Datasets:
christopher
/
oeis

Dataset card Data Studio Files
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2
sequence_id
stringlengths
7
7
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4
573
sequence
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1
348
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8
score
int64
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2.35k
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int64
-14,827
666,262,453B
offset_b
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0
635M
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cross_references
listlengths
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128
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231
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timestamp
timestamp[us]date
1999-12-11 03:00:00
2025-07-19 00:40:46
filename
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29
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32
32
A012501
cos(cos(x)*arctan(x))=1-1/2!*x^2+21/4!*x^4-645/6!*x^6+34153/8!*x^8...
[ "1", "-1", "21", "-645", "34153", "-2966505", "380114493", "-67244074989", "15717842398417", "-4694489063253585", "1744673430747688805", "-789702534539438543573", "427739642844597474379833", "-273184203052102765688128825" ]
[ "sign" ]
6
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2020-09-06T14:23:08
oeisdata/seq/A012/A012501.seq
beca7d9e9af0bb475c1dbbc9967485e2
A012502
sinh(cos(x)*arctan(x))=x-4/3!*x^3+1304/7!*x^7-109120/9!*x^9...
[ "1", "-4", "0", "1304", "-109120", "10816896", "-1441841024", "258762139648", "-60872480247808", "18224782774259712", "-6768839825021124608", "3053776998122900160512", "-1644778710545416370094080" ]
[ "sign" ]
4
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:50:51
oeisdata/seq/A012/A012502.seq
f39855a1a318d37fe2721c3d1189e4d9
A012503
arcsinh(cos(x)*arctan(x))=x-6/3!*x^3+108/5!*x^5-5880/7!*x^7...
[ "1", "-6", "108", "-5880", "624848", "-110121440", "29157594048", "-10831610048896", "5375188617697536", "-3434391975840699904", "2745651126153216330752", "-2684651090523817558325248", "3151501790727433916335149056" ]
[ "sign" ]
6
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2014-01-21T11:44:25
oeisdata/seq/A012/A012503.seq
de38076e59e77594db5178087788810d
A012504
tanh(cos(x)*arctan(x))=x-7/3!*x^3+165/5!*x^5-9931/7!*x^7...
[ "1", "-7", "165", "-9931", "1037033", "-167246319", "38489315917", "-11958291252467", "4819985549046353", "-2445005516326951767", "1523950240372673482357", "-1144729097700954584840347", "1019812687197159075947289145" ]
[ "sign" ]
4
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:50:52
oeisdata/seq/A012/A012504.seq
e2bcc8f94c614711559ff5605db3ed31
A012505
arctanh(cos(x)*arctan(x))=x-3/3!*x^3-27/5!*x^5+777/7!*x^7+48905/9!*x^9...
[ "1", "-3", "-27", "777", "48905", "-4320107", "-424303635", "77237001761", "20512289602833", "-6321209675239123", "-1704909797900721931", "812189572458422888249", "493715837509806144441881", "-331434668084376519747747387" ]
[ "sign" ]
6
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-03-24T11:59:51
oeisdata/seq/A012/A012505.seq
d26ce96d798ebc8ab35f3aa7de66d4a0
A012506
cosh(cos(x)*arctan(x))=1+1/2!*x^2-19/4!*x^4+445/6!*x^6-14663/8!*x^8...
[ "1", "1", "-19", "445", "-14663", "718265", "-50970203", "4876389557", "-548752599567", "47436062951281", "12631837146241245", "-15669443125044502867", "12502889747981009020841", "-9927639811374322485212375" ]
[ "sign" ]
6
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-10-15T17:04:30
oeisdata/seq/A012/A012506.seq
6b666cbff218242225d7b09a43444eee
A012507
sec(cos(x)*arctan(x))=1+1/2!*x^2-15/4!*x^4+105/6!*x^6+8897/8!*x^8...
