ]	[ "sign" ]	6	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2016-11-28T18:12:25	oeisdata/seq/A012/A012236.seq	1175dc725872d01d261c9321dfe8def6
A012237	arctanh(arctan(arctanh(x)))=x+2/3!x^3+32/5!x^5+1168/7!x^7+80768/9!x^9...	[ "1", "2", "32", "1168", "80768", "8855296", "1420471296", "312821661696", "90619729117184", "33397289918332928", "15260151754256547840", "8466388564521610903552", "5606464118961336397856768", "4368144479139164180218642432" ]	[ "nonn" ]	9	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2016-11-28T18:13:59	oeisdata/seq/A012/A012237.seq	037274944eb4f0aa933973740148c624
A012238	cosh(arctan(arctanh(x)))=1+1/2!x^2+1/4!x^4+49/6!x^6+1345/8!x^8...	[ "1", "1", "1", "49", "1345", "105441", "10336833", "1580651409", "316289380737", "83559601907649", "27709107620492673", "11345006679686949105", "5605389007592066373825", "3292126822668986935347105", "2265914784466771293436282305", "1806802766658673683522189272145" ]	[ "nonn" ]	8	0	4	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2015-03-02T17:41:09	oeisdata/seq/A012/A012238.seq	a4849383cf4e22bbec9b4163ff55eb6b
A012239	sech(arctan(arctanh(x)))=1-1/2!x^2+5/4!x^4-109/6!x^6+2729/8!x^8...	[ "1", "-1", "5", "-109", "2729", "-196281", "9832173", "-1827291621", "102520239057", "-58512018759921", "-121510420621227", "-5298654687807230685", "-895543588646311726215", "-1180050438628226991259305" ]	[ "sign" ]	8	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2016-11-28T18:16:20	oeisdata/seq/A012/A012239.seq	759f64ff0f61f98a520f92ff1c9a60cb
A012240	-log(cos(tan(x)))=1/2!x^2+10/4!x^4+232/6!x^6+10064/8!x^8...	[ "1", "10", "232", "10064", "720384", "78009600", "11977120768", "2480763381760", "666957211828224", "225809770695098368", "93981332166180077568", "47151835657444566499328", "28061010401657661222289408" ]	[ "nonn" ]	16	0	2	[ "A009329", "A009387", "A012240" ]	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2014-06-26T02:48:37	oeisdata/seq/A012/A012240.seq	398e91d3a51a4f2e0d6ff20ab1f0ed76
A012241	log(cos(arcsinh(x))) = -1/2!x^2+2/4!x^4-40/6!x^6+1360/8!x^8...	[ "-1", "2", "-40", "1360", "-87680", "8723200", "-1254323200", "245463296000", "-62768582656000", "20318491009024000", "-8121379360440320000", "3928322245164728320000", "-2261534088991670272000000" ]	[ "sign" ]	6	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2023-03-02T12:39:05	oeisdata/seq/A012/A012241.seq	e9ae001bfd4026153f2aa1c923dcde2d
A012242	log(cos(tanh(x)))=-1/2!x^2+6/4!x^4-72/6!x^6+1456/8!x^8...	[ "-1", "6", "-72", "1456", "-47104", "2390784", "-180612096", "18625189888", "-2431403622400", "384624656646144", "-72343735465672704", "16067422146130345984", "-4193787904779561730048", "1276366494840535652499456" ]	[ "sign" ]	6	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2014-05-27T11:08:04	oeisdata/seq/A012/A012242.seq	e5a5ed7a11bd45a61906663d48923fee
A012243	-log(cos(arctanh(x)))=1/2!x^2+10/4!x^4+280/6!x^6+15440/8!x^8...	[ "1", "10", "280", "15440", "1412480", "193606400", "37162777600", "9519986944000", "3139364220928000", "1295834618224640000", "654668849830461440000", "397456058751397068800000", "285567610965661253632000000" ]	[ "nonn" ]	9	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2017-05-28T09:08:01	oeisdata/seq/A012/A012243.seq	fa244bee3b862ef61a15d7c5f70fb219
A012244	a(n+2) = (2n+3)a(n+1) + (n+1)^2a(n), a(0) = 1, a(1) = 1.	[ "1", "1", "4", "24", "204", "2220", "29520", "463680", "8401680", "172504080", "3958113600", "100370793600", "2787459998400", "84139894238400", "2742857884166400", "96034297911552000", "3594206259195552000", "143193586818810528000", "6050501147565883008000", "270263264589232282368000" ]	[ "nonn", "easy" ]	55	0	3	[ "A012244", "A054765", "A054766", "A089975", "A190392" ]	null	N. J. A. Sloane	2020-08-15T16:02:29	oeisdata/seq/A012/A012244.seq	9773620deb845954cedd886468c8e417
A012245	Characteristic function of factorial numbers; also decimal expansion of Liouville's number or Liouville's constant.	[ "1", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1" ]	[ "nonn", "nice", "cons" ]	94	1	1	[ "A000142", "A012245", "A058304" ]	null	N. J. A. Sloane	2025-02-16T08:32:32	oeisdata/seq/A012/A012245.seq	6ebd44e1bd4a7869294e28a77997cfa7
A012246	E.g.f.: exp(sinh(arcsin(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", "1291", "8753", "73169", "634481", "6551251", "69292281", "852920953", "10655767929", "152425617371", "2197620415201", "35839758063521", "585914236294753", "10733139641944739", "196238045270790761" ]	[ "nonn" ]	6	0	4	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2014-04-06T18:41:58	oeisdata/seq/A012/A012246.seq	1dfd607bcb3a23a565bfb1e816cc6333
A012247	exp(sinh(arctan(x)))=1+x+1/2!x^2-3/4!x^4-4/5!x^5+21/6!x^6...	[ "1", "1", "1", "0", "-3", "-4", "21", "136", "185", "-7408", "-67159", "644416", "11805621", "-84562880", "-2380474563", "15811723136", "591392066161", "-4005496370944", "-181472052075695", "1317763889887232", "68002767860495981" ]	[ "sign" ]	6	0	5	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2012-12-11T14:36:11	oeisdata/seq/A012/A012247.seq	332f30eb5ea367b9ce00f05ff55c096f
A012248	Expansion of e.g.f. exp(arcsinh(arcsin(x))).	[ "1", "1", "1", "1", "1", "9", "49", "225", "897", "11025", "96801", "893025", "6803457", "108056025", "1275363153", "18261468225", "207592347393", "4108830350625", "60889593787713", "1187451971330625", "17888210916886017", "428670161650355625", "7679611833095218545", "189043541287806830625", "3530100224793651058305" ]	[ "nonn" ]	16	0	6	[ "A001818", "A012115", "A012248" ]	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2020-11-02T11:07:05	oeisdata/seq/A012/A012248.seq	e1bb554d82b4e20ced2c96376b545b91
A012249	Volume of a certain rational polytope whose points with given denominator count certain sets of Standard Tableaux.	[ "1", "2", "5", "24", "154", "1280", "13005", "156800", "2189726", "34793472", "620169186", "12259602432", "266267950740", "6304157663232", "161624247752253", "4461403146190848", "131936409635518774", "4161949856324648960", "139508340802911502422", "4952126960969786064896" ]	[ "nonn", "more" ]	58	1	2	[ "A012249", "A012250", "A348211" ]	null	D n Verma	2024-02-28T02:21:57	oeisdata/seq/A012/A012249.seq	5a8420350f206e9ac506e242f9bf370f
A012250	a(n) = A012249(2n) / 2^(2n-1).	[ "1", "3", "40", "1225", "67956", "5986134", "769550496", "136151219061", "31753157473180", "9445432588519642", "3491687484842443536", "1570713950508131878618", "845034544811095556274280", "535857105694970626486925100", "395590680969537758258609408640", "336386798400777928783348084420365" ]	[ "nonn" ]	51	1	2	[ "A012249", "A012250" ]	null	D n Verma	2024-02-28T02:23:33	oeisdata/seq/A012/A012250.seq	9dae678f43147a06274bb5c555934df4
A012251	exp(arcsinh(arctan(x)))=1+x+1/2!x^2-2/3!x^3-11/4!x^4+24/5!x^5...	[ "1", "1", "1", "-2", "-11", "24", "349", "-720", "-22455", "40320", "2465241", "-3628800", "-416217603", "479001600", "100729124469", "-87178291200", "-33198564667887", "20922789888000", "14328891118054449", "-6402373705728000", "-7852649782447649403" ]	[ "sign" ]	11	0	4	[ "A010050", "A012138", "A012251" ]	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2013-12-21T22:36:43	oeisdata/seq/A012/A012251.seq	28cda041df097d0d2b68ea4b6a1ea841
A012252	exp(arcsinh(arcsinh(x))) = 1+x+1/2!x^2-1/3!x^3-7/4!x^4+9/5!x^5...	[ "1", "1", "1", "-1", "-7", "9", "169", "-225", "-8751", "11025", "789681", "-893025", "-110381943", "108056025", "22142611737", "-18261468225", "-6041067843807", "4108830350625", "2153812782224097", "-1187451971330625", "-972958293249140583" ]	[ "sign" ]	9	0	5	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2013-10-30T17:49:32	oeisdata/seq/A012/A012252.seq	80ab0e391b7312964b3648043e39e3ce
A012253	exp(arcsinh(tanh(x))) = 1+x+1/2!x^2-2/3!x^3-11/4!x^4+16/5!x^5...	[ "1", "1", "1", "-2", "-11", "16", "301", "-272", "-16631", "7936", "1620601", "-353792", "-250557251", "22368256", "56629836901", "-1903757312", "-17602836565871", "209865342976", "7193368568377201", "-29088885112832", "-3735581618747946491" ]	[ "sign" ]	11	0	4	[ "A000182", "A012079", "A012253" ]	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2013-10-30T10:39:12	oeisdata/seq/A012/A012253.seq	c46687397e50fa8247598eb8ccbfb35a
A012254	exp(arcsinh(arctanh(x)))=1+x+1/2!x^2+2/3!x^3+5/4!x^4+24/5!x^5...	[ "1", "1", "1", "2", "5", "24", "109", "720", "4521", "40320", "330681", "3628800", "36468717", "479001600", "5721101541", "87178291200", "1205289090513", "20922789888000", "328897528901361", "6402373705728000", "112769846051251797", "2432902008176640000" ]	[ "nonn" ]	8	0	4	[ "A010050", "A012091", "A012254" ]	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2013-12-21T22:37:14	oeisdata/seq/A012/A012254.seq	7ecb85693f9e360c4a9e0a492e5609db
A012255	Expansion of e.g.f.: exp(tanh(arcsin(x)))=1+x+1/2!x^2-3/4!x^4-4/5!x^5+21/6!x^6...	[ "1", "1", "1", "0", "-3", "-4", "21", "136", "185", "272", "9641", "222016", "1668021", "21267520", "192801597", "3836913536", "42064398961", "874251520256", "10576096455505", "254117293340672", "3476312353756781", "92635637659667456" ]	[ "sign" ]	6	0	5	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2019-09-30T14:37:10	oeisdata/seq/A012/A012255.seq	031a3946ac263baf2dd4c469d1609c4a
A012256	Expansion of e.g.f.: exp(tanh(arctan(x)))=1+x+1/2!x^2-3/3!x^3-15/4!x^4+41/5!x^5...	[ "1", "1", "1", "-3", "-15", "41", "561", "-1019", "-38623", "12305", "4206881", "7478221", "-661302639", "-3005647943", "140958927825", "1143787246421", "-38921417469119", "-494108406644959", "13433349471318337", "250135591701350045" ]	[ "sign" ]	6	0	4	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2022-12-20T19:02:41	oeisdata/seq/A012/A012256.seq	b194821d8bf6f6cae356771f5d70b353