[ "1", "1", "-15", "105", "8897", "-664815", "-4523343", "8138992953", "-972054629887", "-115219461350367", "72803853486273265", "-6666182957939643127", "-7549270905441932464191", "4123382958180269131627825" ]
[ "sign" ]
4
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:50:52
oeisdata/seq/A012/A012507.seq
4992bf67ce7473ab2d14b1590f77990d
A012508
sech(cos(x)*arctan(x))=1-1/2!*x^2+25/4!*x^4-1105/6!*x^6+91313/8!*x^8...
[ "1", "-1", "25", "-1105", "91313", "-12232385", "2400320393", "-649247356433", "231544408317537", "-105271075840787713", "59429582363323624185", "-40787189186519841731153", "33444147237661076070865681" ]
[ "sign" ]
4
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:50:52
oeisdata/seq/A012/A012508.seq
4b7b9ab89ca8f809be43c21b6b49d6c9
A012509
E.g.f.: -log(cos(x)*cos(x)) (even powers only).
[ "0", "2", "4", "32", "544", "15872", "707584", "44736512", "3807514624", "419730685952", "58177770225664", "9902996106248192", "2030847773013704704", "493842960380415967232", "140503203207887919775744", "46238368375619195682947072", "17427925514250338592341622784", "7458815407441059142195019251712" ]
[ "nonn" ]
44
0
2
[ "A000182", "A012509" ]
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2019-09-29T09:53:28
oeisdata/seq/A012/A012509.seq
627f066543d2f0bc74b3cb75ec689787
A012510
Expansion of e.g.f.: sin(sinh(x)*log(x+1))=2/2!*x^2-3/3!*x^3+12/4!*x^4-40/5!*x^5...
[ "0", "0", "2", "-3", "12", "-40", "70", "189", "-7896", "102528", "-1237862", "14606405", "-176349580", "2218114392", "-29206309106", "404834121405", "-5910831145072", "90961908805184", "-1474337506709838", "25140576842935821", "-450346980602582884" ]
[ "sign" ]
8
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2017-09-22T16:48:28
oeisdata/seq/A012/A012510.seq
5b15192b431e2d92f6c8e9a0adf09ea9
A012511
Expansion of e.g.f.: arcsin(sinh(x)*log(x+1))=2/2!*x^2-3/3!*x^3+12/4!*x^4-40/5!*x^5...
[ "0", "0", "2", "-3", "12", "-40", "310", "-2331", "22344", "-214992", "2532058", "-32683915", "481944980", "-7585016088", "130778587966", "-2420926296075", "48554376131408", "-1038765449765536", "23704180919254962", "-572815315696075155" ]
[ "sign" ]
6
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-02-03T20:10:58
oeisdata/seq/A012/A012511.seq
d8dc80d2f30cdeffe8b3fd326734574a
A012512
Expansion of e.g.f.: tan(sinh(x)*log(x+1))=2/2!*x^2-3/3!*x^3+12/4!*x^4-40/5!*x^5...
[ "0", "0", "2", "-3", "12", "-40", "430", "-3591", "37464", "-373752", "4507738", "-58823875", "870967460", "-13719012528", "234072634822", "-4250060142615", "82733999849648", "-1710175098180496", "37504812533836722", "-867602777991744483" ]
[ "sign" ]
6
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2016-01-18T14:18:33
oeisdata/seq/A012/A012512.seq
18fed6628c8be855122e31db18826a45
A012513
Expansion of e.g.f. arctan(sinh(x) * log(x+1)).
[ "0", "0", "2", "-3", "12", "-40", "-50", "1449", "-23016", "261288", "-2306342", "15798365", "33379940", "-3972201168", "100308059878", "-1917671123655", "28943854480688", "-288514829730256", "-1435208344849998", "189049167829499229" ]
[ "sign" ]
11
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2021-07-04T20:03:22
oeisdata/seq/A012/A012513.seq
25873b2963c1503f0b74307ace42d35e
A012514
Expansion of e.g.f.: sinh(sinh(x)*log(x+1))=2/2!*x^2-3/3!*x^3+12/4!*x^4-40/5!*x^5...
[ "0", "0", "2", "-3", "12", "-40", "310", "-2331", "22344", "-214992", "2290138", "-26031115", "322277780", "-4298532888", "61722080446", "-947673715275", "15499274051408", "-268866053899936", "4930878490414002", "-95317757163840915" ]
[ "sign" ]
6
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2017-02-25T09:25:59
oeisdata/seq/A012/A012514.seq
fce9734497439134092d1dc20c09b179
A012515
Expansion of e.g.f.: tanh(sinh(x)*log(x+1))=2/2!*x^2-3/3!*x^3+12/4!*x^4-40/5!*x^5...
[ "0", "0", "2", "-3", "12", "-40", "-50", "1449", "-23016", "261288", "-2548262", "22451165", "-126287260", "-685717968", "42875324518", "-1054666581255", "20298673936688", "-334720477218256", "4520234227269042", "-36137161587189411" ]
[ "sign" ]
6
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2018-04-11T16:45:44
oeisdata/seq/A012/A012515.seq
9cae246de3555316b1697d7f08d7f02c
A012516
Expansion of e.g.f. arctanh(sinh(x) * log(x+1)).
[ "0", "0", "2", "-3", "12", "-40", "430", "-3591", "37464", "-373752", "4749658", "-65476675", "1030634660", "-17005495728", "307003733062", "-5926728736215", "123925742441648", "-2752109508497296", "65023509028085682", "-1622290259238643683" ]
[ "sign" ]
9
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2018-07-19T21:19:54
oeisdata/seq/A012/A012516.seq
50b6cbaf8037f9a4596634298e7e61e3
A012517
Expansion of e.g.f.: sec(sinh(x)*log(x+1))=1+12/4!*x^4-60/5!*x^5+450/6!*x^6-2940/7!*x^7...
[ "1", "0", "0", "0", "12", "-60", "450", "-2940", "30800", "-336672", "4362120", "-57707760", "847204776", "-13292039904", "228041125312", "-4172767915680", "81658781501440", "-1692115320051584", "37160192133050304", "-860809698597753216" ]
[ "sign" ]
6
0
5
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2022-02-13T12:32:49
oeisdata/seq/A012/A012517.seq
b5c305c457d128540ead4e291b58871e
A012518
E.g.f.: sech(sinh(x)*log(x+1))=1-12/4!*x^4+60/5!*x^5-450/6!*x^6+2940/7!*x^7...
[ "1", "0", "0", "0", "-12", "60", "-450", "2940", "-14000", "34272", "929880", "-22680240", "373861224", "-5345779296", "65277500288", "-619227292320", "1524395375360", "135262063693184", "-5049805793018304", "129393583799366016" ]
[ "sign" ]
6
0
5
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-03-20T17:06:36
oeisdata/seq/A012/A012518.seq
6bea65ec2cc23f40bf1a1c561740818b
A012519
Expansion of e.g.f. arcsin(sinh(x) * exp(x)).
[ "0", "1", "2", "5", "20", "125", "1022", "10145", "119240", "1621625", "25018202", "431595485", "8233157660", "172077583925", "3910293621782", "95985774268025", "2531103994315280", "71356674948823025", "2141700448802291762" ]
[ "nonn" ]
14
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2025-05-11T19:03:32
oeisdata/seq/A012/A012519.seq
91fc3e31b33698011e876c03e9e1677f
A012520
Expansion of e.g.f. arctan(sinh(x) * exp(x)).
[ "0", "1", "2", "2", "-16", "-160", "-688", "3152", "99584", "992000", "31232", "-190094848", "-3600265216", "-20655831040", "737829988352", "25775848957952", "333499542339584", "-4040309414625280", "-311707129046499328", "-7000770202915176448" ]
[ "sign" ]
9
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2018-07-19T21:20:16
oeisdata/seq/A012/A012520.seq
7aceaff8f8f9e8fb02117dd955b3fb7b
A012521
E.g.f.: arctanh(sinh(x)*exp(x)).