A012257	Irregular triangle read by rows: row 0 is {2}; if row n is {r_1, ..., r_k} then row n+1 is {r_k 1's, r_{k-1} 2's, r_{k-2} 3's, etc.}.	[ "2", "1", "1", "1", "2", "1", "1", "2", "1", "1", "2", "3", "1", "1", "1", "2", "2", "3", "4", "1", "1", "1", "1", "2", "2", "2", "3", "3", "4", "4", "5", "6", "7", "1", "1", "1", "1", "1", "1", "1", "2", "2", "2", "2", "2", "2", "3", "3", "3", "3", "3", "4", "4", "4", "4", "5", "5", "5", "5", "6", "6", "6", "7", "7", "7", "8", "8", "9", "9", "10", "10", "11", "12", "13", "14" ]	[ "nonn", "tabf", "nice", "look" ]	50	0	1	[ "A001462", "A011784", "A012257", "A014643", "A112798", "A181819", "A182850", "A182858", "A296150", "A304455" ]	null	Lionel Levine (levine(AT)ultranet.com)	2024-05-11T21:54:59	oeisdata/seq/A012/A012257.seq	78051a5d65289dc3619401d969077dc7
A012258	Expansion of e.g.f.: exp(arctanh(arcsin(x)))=1+x+1/2!x^2+4/3!x^3+13/4!x^4+84/5!x^5...	[ "1", "1", "1", "4", "13", "84", "469", "4152", "32985", "370128", "3818601", "51861888", "658371429", "10494283968", "158197312701", "2894815734912", "50529852678321", "1043916757274880", "20707179214389201", "476720372375608320" ]	[ "nonn" ]	6	0	4	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2019-05-29T20:00:10	oeisdata/seq/A012/A012258.seq	12382c53c1e6048491f11ee1083e5c39
A012259	Expansion of e.g.f. exp(arctanh(tan(x))).	[ "1", "1", "1", "5", "17", "121", "721", "6845", "58337", "698161", "7734241", "111973685", "1526099057", "25947503401", "419784870961", "8200346492525", "153563504618177", "3389281372287841", "72104198836466881", "1774459993676715365", "42270463533824671697", "1147649139272698443481" ]	[ "nonn" ]	50	0	4	[ "A012077", "A012085", "A012259", "A185411", "A202038" ]	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2022-08-25T08:32:57	oeisdata/seq/A012/A012259.seq	ee61d2381c5254514e9d77767db5d51d
A012260	Expansion of e.g.f. exp(arctanh(arctan(x))).	[ "1", "1", "1", "1", "1", "9", "49", "57", "-447", "5169", "78561", "-93807", "-5655231", "31981689", "1014069393", "-3857766903", "-187639949439", "1058896281825", "51144433721793", "-286891166986335", "-16631972691697791", "108826313005021545" ]	[ "sign" ]	14	0	6	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2022-09-08T08:44:38	oeisdata/seq/A012/A012260.seq	0ab3786e429259ebeafaf7c9d3c5b415
A012261	Expansion of e.g.f. exp(arctanh(sinh(x))).	[ "1", "1", "1", "4", "13", "76", "421", "3424", "26713", "277456", "2794441", "35345344", "436186213", "6504742336", "95033434861", "1632531979264", "27555582190513", "535821754153216", "10260037095841681", "222769351470429184", "4771143086720391613" ]	[ "nonn" ]	33	0	4	[ "A012109", "A012261" ]	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2022-09-08T08:44:38	oeisdata/seq/A012/A012261.seq	b1339e3c5ea6e1e3f8d5accb61a53a2a
A012262	Expansion of e.g.f. exp(arctanh(arcsinh(x))).	[ "1", "1", "1", "2", "5", "24", "109", "552", "3177", "28032", "227961", "1778688", "15773229", "212383872", "2521786149", "25215328512", "294715261521", "5734229114880", "91106569198449", "1029078328135680", "14283819393505749", "410202091438571520" ]	[ "sign" ]	19	0	4	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2022-09-08T08:44:38	oeisdata/seq/A012/A012262.seq	4bb4e958b202bf93eb984dbc510f9c4d
A012263	Expansion of e.g.f. exp(arctanh(arctanh(x))).	[ "1", "1", "1", "5", "17", "129", "769", "7797", "66849", "848481", "9506241", "145041093", "2007271089", "35799178401", "589807203777", "12045448529397", "230194642564161", "5298881528389185", "115219444193968257", "2952169020073027845" ]	[ "nonn" ]	15	0	4	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2022-09-08T08:44:38	oeisdata/seq/A012/A012263.seq	2208ad5cc21165162791f8b194e3f79e
A012264	Number of real roots of x - x^3/3! + x^5/5! - ... + (-1)^n*x^(2n+1)/(2n+1)!.	[ "1", "3", "1", "3", "5", "3", "5", "7", "5", "7", "5", "7", "9", "7", "9", "7", "9", "11", "9", "11", "13", "11", "13", "11", "13", "15", "13", "15", "17", "15", "17", "15", "17", "19", "17", "19", "17", "19", "21", "19", "21", "23", "21", "23", "21", "23", "25", "23", "25", "23", "25", "27", "25", "27", "29", "27", "29", "27", "29", "31", "29", "31", "33" ]	[ "nonn", "nice" ]	16	0	2	[ "A012264", "A012265" ]	null	N. J. A. Sloane	2025-07-02T16:01:55	oeisdata/seq/A012/A012264.seq	afe5fdf71bc7ce06423076264945a814
A012265	x - x^3/3! + x^5/5! - ... + (-1)^n*x^(2n+1)/(2n+1)! has 2a(n)+1 real roots.	[ "0", "1", "0", "1", "2", "1", "2", "3", "2", "3", "2", "3", "4", "3", "4", "3", "4", "5", "4", "5", "6", "5", "6", "5", "6", "7", "6", "7", "8", "7", "8", "7", "8", "9", "8", "9", "8", "9", "10", "9", "10", "11", "10", "11", "10", "11", "12", "11", "12", "11", "12", "13", "12", "13", "14", "13", "14", "13", "14", "15", "14", "15", "16" ]	[ "nonn", "easy", "nice" ]	21	0	5	[ "A012264", "A012265" ]	null	N. J. A. Sloane	2025-07-02T16:01:55	oeisdata/seq/A012/A012265.seq	a13bd48da3074d39b90dc503db0be690
A012266	Duplicate of A009468.	[ "0", "0", "2", "6", "22", "100", "428", "1008", "12504", "325152", "5509368", "85326120", "1301444520" ]	[ "dead" ]	6	0	3	null	null	null	2007-05-11T03:00:00	oeisdata/seq/A012/A012266.seq	1c45dadb631613008de68a9ca9fd9d04
A012267	Expansion of e.g.f. arcsin(log(x+1)^2).	[ "0", "0", "2", "-6", "22", "-100", "668", "-6048", "64776", "-763488", "9918072", "-144472680", "2365739880", "-42879666960", "845124232080", "-17930092309920", "408038138491200", "-9939819541747200", "258294825756089760", "-7127596576224545760" ]	[ "sign" ]	27	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2022-09-08T08:44:38	oeisdata/seq/A012/A012267.seq	58890d08b4e56438f8872770b48e6bf0
A012268	Duplicate of A009655.	[ "0", "0", "2", "6", "22", "100", "788", "8568", "103416", "1307808", "17722512", "264361680", "4373968080" ]	[ "dead" ]	6	0	3	null	null	null	2007-05-11T03:00:00	oeisdata/seq/A012/A012268.seq	d36d964c73777c0edf600f352bcda433
A012269	Expansion of e.g.f.: arctan(log(x+1)*log(x+1)).	[ "0", "0", "2", "-6", "22", "-100", "308", "1512", "-51144", "869472", "-12406608", "155319120", "-1563312720", "6008315040", "296596492320", "-12739805608320", "357984190838400", "-8317532611046400", "160961311569285120", "-2183410259228574720" ]	[ "sign" ]	19	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2022-09-08T08:44:38	oeisdata/seq/A012/A012269.seq	8c6a608467e637cbd2e935a7232bc421
A012270	Duplicate of A009585.	[ "0", "0", "2", "6", "22", "100", "668", "6048", "64776", "763488", "9676152", "131167080", "1900043880" ]	[ "dead" ]	6	0	3	null	null	null	2007-05-11T03:00:00	oeisdata/seq/A012/A012270.seq	b27bfca0a22c7b44f9d8696288f0627b
A012271	Expansion of e.g.f. arcsinh(log(x+1)*log(x+1)).	[ "0", "0", "2", "-6", "22", "-100", "428", "-1008", "-12504", "325152", "-5267448", "72020520", "-835748520", "6577169040", "36671947440", "-3513587807520", "114499586712000", "-2893590831936000", "61563908486205600", "-1035793335840588000" ]	[ "sign" ]	15	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2022-09-08T08:44:38	oeisdata/seq/A012/A012271.seq	b6f3d97cd884e6ccf7675ea7fad7c8df
A012272	Duplicate of A009789.	[ "0", "0", "2", "6", "22", "100", "308", "1512", "51144", "869472", "12648528", "168624720", "2029008720" ]	[ "dead" ]	6	0	3	null	null	null	2007-05-11T03:00:00	oeisdata/seq/A012/A012272.seq	1933162699d85326185899e5b2e2744f
A012273	Expansion of e.g.f.: sec(log(x+1)log(x+1)) = 1 + (12/4!)x^4 - (120/5!)x^5 + (1020/6!)x^6 ...	[ "1", "0", "0", "0", "12", "-120", "1020", "-8820", "89628", "-1109808", "15992160", "-253374000", "4306032192", "-78317306496", "1529483150832", "-32072509450800", "719140990648848", "-17146103389588608", "432647748528869376" ]	[ "sign" ]	19	0	5	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2022-09-08T08:44:38	oeisdata/seq/A012/A012273.seq	7f250802a7aaa1a1fe0cf36f3f5d3b92
A012274	Expansion of e.g.f.: sech(log(x+1)*log(x+1)).	[ "1", "0", "0", "0", "-12", "120", "-1020", "8820", "-72828", "505008", "-1376160", "-51546000", "1698674208", "-38050144704", "739129595568", "-12975913969200", "200099389809552", "-2317325113329792", "740464178471424" ]	[ "sign" ]	17	0	5	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2022-09-08T08:44:38	oeisdata/seq/A012/A012274.seq	cd31e306eeecfca02ec302ccd4260e91
A012275	Expansion of e.g.f. arcsin(exp(x)*log(x+1)).	[ "1", "1", "3", "6", "53", "235", "2709", "20188", "278249", "3019693", "48281695", "692436338", "12717929157", "225943945071", "4727712830281", "99660715587704", "2354596166060273", "57197420701626009", "1511830772603161339" ]	[ "nonn" ]	14	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2022-09-08T08:44:38	oeisdata/seq/A012/A012275.seq	291161182e19a172c79d3b46f7eb6bb9
A012276	Expansion of e.g.f. arctan(exp(x)*log(x+1)).	[ "1", "1", "0", "-12", "-37", "55", "2352", "11872", "-55963", "-1946147", "-12422168", "127425716", "4206315423", "29351640435", "-573767182376", "-18652736291104", "-126637724451319", "4546934751296505", "146709365362329136" ]	[ "sign" ]	10	0	4	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2022-09-08T08:44:38	oeisdata/seq/A012/A012276.seq	ad0552d162cbc0db8387a9dd836279a7
A012277	Expansion of e.g.f. arcsinh(exp(x)*log(x+1)).	[ "0", "1", "1", "1", "-6", "-17", "-35", "901", "4284", "4201", "-614267", "-4098107", "8297630", "1150691631", "9449070657", "-66322881767", "-4588041616648", "-41917690024495", "618354247728873", "33330584633391337", "310446365545119298" ]	[ "sign" ]	16	0	5	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2022-09-08T08:44:38	oeisdata/seq/A012/A012277.seq	f237610c68f7aaa34b83bf1ceb598502
A012278	Expansion of e.g.f. arctanh(exp(x)*log(x+1)).	[ "0", "1", "1", "4", "12", "103", "595", "6508", "58800", "786973", "9744373", "155024956", "2434745852", "45189575715", "856361535783", "18256766891140", "403804360914560", "9755015402674937", "246067759361332137", "6656604425348335060", "188304809071878207052", "5645851709034522319007" ]	[ "nonn" ]	28	0	4	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2022-09-08T08:44:38	oeisdata/seq/A012/A012278.seq	aa24ad40915678c36ec69dfd25be6a25
A012279	Expansion of e.g.f. sec(exp(x)*log(x+1)).	[ "1", "0", "1", "3", "16", "70", "580", "3850", "39940", "350544", "4408460", "48605788", "715662176", "9518173080", "160469679136", "2503106438040", "47524013744272", "851125166412928", "17967763294589776", "363412179220061872" ]	[ "nonn" ]	10	0	4	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2022-09-08T08:44:38	oeisdata/seq/A012/A012279.seq	09fbcddf8cf94b7b3667e4c4ce72f75f
A012280	Expansion of e.g.f.: sech(exp(x)*log(x+1)).	[ "1", "0", "-1", "-3", "-6", "30", "270", "1400", "-3080", "-86184", "-893760", "-754688", "61595424", "1201314400", "5341239904", "-68598744240", "-2871938780672", "-25391249097088", "31527888993024", "10819112145879168", "155954430765392768" ]	[ "sign" ]	12	0	4	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2022-09-08T08:44:38	oeisdata/seq/A012/A012280.seq	6ffc1623c1fd2024c5f3a7874e620a8a
A012281	Expansion of e.g.f. sin(sin(x) * log(x+1)).	[ "0", "0", "2", "-3", "4", "-20", "-10", "609", "-3880", "32040", "-352742", "3799565", "-44271460", "571990068", "-7830460482", "113493888585", "-1753811009808", "28760379830416", "-498456016769742", "9112758567973533", "-175322176912457996" ]	[ "sign" ]	18	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2022-09-08T08:44:38	oeisdata/seq/A012/A012281.seq	bbeab93fe14cbfbc1a40f1cfcc4ff28e
A012282	Expansion of e.g.f.: tan(sin(x)*log(x+1)).	[ "0", "0", "2", "-3", "4", "-20", "350", "-3171", "21320", "-172080", "2217658", "-32208715", "433724300", "-5910937812", "92570087766", "-1651187049435", "30890555494032", "-592724842745984", "12014317527212658", "-261952174935402291" ]	[ "sign" ]	19	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2022-09-08T08:44:38	oeisdata/seq/A012/A012282.seq	4aa8829c0bbb30d1d9e70e04e2c94b8e
A012283	Expansion of e.g.f. arctan(sin(x)*log(x+1)).	[ "0", "0", "2", "-3", "4", "-20", "-130", "1869", "-12280", "100080", "-362822", "-7482475", "168953420", "-2715677172", "34715587062", "-205932278475", "-3285394779888", "157209810212416", "-4031590864355982", "71565905502128781" ]	[ "sign" ]	12	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2022-09-08T08:44:38	oeisdata/seq/A012/A012283.seq	37727d3934add2ac15cef65c1dd218be
A012284	Expansion of e.g.f. sinh(sin(x)*log(x+1)).	[ "0", "0", "2", "-3", "4", "-20", "230", "-1911", "12920", "-104040", "1058458", "-11889955", "141336380", "-1804017852", "24962731950", "-371663464095", "5900573560752", "-99478198783184", "1776396441716658", "-33501559023746883", "665305926036550324" ]	[ "sign" ]	12	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2022-09-08T08:44:38	oeisdata/seq/A012/A012284.seq	5352e87f976f5b7f22b0df3333a0e5ee
A012285	Expansion of e.g.f. arcsinh(sin(x)*log(x+1)).	[ "0", "0", "2", "-3", "4", "-20", "-10", "609", "-3880", "32040", "-110822", "-2853235", "62173340", "-984765132", "13116545598", "-105359946615", "-269704385808", "34712027932816", "-1001624343871182", "18826756309101213", "-210544812030819596" ]	[ "sign" ]	12	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2022-09-08T08:44:38	oeisdata/seq/A012/A012285.seq	cf14aa51370e2c96aef6ab890fea5122
A012286	Expansion of e.g.f.: tanh(sin(x)*log(x+1)).	[ "0", "0", "2", "-3", "4", "-20", "-130", "1869", "-12280", "100080", "-604742", "-829675", "62508620", "-1158921972", "17643171702", "-190494456075", "1197368304912", "8324510449216", "-571700218304142", "14677422922560141", "-268070215275170156", "3735756713394119820", "-25728057443748879250" ]	[ "sign" ]	14	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2022-09-08T08:44:38	oeisdata/seq/A012/A012286.seq	e87f43d22c6c00e0b9115139a3858eec
A012287	Expansion of e.g.f. arctanh(sin(x)log(x+1))=2/2!x^2-3/3!x^3+4/4!x^4-20/5!*x^5...	[ "0", "0", "2", "-3", "4", "-20", "350", "-3171", "21320", "-172080", "2459578", "-38861515", "540169100", "-7467693012", "125140866006", "-2480288923035", "50275271244432", "-1015574149625984", "21888753352226418", "-522647511904669491" ]	[ "sign" ]	13	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2022-09-08T08:44:38	oeisdata/seq/A012/A012287.seq	cdb6057d5854c98d28bf56212cee90cd
A012288	Expansion of e.g.f. sec(sin(x)*log(x+1)).	[ "1", "0", "0", "0", "12", "-60", "210", "-1260", "18480", "-235872", "2421960", "-26091120", "365320296", "-5967877344", "97738612608", "-1617354429600", "29014419932160", "-574177721782144", "12059384791998912", "-262395430866467712" ]	[ "sign" ]	12	0	5	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2022-09-08T08:44:38	oeisdata/seq/A012/A012288.seq	4f3fd74348908f4ef80730b64da336f3
A012289	Expansion of e.g.f.: sech(sin(x)*log(x+1)).	[ "1", "0", "0", "0", "-12", "60", "-210", "1260", "-1680", "-66528", "854040", "-9944880", "101761704", "-561845856", "-2175945408", "136635189600", "-3242837295360", "53779020559744", "-655909940939712", "4733948121328512", "61668138518505088" ]	[ "sign" ]	11	0	5	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2022-09-08T08:44:38	oeisdata/seq/A012/A012289.seq	89dbe0c3f5cecca5bbff13b33fc1878c
A012290	Expansion of e.g.f. arctan(sin(x)*exp(x)).	[ "0", "1", "2", "0", "-24", "-140", "-8", "8960", "92736", "12240", "-14154208", "-210017280", "-50776704", "58549241920", "1133642065792", "435228385280", "-500888609593344", "-11981516394489600", "-6690495105515008", "7684815276420464640" ]	[ "sign" ]	20	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2022-09-08T08:44:38	oeisdata/seq/A012/A012290.seq	efa950135a18dad7e3301fe2590087e7
A012291	Expansion of e.g.f. arcsinh(sin(x)*exp(x)).	[ "0", "1", "2", "1", "-12", "-75", "-98", "3141", "37128", "79145", "-4068838", "-70096919", "-208084932", "14605150365", "331136373622", "1267818101421", "-111869011278192", "-3149733764010415", "-14850194074608718", "1567505717936558161" ]	[ "sign" ]	12	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2022-09-08T08:44:38	oeisdata/seq/A012/A012291.seq	ce62470cc10280b234214fbfab0f640c
A012292	Expansion of e.g.f. arctanh(sin(x)exp(x)) = x+2/2!x^2+4/3!x^3+24/4!x^4+180/5!*x^5...	[ "0", "1", "2", "4", "24", "180", "1432", "14544", "176064", "2382800", "36330272", "618520384", "11562021504", "235623136320", "5205288291712", "123834383495424", "3155999144761344", "85799392788650240", "2478387574846218752" ]	[ "nonn" ]	16	0	3	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2022-09-08T08:44:38	oeisdata/seq/A012/A012292.seq	73bc2fbccddd950eec8c4c471697f6f1
A012293	Expansion of e.g.f. sec(sin(x)exp(x))=1+1/2!x^2+6/3!x^3+25/4!x^4+140/5!*x^5...	[ "1", "0", "1", "6", "25", "140", "1177", "10738", "104977", "1188120", "15191889", "211088350", "3187087209", "52357837220", "926871127977", "17553084005322", "354581844112801", "7614153761167920", "173108509344647457", "4153655608324341686" ]	[ "nonn" ]	12	0	4	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2022-09-08T08:44:38	oeisdata/seq/A012/A012293.seq	edc9ea7f1dbd174ec3c3568a31790fa5
A012294	Expansion of e.g.f.: sech(sin(x)*exp(x)).	[ "1", "0", "-1", "-6", "-15", "60", "1023", "6062", "-9247", "-652680", "-7332289", "-13792350", "994947921", "19248140340", "119312444223", "-2747842718122", "-91993600741951", "-1070543140984080", "10423240065585023", "710021632610736714" ]	[ "sign" ]	15	0	4	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2022-09-08T08:44:38	oeisdata/seq/A012/A012294.seq	a486804813b1e09b9ce6c0b355fc48e6
A012295	Duplicate of A009486.	[ "0", "2", "-8", "-88", "6592", "-251488", "4158592", "551599232", "-94759774208", "9549823734272" ]	[ "dead" ]	9	0	2	null	null	null	2023-02-05T09:22:18	oeisdata/seq/A012/A012295.seq	7936b4318108c18d12e22987f038b528
A012296	Duplicate of A009675.	[ "2", "-8", "272", "-13568", "1048832", "-128073728", "21002749952", "-4567924441088" ]	[ "dead" ]	9	0	1	null	null	null	2023-02-05T09:24:24	oeisdata/seq/A012/A012296.seq	0e238819f647ecb272e271511896af4a
A012297	Expansion of e.g.f. arctan(sin(x)*sin(x)), even powers only.	[ "2", "-8", "-208", "13312", "161792", "-138042368", "9993992192", "4147254525952", "-1386315007787008", "-171033573395529728", "284350624150760456192", "-45336566464274820497408", "-87136608072231186709086208" ]	[ "sign" ]	11	0	1	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2022-09-08T08:44:38	oeisdata/seq/A012/A012297.seq	caf5c8571c102947d1283c7e959ee97b
A012298	Duplicate of A009596.	[ "0", "2", "-8", "152", "-6848", "312992", "-17468288", "1385712512", "-143250864128", "17321985331712" ]	[ "dead" ]	10	0	2	null	null	null	2023-02-05T09:21:48	oeisdata/seq/A012/A012298.seq	27cd3df7e99120ec17d9a05e263ec376
A012299	Expansion of e.g.f. arcsinh(sin(x)*sin(x)), even-indexed terms only.	[ "0", "2", "-8", "-88", "6592", "-9568", "-49063808", "4426189952", "1122968737792", "-441081682390528", "-23926396899780608", "74405808039377364992", "-16597462789247237931008", "-19016633437725878038847488" ]	[ "sign" ]	20	0	2	null	null	Patrick Demichel (patrick.demichel(AT)hp.com)	2024-03-28T21:54:08	oeisdata/seq/A012/A012299.seq	abac0e768e5ebc33d7710261ad52f9bd
A012300	Duplicate of A009801.	[ "2", "-8", "-208", "13312", "-80128", "-84819968", "9993992192", "759755210752" ]	[ "dead" ]	7	0	1	null	null	null	2023-02-05T11:55:58	oeisdata/seq/A012/A012300.seq	949ec6bceb6eb90e0c8d12ee22599e22