[ "0", "1", "2", "6", "32", "240", "2192", "23856", "303872", "4427520", "72545792", "1320608256", "26445350912", "577722163200", "13672510932992", "348466876717056", "9515645659185152", "277168473987809280", "8577847096804769792", "281084141232170336256", "9722444816080638574592", "353990026542011001077760" ]
[ "nonn" ]
18
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-10-24T10:14:46
oeisdata/seq/A012/A012521.seq
ff17a9fad94ba474e2c48704ef8da8d4
A012522
sec(sinh(x)*exp(x))=1+1/2!*x^2+6/3!*x^3+33/4!*x^4+220/5!*x^5...
[ "1", "0", "1", "6", "33", "220", "1857", "18578", "210497", "2666808", "37529089", "581350110", "9823649121", "179778809236", "3542606470977", "74792059538282", "1684263304319105", "40298130761503344", "1020885056930919937" ]
[ "nonn" ]
4
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:50:52
oeisdata/seq/A012/A012522.seq
ebe761d6e39c0b1911e4659385f3c138
A012523
sech(sinh(x)*exp(x))=1-1/2!*x^2-6/3!*x^3-23/4!*x^4-20/5!*x^5...
[ "1", "0", "-1", "-6", "-23", "-20", "743", "9422", "64433", "19032", "-7391889", "-131529310", "-1204724391", "2412614724", "343942765463", "7487171500918", "80039031954145", "-547487821933904", "-48046886269866657", "-1195424254383765686" ]
[ "sign" ]
6
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-12-15T17:50:41
oeisdata/seq/A012/A012523.seq
0a78de928c077963ad0f0d3bc3850d26
A012524
Expansion of sin(sinh(x)*sin(x)).
[ "2", "-128", "50432", "-63423488", "186761510912", "-1077443663495168", "10868880846196047872", "-176707410321941586771968", "4359687422323728561012211712" ]
[ "sign" ]
7
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:50:52
oeisdata/seq/A012/A012524.seq
31b2cad1378f56146cdf2ea0ea6dff15
A012525
arcsin(sinh(x)*sin(x)) = 2/2!*x^2+112/6!*x^6+252032/10!*x^10...
[ "2", "112", "252032", "3534410752", "172897986486272", "21863258933621358592", "5949965523659671600627712", "3079247941776170929023071813632" ]
[ "nonn" ]
6
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2023-03-02T14:17:11
oeisdata/seq/A012/A012525.seq
0ce81bbefdf91795cad55acf32bc65ab
A012526
tan(sinh(x)*sin(x))=2/2!*x^2+232/6!*x^6+443552/10!*x^10...
[ "2", "232", "443552", "4070626432", "114229813187072", "7662813919487567872", "1050565400687692105490432", "264025846282089475815489175552" ]
[ "nonn" ]
7
0
1
null
null
R. H. Hardin, Patrick Demichel (patrick.demichel(AT)hp.com)
2012-03-31T12:34:57
oeisdata/seq/A012/A012526.seq
dee6204a1cf335eae340e910ae8f6c3b
A012527
arctan(sinh(x)*sin(x))=2/2!*x^2-248/6!*x^6+766112/10!*x^10...
[ "2", "-248", "766112", "-13434220928", "784153824645632", "-115100516909469022208", "35709161573583248175767552", "-20800482387908029348756471513088" ]
[ "sign" ]
5
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:50:52
oeisdata/seq/A012/A012527.seq
9d88cfdb8e03345f8ac90253b98065f5
A012528
sinh(sinh(x)*sin(x))=2/2!*x^2+112/6!*x^6+10112/10!*x^10...
[ "2", "112", "10112", "-17297408", "-15034114048", "164133555208192", "55023491428646912", "-16342277967934744690688", "148703244592249785068552192", "6917318875805359573600621821952", "-349192103360082371369402852240785408", "-3233378223427683795744541104589701644288" ]
[ "sign" ]
12
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2014-12-15T11:56:27
oeisdata/seq/A012/A012528.seq
72d55d8dfe0e7caee9ce8b3d892df155
A012529
Expansion of tanh(sinh(x)*sin(x)).