A012201

cosh(arctan(arcsin(x)))=1+1/2!*x^2-3/4!*x^4+69/6!*x^6-1159/8!*x^8...

[ "1", "1", "-3", "69", "-1159", "115081", "-3250827", "1156388557", "-12628752143", "42394317198097", "2830775181039853", "4335882574518729045", "967557162609958010985", "1031578849176135526526105" ]

[ "sign" ]

6

0

3

null

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

2020-08-26T14:48:02

oeisdata/seq/A012/A012201.seq

ab64d2c92bedd5bea6441e4d4a3a6e6c

A012202

sech(arctan(arcsin(x)))=1-1/2!*x^2+9/4!*x^4-249/6!*x^6+11953/8!*x^8...

[ "1", "-1", "9", "-249", "11953", "-992401", "115133433", "-19289685193", "4104153335777", "-1154213252748193", "390283459641717353", "-165544701587974757145", "81456402896849322863505", "-48584594120969426596224305" ]

[ "sign" ]

6

0

3

null

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

2018-04-08T21:20:56

oeisdata/seq/A012/A012202.seq

78219b33866b03eedbffad857d445e64

A012203

E.g.f.: exp(arctan(arctan(x))) = 1+x+1/2!*x^2-3/3!*x^3-15/4!*x^4+49/5!*x^5...

[ "1", "1", "1", "-3", "-15", "49", "609", "-1859", "-48031", "119617", "6247681", "-10283171", "-1214813487", "678311217", "330587407201", "246695568861", "-120086685689663", "-270153706006015", "56186566871496961", "221300400903581245" ]

[ "sign" ]

11

0

4

null

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

2014-08-15T03:18:10

oeisdata/seq/A012/A012203.seq

2b69f18d2595ec472a14a3c37e070d8f

A012204

arcsin(arctan(arctan(x)))=x-3/3!*x^3+57/5!*x^5-2755/7!*x^7+251601/9!*x^9...

[ "1", "-3", "57", "-2755", "251601", "-37281923", "8163849353", "-2479580033411", "997801392400929", "-513852593272870403", "329599574990913085529", "-257652341842242812773955", "241116753509976748759134193" ]

[ "sign" ]

6

0

2

null

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

2016-11-28T17:43:54

oeisdata/seq/A012/A012204.seq

9d8736241d255df56e6e80c8863dbc0c

A012205

arctan(arctan(arctan(x)))=x-6/3!*x^3+192/5!*x^5-14704/7!*x^7...

[ "1", "-6", "192", "-14704", "2058624", "-457982720", "148443124736", "-66066559066112", "38672430452342784", "-28812765976119148544", "26627757204719641296896", "-29895731887419723149213696", "40082507396600200285753704448" ]

[ "sign" ]

6

0

2

null

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

2016-11-28T17:45:48

oeisdata/seq/A012/A012205.seq

df1f2e8c1034f75a211e77064b55ad6d

A012206

sinh(arctan(arctan(x)))=x-3/3!*x^3+49/5!*x^5-1859/7!*x^7+119617/9!*x^9...

[ "1", "-3", "49", "-1859", "119617", "-10283171", "678311217", "246695568861", "-270153706006015", "221300400903581245", "-191103844337252819535", "185242544952868387351165", "-204711474044267911803243455" ]

[ "sign" ]

6

0

2

null

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

2016-11-28T17:47:46

oeisdata/seq/A012/A012206.seq

af3242a68b53776487495779c2e1baa9

A012207

arcsinh(arctan(arctan(x)))=x-5/3!*x^3+137/5!*x^5-9141/7!*x^7...

[ "1", "-5", "137", "-9141", "1130993", "-225155941", "66037540345", "-26862446793685", "14500070037397089", "-10041538909269213637", "8686453887771982767337", "-9185311291945403768547829", "11662015255583014905028727633" ]

[ "sign" ]

6

0

2

null

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

2013-07-16T16:02:51

oeisdata/seq/A012/A012207.seq

46b7d49bcef5928d32f2eb17d4e7e5dc

A012208

tanh(arctan(arctan(x)))=x-6/3!*x^3+184/5!*x^5-13136/7!*x^7...

[ "1", "-6", "184", "-13136", "1679488", "-335723264", "96492653568", "-37665610561536", "19158060131778560", "-12304193595906129920", "9734505561510299566080", "-9299736312230986726768640", "10553185490408007072659537920" ]

[ "sign" ]

6

0

2

null

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

2014-11-15T17:34:25

oeisdata/seq/A012/A012208.seq

c9019e09c2f62dfbe135dcef77061c2f

A012209

arctanh(arctan(arctan(x)))=x-2/3!*x^3+32/5!*x^5-1392/7!*x^7+118400/9!*x^9...

[ "1", "-2", "32", "-1392", "118400", "-16678144", "3517084672", "-1037502889984", "407811782836224", "-205957880207835136", "129921324821854289920", "-100089923129501690626048", "92456928301505596639674368" ]

[ "sign" ]

6

0

2

null

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

2016-11-28T17:51:28

oeisdata/seq/A012/A012209.seq

d193edc8b02b85b63f4112dc697f0065

A012210

cosh(arctan(arctan(x)))=1+1/2!*x^2-15/4!*x^4+609/6!*x^6-48031/8!*x^8...

[ "1", "1", "-15", "609", "-48031", "6247681", "-1214813487", "330587407201", "-120086685689663", "56186566871496961", "-32929237073496552527", "23637878950680710828385", "-20404361373477159717443295" ]

[ "sign" ]

6

0

3

null

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

2016-11-28T17:53:24

oeisdata/seq/A012/A012210.seq

27656fe9d8695d8a23c801a1c0b5eb39

A012211

sech(arctan(arctan(x)))=1-1/2!*x^2+21/4!*x^4-1149/6!*x^6+119305/8!*x^8...

[ "1", "-1", "21", "-1149", "119305", "-20082841", "4984310493", "-1711500674389", "776816116717457", "-450301381427975089", "324553968807761095973", "-284661632752853556677805", "298518404617173649259722905" ]

[ "sign" ]

6

0

3

null

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

2016-11-28T17:54:34

oeisdata/seq/A012/A012211.seq

5f99add3ead5b640ac87167e327d6f52

A012212

Number of squarefree palindromes over {0, 1, 2} of length 2n+1.

[ "3", "6", "6", "12", "12", "12", "12", "18", "18", "24", "36", "48", "60", "84", "102", "138", "186", "246", "306", "378", "486", "630", "816", "1050", "1350", "1782", "2328", "2988", "3870", "5076", "6624", "8616", "11112", "14454", "18882", "24630", "31944", "41442", "53988", "70422", "91614", "119046", "154896", "201834", "262824", "341688" ]

[ "nonn", "base" ]

16

0

1

[ "A006156", "A012212" ]

null

Jeffrey Shallit

2018-08-27T16:28:41

oeisdata/seq/A012/A012212.seq

cdb404120e7a5698d2571db4a740a14c

A012213

exp(arctan(arcsinh(x)))=1+x+1/2!*x^2-2/3!*x^3-11/4!*x^4+24/5!*x^5...

[ "1", "1", "1", "-2", "-11", "24", "349", "-664", "-22007", "28416", "2312601", "-942336", "-365164227", "-260697984", "80916522933", "165900454656", "-23968582079343", "-85943912448000", "9151870592718513", "48584004553543680", "-4378918837383018747" ]

[ "sign" ]

4

0

4

null

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

2012-02-24T12:50:44

oeisdata/seq/A012/A012213.seq

2a28f952545ab308273a4f67b482c8ca

A012214

arcsin(arctan(arcsinh(x)))=x-2/3!*x^3+32/5!*x^5-1280/7!*x^7+96896/9!*x^9...

[ "1", "-2", "32", "-1280", "96896", "-11867008", "2142673920", "-535571951616", "177110831202304", "-74879716881661952", "39403647907518971904", "-25258353322454300164096", "19376893280575897343623168" ]

[ "sign" ]

4

0

2

null

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

2012-02-24T12:50:44

oeisdata/seq/A012/A012214.seq

2a259dc180a60da5a28714901c67a9c8

A012215

arctan(arctan(arcsinh(x)))=x-5/3!*x^3+137/5!*x^5-9029/7!*x^7...

[ "1", "-5", "137", "-9029", "1089713", "-209177605", "58539026361", "-22507046465157", "11386223123252449", "-7334290106238920453", "5861710212500532385641", "-5692596379677558396424645", "6602985113623111671589590673" ]

[ "sign" ]

7

0

2

null

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

2012-10-20T16:04:35

oeisdata/seq/A012/A012215.seq

1af0921aad8008a470140975fc8bbc40

A012216

sinh(arctan(arcsinh(x)))=x-2/3!*x^3+24/5!*x^5-664/7!*x^7+28416/9!*x^9...

[ "1", "-2", "24", "-664", "28416", "-942336", "-260697984", "165900454656", "-85943912448000", "48584004553543680", "-31574321393019125760", "23832746038658540666880", "-20858343927838973179822080", "21048655959583804491297914880" ]

[ "sign" ]

8

0

2

[ "A012213", "A012216" ]

null

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

2024-10-04T11:28:17

oeisdata/seq/A012/A012216.seq

35749cc4c86a7981bd1c2b0345170482

A012217

arcsinh(arctan(arcsinh(x)))=x-4/3!*x^3+92/5!*x^5-5216/7!*x^7...

[ "1", "-4", "92", "-5216", "551504", "-94170176", "23756009664", "-8329952294400", "3882725102061824", "-2324928136769545216", "1740643970081187412992", "-1594058498088175066406912", "1753510369493317462917828608" ]

[ "sign" ]

6

0

2

null

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

2013-03-10T15:53:31

oeisdata/seq/A012/A012217.seq

20ea46870a2b12c4d7992f6231f7344d

A012218

tanh(arctan(arcsinh(x)))=x-5/3!*x^3+129/5!*x^5-7741/7!*x^7...