[ "2", "-248", "524192", "-5362156928", "167986518651392", "-12583779264376322048", "1926593546409409355620352", "-540704478247409702156924715008" ]
[ "sign" ]
7
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:50:52
oeisdata/seq/A012/A012529.seq
e9e27270f898bf3325f55213c0aa324a
A012530
arctanh(sinh(x)*sin(x)) = 2/2!*x^2+232/6!*x^6+685472/10!*x^10...
[ "2", "232", "685472", "11496925312", "641870470410752", "90115671250751137792", "26741121618547455928082432", "14898765702188922919730883100672", "14301272675149517137926114108443328512", "22156614594176569412220482693952524899581952" ]
[ "nonn" ]
14
0
1
[ "A009359", "A012530" ]
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-11-03T07:52:54
oeisdata/seq/A012/A012530.seq
d6781228337566156b48e94751330698
A012531
sec(sinh(x)*sin(x)) = 1+12/4!*x^4+7952/8!*x^8+36180672/12!*x^12...
[ "1", "12", "7952", "36180672", "603907465472", "26832156798077952", "2614680400223651827712", "490948618119249163449188352", "161900900520087402624595511017472" ]
[ "nonn" ]
7
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2022-09-22T10:56:49
oeisdata/seq/A012/A012531.seq
13929a168486c8fbf435dcdf1b41d8fa
A012532
sech(sinh(x)*sin(x)) = 1-12/4!*x^4+8848/8!*x^8-45051072/12!*x^12...
[ "1", "-12", "8848", "-45051072", "840261660928", "-41695924253002752", "4537436258866404364288", "-951427888272965045905047552", "350377450379688317757442429616128", "-211362906255307072670284412178232246272", "197818950974274356812042952303539935429787648" ]
[ "sign" ]
8
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2017-11-12T10:35:46
oeisdata/seq/A012/A012532.seq
463a4498c7edf5a3991d52304705b9ed
A012533
exp(sinh(x)*arcsin(x))=1+2/2!*x^2+20/4!*x^4+440/6!*x^6+17488/8!*x^8...
[ "1", "2", "20", "440", "17488", "1122208", "108352576", "14910020736", "2796629584128", "688871838614016", "216055818814010368", "84109725396766971904", "39796388326939272466432", "22489039556700087459291136", "14957634359368597313889648640", "11564305283318420635370333569024" ]
[ "nonn" ]
6
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2014-05-29T17:20:55
oeisdata/seq/A012/A012533.seq
673c26393fa8d717a9f6724146b6d3d0
A012534
sin(sinh(x)*arcsin(x))=2/2!*x^2+8/4!*x^4-40/6!*x^6-4352/8!*x^8...
[ "2", "8", "-40", "-4352", "-233312", "-14783360", "-1406171520", "-215345283072", "-48522307444224", "-14515971445110784", "-5456413300747012096", "-2505550929805243777024", "-1379341726073854089519104" ]
[ "sign" ]
4
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:50:52
oeisdata/seq/A012/A012534.seq
6e25f570ca8b75bc7534058cfff8a5d6
A012535
arcsin(sinh(x)*arcsin(x))=2/2!*x^2+8/4!*x^4+200/6!*x^6+9088/8!*x^8...
[ "2", "8", "200", "9088", "815008", "107966080", "21110274432", "5547859611648", "1915915213103616", "835475489428146176", "450640330168225851392", "294111441801356743442432", "228643425697131126294224896" ]
[ "nonn" ]
4
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:50:52
oeisdata/seq/A012/A012535.seq
fc4ab889b8109939ff5013e5faddb7a1
A012536
tan(sinh(x)*arcsin(x))=2/2!*x^2+8/4!*x^4+320/6!*x^6+15808/8!*x^8...
[ "0", "2", "8", "320", "15808", "1429888", "189299200", "34859305728", "8524943044608", "2667935751684096", "1040196824976736256", "494214397360327786496", "281064144909266002903040", "188495115535527543004266496" ]
[ "nonn" ]
8
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-02-06T10:15:01
oeisdata/seq/A012/A012536.seq
9b26eb835952b2acdcdcf9b3191131f5
A012537
arctan(sinh(x)*arcsin(x))=2/2!*x^2+8/4!*x^4-160/6!*x^6-11072/8!*x^8...
[ "2", "8", "-160", "-11072", "59008", "103467520", "9545313024", "-2353856581632", "-975598930427904", "37877907269697536", "166837459499821137920", "45962446989093848219648", "-37193338901666118751944704" ]
[ "sign" ]
7
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-11-21T12:46:01
oeisdata/seq/A012/A012537.seq
363dcb1dd3f065c4b8ae4d8d13c436fa
A012538
cos(sinh(x)*arcsin(x))=1-12/4!*x^4-240/6!*x^6-5040/8!*x^8...
[ "1", "0", "-12", "-240", "-5040", "-145920", "-9256896", "-1349048064", "-289962366720", "-78050616729600", "-25779840881748992", "-10375373322500206592", "-5028804353588061089792", "-2895752923791276634275840" ]
[ "sign" ]
4
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:50:52
oeisdata/seq/A012/A012538.seq
358556c985abf0348bca974af47744ee
A012539
sinh(sinh(x)*arcsin(x))=2/2!*x^2+8/4!*x^4+200/6!*x^6+9088/8!*x^8...
[ "2", "8", "200", "9088", "573088", "54743680", "7549206912", "1418652930048", "349780182483456", "109789748881688576", "42770510180602898432", "20248998750034801098752", "11448712479091073092919296" ]
[ "nonn" ]
4
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:50:52
oeisdata/seq/A012/A012539.seq
322de47c5052269b2e14c08189be3bb3
A012540
tanh(sinh(x)*arcsin(x))=2/2!*x^2+8/4!*x^4-160/6!*x^6-11072/8!*x^8...
[ "2", "8", "-160", "-11072", "-182912", "50245120", "7608017664", "26249146368", "-262793796747264", "-58964881233854464", "7005062900187299840", "9928554014089367257088", "2780197098515017535389696" ]
[ "sign" ]
6
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2022-04-18T17:43:04
oeisdata/seq/A012/A012540.seq
739df40ff27f4e61186d045a2543f751
A012541
arctanh(sinh(x)*arcsin(x))=2/2!*x^2+8/4!*x^4+320/6!*x^6+15808/8!*x^8...
[ "0", "2", "8", "320", "15808", "1671808", "242521600", "52294963968", "14823920529408", "5496196568825856", "2548323017071149056", "1453790822661022908416", "997862723859007908085760", "812410035086507459409412096" ]
[ "nonn" ]
10
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-02-05T09:34:42
oeisdata/seq/A012/A012541.seq
b9ede5d7dd10ad92dedbd89d15838e36
A012542
cosh(sinh(x)*arcsin(x))=1+12/4!*x^4+240/6!*x^6+8400/8!*x^8...
[ "1", "0", "12", "240", "8400", "549120", "53608896", "7360813824", "1377976654080", "339091656130560", "106266069932321792", "41339215216164073472", "19547389576904471367680", "11040327077609014366371840" ]
[ "nonn" ]
6
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2020-10-20T15:23:47
oeisdata/seq/A012/A012542.seq
72eb41e6591ff877bb67199accf9ac31
A012543
sec(sinh(x)*arcsin(x))=1+12/4!*x^4+240/6!*x^6+15120/8!*x^8...
[ "1", "0", "12", "240", "15120", "1355520", "182229696", "33914060544", "8338432876800", "2621544212398080", "1025337444571630592", "488344333262321119232", "278250960368816815149056", "186888075247900824522915840" ]
[ "nonn" ]
6
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-04-13T10:20:17
oeisdata/seq/A012/A012543.seq
3cd3c5f823f50f08b27e585e4a9824d3
A012544
sech(sinh(x)*arcsin(x))=1-12/4!*x^4-240/6!*x^6+1680/8!*x^8...