[ "1", "-5", "129", "-7741", "830529", "-139115349", "33466193409", "-10924199283981", "4643317555286145", "-2490727724722757925", "1645111995753399461505", "-1311624218654589461390685", "1241813393715548870981284545" ]

[ "sign" ]

4

0

2

null

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

2012-02-24T12:50:44

oeisdata/seq/A012/A012218.seq

ddcec7a6ed6697d5d3a5ae45c6b1a788

A012219

arctanh(arctan(arcsinh(x)))=x-1/3!*x^3+17/5!*x^5-617/7!*x^7+44417/9!*x^9...

[ "1", "-1", "17", "-617", "44417", "-5210129", "909126033", "-220910314809", "71341157623169", "-29556627270426145", "15282372258542389905", "-9645984260739983339273", "7298836347461102485422593", "-6521512480584315170326457393" ]

[ "sign" ]

6

0

3

null

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

2016-11-28T17:57:52

oeisdata/seq/A012/A012219.seq

1560c4c057bfd8973edb6bc94230e848

A012220

cosh(arctan(arcsinh(x)))=1+1/2!*x^2-11/4!*x^4+349/6!*x^6-22007/8!*x^8...

[ "1", "1", "-11", "349", "-22007", "2312601", "-365164227", "80916522933", "-23968582079343", "9151870592718513", "-4378918837383018747", "2566828786036427906445", "-1809533477302236292739175", "1510703360292377534570508105" ]

[ "sign" ]

6

0

3

null

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

2020-11-06T16:12:18

oeisdata/seq/A012/A012220.seq

8974768180a4a77c1b566a6883e09054

A012221

sech(arctan(arcsinh(x)))=1-1/2!*x^2+17/4!*x^4-769/6!*x^6+66401/8!*x^8...

[ "1", "-1", "17", "-769", "66401", "-9313281", "1927198833", "-551835917697", "208856369686977", "-100945109069282817", "60655475821737151953", "-44346899335054478649345", "38762487400695339770533665" ]

[ "sign" ]

4

0

3

null

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

2012-02-24T12:50:44

oeisdata/seq/A012/A012221.seq

7713e6a3a53314cc5f23aa80c201080f

A012222

Expansion of e.g.f.: exp(arctan(tanh(x)))=1+x+1/2!*x^2-3/3!*x^3-15/4!*x^4+41/5!*x^5...

[ "1", "1", "1", "-3", "-15", "41", "561", "-1243", "-40415", "58001", "4825121", "-1956083", "-866056815", "-740509639", "218527875281", "509169335477", "-73838559553215", "-295854887910879", "32207514779999041", "189240977761969437" ]

[ "sign" ]

6

0

4

null

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

2025-03-17T16:51:25

oeisdata/seq/A012/A012222.seq

eaab5e2ff339193600db62ac21bd5cd2

A012223

arcsin(arctan(tanh(x)))=x-3/3!*x^3+49/5!*x^5-2139/7!*x^7+181921/9!*x^9...

[ "1", "-3", "49", "-2139", "181921", "-25347539", "5231635473", "-1498270773419", "568381637171521", "-275844413823596835", "166680279670474243825", "-122705715387723016322939", "108112687783657068510670305" ]

[ "sign" ]

4

0

2

null

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

2012-02-24T12:50:44

oeisdata/seq/A012/A012223.seq

aef087936bb2242e8b257a1a910298b7

A012224

arctan(arctan(tanh(x)))=x-6/3!*x^3+184/5!*x^5-13584/7!*x^7...

[ "1", "-6", "184", "-13584", "1840768", "-397140224", "124961670144", "-54024939321344", "30732245464219648", "-22258174840910315520", "20000813079319781048320", "-21837489688957057049821184", "28476242253811580631861166080" ]

[ "sign" ]

6

0

2

null

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

2016-11-28T17:59:41

oeisdata/seq/A012/A012224.seq

d7da58d350eea39afddedbfa4eaa286a

A012225

sinh(arctan(tanh(x)))=x-3/3!*x^3+41/5!*x^5-1243/7!*x^7+58001/9!*x^9...

[ "1", "-3", "41", "-1243", "58001", "-1956083", "-740509639", "509169335477", "-295854887910879", "189240977761969437", "-139751997081117953719", "120179815628074668521797", "-120043777513489781645646159" ]

[ "sign" ]

4

0

2

null

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

2012-02-24T12:50:44

oeisdata/seq/A012/A012225.seq

6d697e362d1200f8ee39c26e68f69a9d

A012226

arcsinh(arctan(tanh(x)))=x-5/3!*x^3+129/5!*x^5-8189/7!*x^7...

[ "1", "-5", "129", "-8189", "972609", "-186825429", "53036534017", "-20924521480269", "10970414196349569", "-7386311927549483045", "6216439933812148586625", "-6398271924540885631183389", "7909256594572491509610323905" ]

[ "sign" ]

6

0

2

null

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

2019-08-24T10:22:13

oeisdata/seq/A012/A012226.seq

a9598866e4664ca55163d1c2e1b00514

A012227

tanh(arctan(tanh(x)))=x-6/3!*x^3+176/5!*x^5-12016/7!*x^7...

[ "1", "-6", "176", "-12016", "1469696", "-280971776", "77198422016", "-28793654081536", "13988424620507136", "-8578076577450295296", "6478101995566379565056", "-5906079803365219349037056", "6394716233788355978540875776" ]

[ "sign" ]

7

0

2

[ "A012227", "A101921" ]

null

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

2018-12-08T19:37:13

oeisdata/seq/A012/A012227.seq

c5594dca78995cb16fcb1136d6a74c7f

A012228

arctanh(arctan(tanh(x)))=x-2/3!*x^3+24/5!*x^5-944/7!*x^7+77952/9!*x^9...

[ "1", "-2", "24", "-944", "77952", "-10623744", "2145104896", "-602082207744", "224357319278592", "-107165894175948800", "63836869263529082880", "-46390243522547859062784", "40392288941602607862906880" ]

[ "sign" ]

6

0

2

null

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

2016-11-28T18:01:33

oeisdata/seq/A012/A012228.seq

b80c16bcb5ff2dfe0b91e3decb006baf

A012229

cosh(arctan(tanh(x)))=1+1/2!*x^2-15/4!*x^4+561/6!*x^6-40415/8!*x^8...

[ "1", "1", "-15", "561", "-40415", "4825121", "-866056815", "218527875281", "-73838559553215", "32207514779999041", "-17624680185473393615", "11826144583278421964401", "-9549876975469294700602015", "9137286945784401729622059361" ]

[ "sign" ]

6

0

3

null

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

2019-03-11T17:56:59

oeisdata/seq/A012/A012229.seq

00685236bc6b2b9f37983e31ef7f864a

A012230

sech(arctan(tanh(x)))=1-1/2!*x^2+21/4!*x^4-1101/6!*x^6+109001/8!*x^8...

[ "1", "-1", "21", "-1101", "109001", "-17491001", "4139085981", "-1355308485701", "586612833746961", "-324261948714025201", "222851423174495787941", "-186365710421614910029501", "186332939048243649892744921" ]

[ "sign" ]

6

0

3

null

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

2017-10-01T12:13:39

oeisdata/seq/A012/A012230.seq

233ea5d7be34e07ba9ad8a2775f0d0d1

A012231

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

[ "1", "1", "1", "1", "1", "9", "49", "281", "1345", "13233", "105441", "1179729", "10336833", "144386553", "1580651409", "25501409961", "316289380737", "5869292202465", "83559601907649", "1744083324947745", "27709107620492673", "643531258862953065" ]

[ "nonn" ]

6

0

6

null

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

2016-11-28T18:05:20

oeisdata/seq/A012/A012231.seq

80b6c879fd51a72100290a4ba86bcdaa

A012232

arcsin(arctan(arctanh(x)))=x+1/3!*x^3+17/5!*x^5+505/7!*x^7+32321/9!*x^9...

[ "1", "1", "17", "505", "32321", "3196337", "474305361", "96903709929", "26267702181889", "9102885308254561", "3930753230143374609", "2069316409758628885721", "1305070038882436410153793", "971558826878073011961325841" ]

[ "nonn" ]

6

0

3

null

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

2016-11-28T18:07:01

oeisdata/seq/A012/A012232.seq

c4b9bf19cf311773e8d7d304f02094c4

A012233

arctan(arctan(arctanh(x)))=x-2/3!*x^3+32/5!*x^5-944/7!*x^7+64640/9!*x^9...

[ "1", "-2", "32", "-944", "64640", "-5881600", "919673856", "-172830523392", "48225099218944", "-15466881283850240", "6745794347282989056", "-3302151520495305490432", "2072514460288282576027648", "-1438958551527596730993344512" ]

[ "sign" ]

6

0

2

null

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

2016-11-28T18:08:29

oeisdata/seq/A012/A012233.seq

5ca0782b1fe02733a59bc27ea3506514

A012234

sinh(arctan(arctanh(x)))=x+1/3!*x^3+9/5!*x^5+281/7!*x^7+13233/9!*x^9...

[ "1", "1", "9", "281", "13233", "1179729", "144386553", "25501409961", "5869292202465", "1744083324947745", "643531258862953065", "289976769842011018425", "156375721502624955046545", "99525811638120512862203505" ]

[ "nonn" ]

6

0

3

null

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

2016-11-28T18:09:35

oeisdata/seq/A012/A012234.seq

822c53fe7ba4724dfa44c072cda4f287

A012235

E.g.f.: arcsinh(arctan(arctanh(x)))=x-1/3!*x^3+17/5!*x^5-281/7!*x^7+24257/9!*x^9...

[ "1", "-1", "17", "-281", "24257", "-1331441", "275798481", "-33388170825", "12274116245249", "-2689107736315873", "1507045832586910737", "-530866838718138680441", "415346005609060387325633", "-217242204344672574488013521" ]

[ "sign" ]

8

0

3

null

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

2016-11-28T18:10:58

oeisdata/seq/A012/A012235.seq

b9a090d588955d7ddc41f46a22c04983

A012236

tanh(arctan(arctanh(x)))=x-2/3!*x^3+24/5!*x^5-496/7!*x^7+24192/9!*x^9...

[ "1", "-2", "24", "-496", "24192", "-1246464", "150408192", "-12132673536", "3380973895680", "-253363927449600", "217523969745223680", "4682388187242823680", "35388810383588767825920", "8821171867345211810119680" ]

[ "sign" ]

6

0

2

null

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

2016-11-28T18:12:25

oeisdata/seq/A012/A012236.seq

1175dc725872d01d261c9321dfe8def6

A012237

arctanh(arctan(arctanh(x)))=x+2/3!*x^3+32/5!*x^5+1168/7!*x^7+80768/9!*x^9...

[ "1", "2", "32", "1168", "80768", "8855296", "1420471296", "312821661696", "90619729117184", "33397289918332928", "15260151754256547840", "8466388564521610903552", "5606464118961336397856768", "4368144479139164180218642432" ]

[ "nonn" ]

9

0

2

null

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

2016-11-28T18:13:59

oeisdata/seq/A012/A012237.seq

037274944eb4f0aa933973740148c624

A012238

cosh(arctan(arctanh(x)))=1+1/2!*x^2+1/4!*x^4+49/6!*x^6+1345/8!*x^8...

[ "1", "1", "1", "49", "1345", "105441", "10336833", "1580651409", "316289380737", "83559601907649", "27709107620492673", "11345006679686949105", "5605389007592066373825", "3292126822668986935347105", "2265914784466771293436282305", "1806802766658673683522189272145" ]

[ "nonn" ]

8

0

4

null

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

2015-03-02T17:41:09

oeisdata/seq/A012/A012238.seq

a4849383cf4e22bbec9b4163ff55eb6b

A012239

sech(arctan(arctanh(x)))=1-1/2!*x^2+5/4!*x^4-109/6!*x^6+2729/8!*x^8...

[ "1", "-1", "5", "-109", "2729", "-196281", "9832173", "-1827291621", "102520239057", "-58512018759921", "-121510420621227", "-5298654687807230685", "-895543588646311726215", "-1180050438628226991259305" ]

[ "sign" ]

8

0

3

null

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

2016-11-28T18:16:20

oeisdata/seq/A012/A012239.seq

759f64ff0f61f98a520f92ff1c9a60cb

A012240

-log(cos(tan(x)))=1/2!*x^2+10/4!*x^4+232/6!*x^6+10064/8!*x^8...

[ "1", "10", "232", "10064", "720384", "78009600", "11977120768", "2480763381760", "666957211828224", "225809770695098368", "93981332166180077568", "47151835657444566499328", "28061010401657661222289408" ]

[ "nonn" ]

16

0

2

[ "A009329", "A009387", "A012240" ]

null

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

2014-06-26T02:48:37

oeisdata/seq/A012/A012240.seq

398e91d3a51a4f2e0d6ff20ab1f0ed76

A012241

log(cos(arcsinh(x))) = -1/2!*x^2+2/4!*x^4-40/6!*x^6+1360/8!*x^8...

[ "-1", "2", "-40", "1360", "-87680", "8723200", "-1254323200", "245463296000", "-62768582656000", "20318491009024000", "-8121379360440320000", "3928322245164728320000", "-2261534088991670272000000" ]

[ "sign" ]

6

0

2

null

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

2023-03-02T12:39:05

oeisdata/seq/A012/A012241.seq

e9ae001bfd4026153f2aa1c923dcde2d

A012242

log(cos(tanh(x)))=-1/2!*x^2+6/4!*x^4-72/6!*x^6+1456/8!*x^8...

[ "-1", "6", "-72", "1456", "-47104", "2390784", "-180612096", "18625189888", "-2431403622400", "384624656646144", "-72343735465672704", "16067422146130345984", "-4193787904779561730048", "1276366494840535652499456" ]

[ "sign" ]

6

0

2

null

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

2014-05-27T11:08:04

oeisdata/seq/A012/A012242.seq

e5a5ed7a11bd45a61906663d48923fee

A012243

-log(cos(arctanh(x)))=1/2!*x^2+10/4!*x^4+280/6!*x^6+15440/8!*x^8...

[ "1", "10", "280", "15440", "1412480", "193606400", "37162777600", "9519986944000", "3139364220928000", "1295834618224640000", "654668849830461440000", "397456058751397068800000", "285567610965661253632000000" ]

[ "nonn" ]

9

0

2

null

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

2017-05-28T09:08:01

oeisdata/seq/A012/A012243.seq

fa244bee3b862ef61a15d7c5f70fb219

A012244

a(n+2) = (2n+3)*a(n+1) + (n+1)^2*a(n), a(0) = 1, a(1) = 1.

[ "1", "1", "4", "24", "204", "2220", "29520", "463680", "8401680", "172504080", "3958113600", "100370793600", "2787459998400", "84139894238400", "2742857884166400", "96034297911552000", "3594206259195552000", "143193586818810528000", "6050501147565883008000", "270263264589232282368000" ]

[ "nonn", "easy" ]

55

0

3

[ "A012244", "A054765", "A054766", "A089975", "A190392" ]

null

N. J. A. Sloane

2020-08-15T16:02:29

oeisdata/seq/A012/A012244.seq

9773620deb845954cedd886468c8e417

A012245

Characteristic function of factorial numbers; also decimal expansion of Liouville's number or Liouville's constant.

[ "1", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1" ]

[ "nonn", "nice", "cons" ]

94

1

[ "A000142", "A012245", "A058304" ]

null

N. J. A. Sloane

2025-02-16T08:32:32

oeisdata/seq/A012/A012245.seq

6ebd44e1bd4a7869294e28a77997cfa7

A012246

E.g.f.: exp(sinh(arcsin(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", "1291", "8753", "73169", "634481", "6551251", "69292281", "852920953", "10655767929", "152425617371", "2197620415201", "35839758063521", "585914236294753", "10733139641944739", "196238045270790761" ]

[ "nonn" ]

6

0

4

null

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

2014-04-06T18:41:58

oeisdata/seq/A012/A012246.seq

1dfd607bcb3a23a565bfb1e816cc6333

A012247

exp(sinh(arctan(x)))=1+x+1/2!*x^2-3/4!*x^4-4/5!*x^5+21/6!*x^6...

[ "1", "1", "1", "0", "-3", "-4", "21", "136", "185", "-7408", "-67159", "644416", "11805621", "-84562880", "-2380474563", "15811723136", "591392066161", "-4005496370944", "-181472052075695", "1317763889887232", "68002767860495981" ]

[ "sign" ]

6

0

5

null

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

2012-12-11T14:36:11

oeisdata/seq/A012/A012247.seq

332f30eb5ea367b9ce00f05ff55c096f

A012248

Expansion of e.g.f. exp(arcsinh(arcsin(x))).

[ "1", "1", "1", "1", "1", "9", "49", "225", "897", "11025", "96801", "893025", "6803457", "108056025", "1275363153", "18261468225", "207592347393", "4108830350625", "60889593787713", "1187451971330625", "17888210916886017", "428670161650355625", "7679611833095218545", "189043541287806830625", "3530100224793651058305" ]

[ "nonn" ]

16

0

6

[ "A001818", "A012115", "A012248" ]

null

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

2020-11-02T11:07:05

oeisdata/seq/A012/A012248.seq

e1bb554d82b4e20ced2c96376b545b91

A012249

Volume of a certain rational polytope whose points with given denominator count certain sets of Standard Tableaux.

[ "1", "2", "5", "24", "154", "1280", "13005", "156800", "2189726", "34793472", "620169186", "12259602432", "266267950740", "6304157663232", "161624247752253", "4461403146190848", "131936409635518774", "4161949856324648960", "139508340802911502422", "4952126960969786064896" ]

[ "nonn", "more" ]

58

1

2

[ "A012249", "A012250", "A348211" ]

null

D n Verma

2024-02-28T02:21:57

oeisdata/seq/A012/A012249.seq

5a8420350f206e9ac506e242f9bf370f

A012250

a(n) = A012249(2*n) / 2^(2*n-1).

[ "1", "3", "40", "1225", "67956", "5986134", "769550496", "136151219061", "31753157473180", "9445432588519642", "3491687484842443536", "1570713950508131878618", "845034544811095556274280", "535857105694970626486925100", "395590680969537758258609408640", "336386798400777928783348084420365" ]

[ "nonn" ]

51

1

2

[ "A012249", "A012250" ]

null

D n Verma

2024-02-28T02:23:33

oeisdata/seq/A012/A012250.seq

9dae678f43147a06274bb5c555934df4

A012251

exp(arcsinh(arctan(x)))=1+x+1/2!*x^2-2/3!*x^3-11/4!*x^4+24/5!*x^5...

[ "1", "1", "1", "-2", "-11", "24", "349", "-720", "-22455", "40320", "2465241", "-3628800", "-416217603", "479001600", "100729124469", "-87178291200", "-33198564667887", "20922789888000", "14328891118054449", "-6402373705728000", "-7852649782447649403" ]

[ "sign" ]

11

0

4

[ "A010050", "A012138", "A012251" ]

null

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

2013-12-21T22:36:43

oeisdata/seq/A012/A012251.seq

28cda041df097d0d2b68ea4b6a1ea841

A012252

exp(arcsinh(arcsinh(x))) = 1+x+1/2!*x^2-1/3!*x^3-7/4!*x^4+9/5!*x^5...

[ "1", "1", "1", "-1", "-7", "9", "169", "-225", "-8751", "11025", "789681", "-893025", "-110381943", "108056025", "22142611737", "-18261468225", "-6041067843807", "4108830350625", "2153812782224097", "-1187451971330625", "-972958293249140583" ]

[ "sign" ]

9

0

5

null

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

2013-10-30T17:49:32

oeisdata/seq/A012/A012252.seq

80ab0e391b7312964b3648043e39e3ce

A012253

exp(arcsinh(tanh(x))) = 1+x+1/2!*x^2-2/3!*x^3-11/4!*x^4+16/5!*x^5...

[ "1", "1", "1", "-2", "-11", "16", "301", "-272", "-16631", "7936", "1620601", "-353792", "-250557251", "22368256", "56629836901", "-1903757312", "-17602836565871", "209865342976", "7193368568377201", "-29088885112832", "-3735581618747946491" ]

[ "sign" ]

11

0

4

[ "A000182", "A012079", "A012253" ]

null

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

2013-10-30T10:39:12

oeisdata/seq/A012/A012253.seq

c46687397e50fa8247598eb8ccbfb35a

A012254

exp(arcsinh(arctanh(x)))=1+x+1/2!*x^2+2/3!*x^3+5/4!*x^4+24/5!*x^5...

[ "1", "1", "1", "2", "5", "24", "109", "720", "4521", "40320", "330681", "3628800", "36468717", "479001600", "5721101541", "87178291200", "1205289090513", "20922789888000", "328897528901361", "6402373705728000", "112769846051251797", "2432902008176640000" ]

[ "nonn" ]

8

0

4

[ "A010050", "A012091", "A012254" ]

null

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

2013-12-21T22:37:14

oeisdata/seq/A012/A012254.seq

7ecb85693f9e360c4a9e0a492e5609db

A012255

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

[ "1", "1", "1", "0", "-3", "-4", "21", "136", "185", "272", "9641", "222016", "1668021", "21267520", "192801597", "3836913536", "42064398961", "874251520256", "10576096455505", "254117293340672", "3476312353756781", "92635637659667456" ]

[ "sign" ]

6

0

5

null

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

2019-09-30T14:37:10

oeisdata/seq/A012/A012255.seq

031a3946ac263baf2dd4c469d1609c4a

A012256

Expansion of e.g.f.: exp(tanh(arctan(x)))=1+x+1/2!*x^2-3/3!*x^3-15/4!*x^4+41/5!*x^5...

[ "1", "1", "1", "-3", "-15", "41", "561", "-1019", "-38623", "12305", "4206881", "7478221", "-661302639", "-3005647943", "140958927825", "1143787246421", "-38921417469119", "-494108406644959", "13433349471318337", "250135591701350045" ]

[ "sign" ]

6

0

4

null

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

2022-12-20T19:02:41

oeisdata/seq/A012/A012256.seq

b194821d8bf6f6cae356771f5d70b353

A012257

Irregular triangle read by rows: row 0 is {2}; if row n is {r_1, ..., r_k} then row n+1 is {r_k 1's, r_{k-1} 2's, r_{k-2} 3's, etc.}.

[ "2", "1", "1", "1", "2", "1", "1", "2", "1", "1", "2", "3", "1", "1", "1", "2", "2", "3", "4", "1", "1", "1", "1", "2", "2", "2", "3", "3", "4", "4", "5", "6", "7", "1", "1", "1", "1", "1", "1", "1", "2", "2", "2", "2", "2", "2", "3", "3", "3", "3", "3", "4", "4", "4", "4", "5", "5", "5", "5", "6", "6", "6", "7", "7", "7", "8", "8", "9", "9", "10", "10", "11", "12", "13", "14" ]

[ "nonn", "tabf", "nice", "look" ]

50

0

1

[ "A001462", "A011784", "A012257", "A014643", "A112798", "A181819", "A182850", "A182858", "A296150", "A304455" ]

null

Lionel Levine (levine(AT)ultranet.com)

2024-05-11T21:54:59

oeisdata/seq/A012/A012257.seq

78051a5d65289dc3619401d969077dc7

A012258

Expansion of e.g.f.: exp(arctanh(arcsin(x)))=1+x+1/2!*x^2+4/3!*x^3+13/4!*x^4+84/5!*x^5...

[ "1", "1", "1", "4", "13", "84", "469", "4152", "32985", "370128", "3818601", "51861888", "658371429", "10494283968", "158197312701", "2894815734912", "50529852678321", "1043916757274880", "20707179214389201", "476720372375608320" ]

[ "nonn" ]

6

0

4

null

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

2019-05-29T20:00:10

oeisdata/seq/A012/A012258.seq

12382c53c1e6048491f11ee1083e5c39

A012259

Expansion of e.g.f. exp(arctanh(tan(x))).

[ "1", "1", "1", "5", "17", "121", "721", "6845", "58337", "698161", "7734241", "111973685", "1526099057", "25947503401", "419784870961", "8200346492525", "153563504618177", "3389281372287841", "72104198836466881", "1774459993676715365", "42270463533824671697", "1147649139272698443481" ]

[ "nonn" ]

50

0

4

[ "A012077", "A012085", "A012259", "A185411", "A202038" ]

null

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

2022-08-25T08:32:57

oeisdata/seq/A012/A012259.seq

ee61d2381c5254514e9d77767db5d51d

A012260

Expansion of e.g.f. exp(arctanh(arctan(x))).

[ "1", "1", "1", "1", "1", "9", "49", "57", "-447", "5169", "78561", "-93807", "-5655231", "31981689", "1014069393", "-3857766903", "-187639949439", "1058896281825", "51144433721793", "-286891166986335", "-16631972691697791", "108826313005021545" ]

[ "sign" ]

14

0

6

null

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

2022-09-08T08:44:38

oeisdata/seq/A012/A012260.seq

0ab3786e429259ebeafaf7c9d3c5b415

A012261

Expansion of e.g.f. exp(arctanh(sinh(x))).

[ "1", "1", "1", "4", "13", "76", "421", "3424", "26713", "277456", "2794441", "35345344", "436186213", "6504742336", "95033434861", "1632531979264", "27555582190513", "535821754153216", "10260037095841681", "222769351470429184", "4771143086720391613" ]

[ "nonn" ]

33

0

4

[ "A012109", "A012261" ]

null

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

2022-09-08T08:44:38

oeisdata/seq/A012/A012261.seq

b1339e3c5ea6e1e3f8d5accb61a53a2a

A012262

Expansion of e.g.f. exp(arctanh(arcsinh(x))).

[ "1", "1", "1", "2", "5", "24", "109", "552", "3177", "28032", "227961", "1778688", "15773229", "212383872", "2521786149", "25215328512", "294715261521", "5734229114880", "91106569198449", "1029078328135680", "14283819393505749", "410202091438571520" ]

[ "sign" ]

19

0

4

null

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

2022-09-08T08:44:38

oeisdata/seq/A012/A012262.seq

4bb4e958b202bf93eb984dbc510f9c4d

A012263

Expansion of e.g.f. exp(arctanh(arctanh(x))).

[ "1", "1", "1", "5", "17", "129", "769", "7797", "66849", "848481", "9506241", "145041093", "2007271089", "35799178401", "589807203777", "12045448529397", "230194642564161", "5298881528389185", "115219444193968257", "2952169020073027845" ]

[ "nonn" ]

15

0

4

null

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

2022-09-08T08:44:38

oeisdata/seq/A012/A012263.seq

2208ad5cc21165162791f8b194e3f79e

A012264

Number of real roots of x - x^3/3! + x^5/5! - ... + (-1)^n*x^(2n+1)/(2n+1)!.

[ "1", "3", "1", "3", "5", "3", "5", "7", "5", "7", "5", "7", "9", "7", "9", "7", "9", "11", "9", "11", "13", "11", "13", "11", "13", "15", "13", "15", "17", "15", "17", "15", "17", "19", "17", "19", "17", "19", "21", "19", "21", "23", "21", "23", "21", "23", "25", "23", "25", "23", "25", "27", "25", "27", "29", "27", "29", "27", "29", "31", "29", "31", "33" ]

[ "nonn", "nice" ]

16

0

2

[ "A012264", "A012265" ]

null

N. J. A. Sloane

2025-07-02T16:01:55

oeisdata/seq/A012/A012264.seq

afe5fdf71bc7ce06423076264945a814

A012265

x - x^3/3! + x^5/5! - ... + (-1)^n*x^(2n+1)/(2n+1)! has 2a(n)+1 real roots.

[ "0", "1", "0", "1", "2", "1", "2", "3", "2", "3", "2", "3", "4", "3", "4", "3", "4", "5", "4", "5", "6", "5", "6", "5", "6", "7", "6", "7", "8", "7", "8", "7", "8", "9", "8", "9", "8", "9", "10", "9", "10", "11", "10", "11", "10", "11", "12", "11", "12", "11", "12", "13", "12", "13", "14", "13", "14", "13", "14", "15", "14", "15", "16" ]

[ "nonn", "easy", "nice" ]

21

0

5

[ "A012264", "A012265" ]

null

N. J. A. Sloane

2025-07-02T16:01:55

oeisdata/seq/A012/A012265.seq

a13bd48da3074d39b90dc503db0be690

A012266

Duplicate of A009468.

[ "0", "0", "2", "6", "22", "100", "428", "1008", "12504", "325152", "5509368", "85326120", "1301444520" ]

[ "dead" ]

6

0

3

null

2007-05-11T03:00:00

oeisdata/seq/A012/A012266.seq

1c45dadb631613008de68a9ca9fd9d04

A012267

Expansion of e.g.f. arcsin(log(x+1)^2).

[ "0", "0", "2", "-6", "22", "-100", "668", "-6048", "64776", "-763488", "9918072", "-144472680", "2365739880", "-42879666960", "845124232080", "-17930092309920", "408038138491200", "-9939819541747200", "258294825756089760", "-7127596576224545760" ]

[ "sign" ]

27

0

3

null

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

2022-09-08T08:44:38

oeisdata/seq/A012/A012267.seq

58890d08b4e56438f8872770b48e6bf0

A012268

Duplicate of A009655.

[ "0", "0", "2", "6", "22", "100", "788", "8568", "103416", "1307808", "17722512", "264361680", "4373968080" ]

[ "dead" ]

6

0

3

null

2007-05-11T03:00:00

oeisdata/seq/A012/A012268.seq

d36d964c73777c0edf600f352bcda433

A012269

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

[ "0", "0", "2", "-6", "22", "-100", "308", "1512", "-51144", "869472", "-12406608", "155319120", "-1563312720", "6008315040", "296596492320", "-12739805608320", "357984190838400", "-8317532611046400", "160961311569285120", "-2183410259228574720" ]

[ "sign" ]

19

0

3

null

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

2022-09-08T08:44:38

oeisdata/seq/A012/A012269.seq

8c6a608467e637cbd2e935a7232bc421

A012270

Duplicate of A009585.

[ "0", "0", "2", "6", "22", "100", "668", "6048", "64776", "763488", "9676152", "131167080", "1900043880" ]

[ "dead" ]

6

0

3

null

2007-05-11T03:00:00

oeisdata/seq/A012/A012270.seq

b27bfca0a22c7b44f9d8696288f0627b

A012271

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

[ "0", "0", "2", "-6", "22", "-100", "428", "-1008", "-12504", "325152", "-5267448", "72020520", "-835748520", "6577169040", "36671947440", "-3513587807520", "114499586712000", "-2893590831936000", "61563908486205600", "-1035793335840588000" ]

[ "sign" ]

15

0

3

null

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

2022-09-08T08:44:38

oeisdata/seq/A012/A012271.seq

b6f3d97cd884e6ccf7675ea7fad7c8df

A012272

Duplicate of A009789.

[ "0", "0", "2", "6", "22", "100", "308", "1512", "51144", "869472", "12648528", "168624720", "2029008720" ]

[ "dead" ]

6

0

3

null

2007-05-11T03:00:00

oeisdata/seq/A012/A012272.seq

1933162699d85326185899e5b2e2744f

A012273

Expansion of e.g.f.: sec(log(x+1)*log(x+1)) = 1 + (12/4!)*x^4 - (120/5!)*x^5 + (1020/6!)*x^6 ...

[ "1", "0", "0", "0", "12", "-120", "1020", "-8820", "89628", "-1109808", "15992160", "-253374000", "4306032192", "-78317306496", "1529483150832", "-32072509450800", "719140990648848", "-17146103389588608", "432647748528869376" ]

[ "sign" ]

19

0

5

null

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

2022-09-08T08:44:38

oeisdata/seq/A012/A012273.seq

7f250802a7aaa1a1fe0cf36f3f5d3b92

A012274

Expansion of e.g.f.: sech(log(x+1)*log(x+1)).

[ "1", "0", "0", "0", "-12", "120", "-1020", "8820", "-72828", "505008", "-1376160", "-51546000", "1698674208", "-38050144704", "739129595568", "-12975913969200", "200099389809552", "-2317325113329792", "740464178471424" ]

[ "sign" ]

17

0

5

null

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

2022-09-08T08:44:38

oeisdata/seq/A012/A012274.seq

cd31e306eeecfca02ec302ccd4260e91

A012275

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

[ "1", "1", "3", "6", "53", "235", "2709", "20188", "278249", "3019693", "48281695", "692436338", "12717929157", "225943945071", "4727712830281", "99660715587704", "2354596166060273", "57197420701626009", "1511830772603161339" ]

[ "nonn" ]

14

0

3

null

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

2022-09-08T08:44:38

oeisdata/seq/A012/A012275.seq

291161182e19a172c79d3b46f7eb6bb9

A012276

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

[ "1", "1", "0", "-12", "-37", "55", "2352", "11872", "-55963", "-1946147", "-12422168", "127425716", "4206315423", "29351640435", "-573767182376", "-18652736291104", "-126637724451319", "4546934751296505", "146709365362329136" ]

[ "sign" ]

10

0

4

null

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

2022-09-08T08:44:38

oeisdata/seq/A012/A012276.seq

ad0552d162cbc0db8387a9dd836279a7

A012277

Expansion of e.g.f. arcsinh(exp(x)*log(x+1)).

[ "0", "1", "1", "1", "-6", "-17", "-35", "901", "4284", "4201", "-614267", "-4098107", "8297630", "1150691631", "9449070657", "-66322881767", "-4588041616648", "-41917690024495", "618354247728873", "33330584633391337", "310446365545119298" ]

[ "sign" ]

16

0

5

null

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

2022-09-08T08:44:38

oeisdata/seq/A012/A012277.seq

f237610c68f7aaa34b83bf1ceb598502

A012278

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

[ "0", "1", "1", "4", "12", "103", "595", "6508", "58800", "786973", "9744373", "155024956", "2434745852", "45189575715", "856361535783", "18256766891140", "403804360914560", "9755015402674937", "246067759361332137", "6656604425348335060", "188304809071878207052", "5645851709034522319007" ]

[ "nonn" ]

28

0

4

null

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

2022-09-08T08:44:38

oeisdata/seq/A012/A012278.seq

aa24ad40915678c36ec69dfd25be6a25

A012279

Expansion of e.g.f. sec(exp(x)*log(x+1)).

[ "1", "0", "1", "3", "16", "70", "580", "3850", "39940", "350544", "4408460", "48605788", "715662176", "9518173080", "160469679136", "2503106438040", "47524013744272", "851125166412928", "17967763294589776", "363412179220061872" ]

[ "nonn" ]

10

0

4

null

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

2022-09-08T08:44:38

oeisdata/seq/A012/A012279.seq

09fbcddf8cf94b7b3667e4c4ce72f75f

A012280

Expansion of e.g.f.: sech(exp(x)*log(x+1)).

[ "1", "0", "-1", "-3", "-6", "30", "270", "1400", "-3080", "-86184", "-893760", "-754688", "61595424", "1201314400", "5341239904", "-68598744240", "-2871938780672", "-25391249097088", "31527888993024", "10819112145879168", "155954430765392768" ]

[ "sign" ]

12

0

4

null

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

2022-09-08T08:44:38

oeisdata/seq/A012/A012280.seq

6ffc1623c1fd2024c5f3a7874e620a8a

A012281

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

[ "0", "0", "2", "-3", "4", "-20", "-10", "609", "-3880", "32040", "-352742", "3799565", "-44271460", "571990068", "-7830460482", "113493888585", "-1753811009808", "28760379830416", "-498456016769742", "9112758567973533", "-175322176912457996" ]

[ "sign" ]

18

0

3

null

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

2022-09-08T08:44:38

oeisdata/seq/A012/A012281.seq

bbeab93fe14cbfbc1a40f1cfcc4ff28e

A012282

Expansion of e.g.f.: tan(sin(x)*log(x+1)).

[ "0", "0", "2", "-3", "4", "-20", "350", "-3171", "21320", "-172080", "2217658", "-32208715", "433724300", "-5910937812", "92570087766", "-1651187049435", "30890555494032", "-592724842745984", "12014317527212658", "-261952174935402291" ]

[ "sign" ]

19

0

3

null

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

2022-09-08T08:44:38

oeisdata/seq/A012/A012282.seq

4aa8829c0bbb30d1d9e70e04e2c94b8e

A012283

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

[ "0", "0", "2", "-3", "4", "-20", "-130", "1869", "-12280", "100080", "-362822", "-7482475", "168953420", "-2715677172", "34715587062", "-205932278475", "-3285394779888", "157209810212416", "-4031590864355982", "71565905502128781" ]

[ "sign" ]

12

0

3

null

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

2022-09-08T08:44:38

oeisdata/seq/A012/A012283.seq

37727d3934add2ac15cef65c1dd218be

A012284

Expansion of e.g.f. sinh(sin(x)*log(x+1)).

[ "0", "0", "2", "-3", "4", "-20", "230", "-1911", "12920", "-104040", "1058458", "-11889955", "141336380", "-1804017852", "24962731950", "-371663464095", "5900573560752", "-99478198783184", "1776396441716658", "-33501559023746883", "665305926036550324" ]

[ "sign" ]

12

0

3

null

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

2022-09-08T08:44:38

oeisdata/seq/A012/A012284.seq

5352e87f976f5b7f22b0df3333a0e5ee

A012285

Expansion of e.g.f. arcsinh(sin(x)*log(x+1)).

[ "0", "0", "2", "-3", "4", "-20", "-10", "609", "-3880", "32040", "-110822", "-2853235", "62173340", "-984765132", "13116545598", "-105359946615", "-269704385808", "34712027932816", "-1001624343871182", "18826756309101213", "-210544812030819596" ]

[ "sign" ]

12

0

3

null

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

2022-09-08T08:44:38

oeisdata/seq/A012/A012285.seq

cf14aa51370e2c96aef6ab890fea5122

A012286

Expansion of e.g.f.: tanh(sin(x)*log(x+1)).

[ "0", "0", "2", "-3", "4", "-20", "-130", "1869", "-12280", "100080", "-604742", "-829675", "62508620", "-1158921972", "17643171702", "-190494456075", "1197368304912", "8324510449216", "-571700218304142", "14677422922560141", "-268070215275170156", "3735756713394119820", "-25728057443748879250" ]

[ "sign" ]

14

0

3

null

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

2022-09-08T08:44:38

oeisdata/seq/A012/A012286.seq

e87f43d22c6c00e0b9115139a3858eec

A012287

Expansion of e.g.f. arctanh(sin(x)*log(x+1))=2/2!*x^2-3/3!*x^3+4/4!*x^4-20/5!*x^5...

[ "0", "0", "2", "-3", "4", "-20", "350", "-3171", "21320", "-172080", "2459578", "-38861515", "540169100", "-7467693012", "125140866006", "-2480288923035", "50275271244432", "-1015574149625984", "21888753352226418", "-522647511904669491" ]

[ "sign" ]

13

0

3

null

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

2022-09-08T08:44:38

oeisdata/seq/A012/A012287.seq

cdb6057d5854c98d28bf56212cee90cd

A012288

Expansion of e.g.f. sec(sin(x)*log(x+1)).

[ "1", "0", "0", "0", "12", "-60", "210", "-1260", "18480", "-235872", "2421960", "-26091120", "365320296", "-5967877344", "97738612608", "-1617354429600", "29014419932160", "-574177721782144", "12059384791998912", "-262395430866467712" ]

[ "sign" ]

12

0

5

null

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

2022-09-08T08:44:38

oeisdata/seq/A012/A012288.seq

4f3fd74348908f4ef80730b64da336f3

A012289

Expansion of e.g.f.: sech(sin(x)*log(x+1)).

[ "1", "0", "0", "0", "-12", "60", "-210", "1260", "-1680", "-66528", "854040", "-9944880", "101761704", "-561845856", "-2175945408", "136635189600", "-3242837295360", "53779020559744", "-655909940939712", "4733948121328512", "61668138518505088" ]

[ "sign" ]

11

0

5

null

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

2022-09-08T08:44:38

oeisdata/seq/A012/A012289.seq

89dbe0c3f5cecca5bbff13b33fc1878c

A012290

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

[ "0", "1", "2", "0", "-24", "-140", "-8", "8960", "92736", "12240", "-14154208", "-210017280", "-50776704", "58549241920", "1133642065792", "435228385280", "-500888609593344", "-11981516394489600", "-6690495105515008", "7684815276420464640" ]

[ "sign" ]

20

0

3

null

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

2022-09-08T08:44:38

oeisdata/seq/A012/A012290.seq

efa950135a18dad7e3301fe2590087e7

A012291

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

[ "0", "1", "2", "1", "-12", "-75", "-98", "3141", "37128", "79145", "-4068838", "-70096919", "-208084932", "14605150365", "331136373622", "1267818101421", "-111869011278192", "-3149733764010415", "-14850194074608718", "1567505717936558161" ]

[ "sign" ]

12

0

3

null

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

2022-09-08T08:44:38

oeisdata/seq/A012/A012291.seq

ce62470cc10280b234214fbfab0f640c

A012292

Expansion of e.g.f. arctanh(sin(x)*exp(x)) = x+2/2!*x^2+4/3!*x^3+24/4!*x^4+180/5!*x^5...

[ "0", "1", "2", "4", "24", "180", "1432", "14544", "176064", "2382800", "36330272", "618520384", "11562021504", "235623136320", "5205288291712", "123834383495424", "3155999144761344", "85799392788650240", "2478387574846218752" ]

[ "nonn" ]

16

0

3

null

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

2022-09-08T08:44:38

oeisdata/seq/A012/A012292.seq

73bc2fbccddd950eec8c4c471697f6f1

A012293

Expansion of e.g.f. sec(sin(x)*exp(x))=1+1/2!*x^2+6/3!*x^3+25/4!*x^4+140/5!*x^5...

[ "1", "0", "1", "6", "25", "140", "1177", "10738", "104977", "1188120", "15191889", "211088350", "3187087209", "52357837220", "926871127977", "17553084005322", "354581844112801", "7614153761167920", "173108509344647457", "4153655608324341686" ]

[ "nonn" ]

12

0

4

null

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

2022-09-08T08:44:38

oeisdata/seq/A012/A012293.seq

edc9ea7f1dbd174ec3c3568a31790fa5

A012294

Expansion of e.g.f.: sech(sin(x)*exp(x)).

[ "1", "0", "-1", "-6", "-15", "60", "1023", "6062", "-9247", "-652680", "-7332289", "-13792350", "994947921", "19248140340", "119312444223", "-2747842718122", "-91993600741951", "-1070543140984080", "10423240065585023", "710021632610736714" ]

[ "sign" ]

15

0

4

null

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

2022-09-08T08:44:38

oeisdata/seq/A012/A012294.seq

a486804813b1e09b9ce6c0b355fc48e6

A012295

Duplicate of A009486.

[ "0", "2", "-8", "-88", "6592", "-251488", "4158592", "551599232", "-94759774208", "9549823734272" ]

[ "dead" ]

9

0

2

null

2023-02-05T09:22:18

oeisdata/seq/A012/A012295.seq

7936b4318108c18d12e22987f038b528

A012296

Duplicate of A009675.

[ "2", "-8", "272", "-13568", "1048832", "-128073728", "21002749952", "-4567924441088" ]

[ "dead" ]

9

0

1

null

2023-02-05T09:24:24

oeisdata/seq/A012/A012296.seq

0e238819f647ecb272e271511896af4a

A012297

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

[ "2", "-8", "-208", "13312", "161792", "-138042368", "9993992192", "4147254525952", "-1386315007787008", "-171033573395529728", "284350624150760456192", "-45336566464274820497408", "-87136608072231186709086208" ]

[ "sign" ]

11

0

1

null

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

2022-09-08T08:44:38

oeisdata/seq/A012/A012297.seq

caf5c8571c102947d1283c7e959ee97b

A012298

Duplicate of A009596.

[ "0", "2", "-8", "152", "-6848", "312992", "-17468288", "1385712512", "-143250864128", "17321985331712" ]

[ "dead" ]

10

0

2

null

2023-02-05T09:21:48

oeisdata/seq/A012/A012298.seq

27cd3df7e99120ec17d9a05e263ec376

A012299

Expansion of e.g.f. arcsinh(sin(x)*sin(x)), even-indexed terms only.

[ "0", "2", "-8", "-88", "6592", "-9568", "-49063808", "4426189952", "1122968737792", "-441081682390528", "-23926396899780608", "74405808039377364992", "-16597462789247237931008", "-19016633437725878038847488" ]

[ "sign" ]

20

0

2

null

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

2024-03-28T21:54:08

oeisdata/seq/A012/A012299.seq

abac0e768e5ebc33d7710261ad52f9bd

A012300

Duplicate of A009801.

[ "2", "-8", "-208", "13312", "-80128", "-84819968", "9993992192", "759755210752" ]

[ "dead" ]

7

0

1

null

2023-02-05T11:55:58

oeisdata/seq/A012/A012300.seq

949ec6bceb6eb90e0c8d12ee22599e22