[ "1", "0", "-12", "-240", "1680", "660480", "39530304", "-3855231744", "-1466146656000", "-147651751649280", "43245441015313408", "21785411128189063168", "453349606338812022784", "-4374564365537166405795840" ]
[ "sign" ]
6
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2023-06-03T11:24:08
oeisdata/seq/A012/A012544.seq
b3d3973f67d36ee6096e918f0f067b89
A012545
Duplicate of A009514.
[ "2", "12", "22", "-6888", "-664918", "-59975388", "-5718140738", "-547324724688" ]
[ "dead" ]
7
0
1
null
null
null
2023-02-05T11:55:23
oeisdata/seq/A012/A012545.seq
c54094d539d53c1fcfcff8ebec14028f
A012546
arcsin(sinh(x)*tan(x))=2/2!*x^2+12/4!*x^4+262/6!*x^6+13272/8!*x^8...
[ "2", "12", "262", "13272", "1199882", "172207332", "35836412302", "10199550294192", "3802117533461522", "1797033345886449852", "1049846428673838251542", "742763896072793206770312", "625784289590468519088366362" ]
[ "nonn" ]
7
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-11-21T12:46:01
oeisdata/seq/A012/A012546.seq
042b9ac019fa7d8a5ac12f38670b073c
A012547
Duplicate of A009706.
[ "2", "12", "382", "23352", "2223002", "318236292", "63069898582", "16506522005232" ]
[ "dead" ]
4
0
1
null
null
null
2008-06-29T03:00:00
oeisdata/seq/A012/A012547.seq
abdf990ab5c0b8b58c8e759155ec2619
A012548
Expansion of e.g.f. arctan(sinh(x)*tan(x)) (even powers only).
[ "0", "2", "12", "-98", "-16968", "-780838", "93371652", "31402903222", "2306688997872", "-1741952370835918", "-849143623135762308", "-14075683397521166258", "228742196475611564627112", "136676421833398225367464202", "-34106209758743782233592937868", "-128144470665734286260829913072538" ]
[ "sign" ]
9
0
2
[ "A012548", "A012816" ]
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2024-04-23T19:56:48
oeisdata/seq/A012/A012548.seq
6474f7b108d3874a5d723a39551b9da7
A012549
Duplicate of A009610.
[ "2", "12", "262", "13272", "957962", "92373732", "11700940942", "1898239676592" ]
[ "dead" ]
4
0
1
null
null
null
2008-06-29T03:00:00
oeisdata/seq/A012/A012549.seq
f0ad31a4f731d670daacdcfb6244f210
A012550
Duplicate of A009816.
[ "2", "12", "-98", "-16968", "-1022758", "13538052", "18891204022", "3769346994672" ]
[ "dead" ]
7
0
1
null
null
null
2023-02-05T11:55:47
oeisdata/seq/A012/A012550.seq
3a65c7bde4fbcc2994d67f3f454db6c4
A012551
arctanh(sinh(x)*tan(x))=2/2!*x^2+12/4!*x^4+382/6!*x^6+23352/8!*x^8...
[ "2", "12", "382", "23352", "2464922", "398069892", "91079960662", "28062488827632", "11197997254599602", "5618500857338248572", "3461960315033768973742", "2569953015248391982844712", "2262189595338137069466955082" ]
[ "nonn" ]
8
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-10-24T10:14:43
oeisdata/seq/A012/A012551.seq
4ee501e634a2e715fcff2cb20d4f9d21
A012552
sec(sinh(x)*tan(x))=1+12/4!*x^4+360/6!*x^6+21392/8!*x^8...
[ "1", "0", "12", "360", "21392", "2157120", "312620352", "62372069760", "16405335464192", "5496449323898880", "2285903378752576512", "1155546066959150254080", "697824091645377743654912", "496179920290601448240168960" ]
[ "nonn" ]
6
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2021-11-12T15:19:43
oeisdata/seq/A012/A012552.seq
ac9017c13f637383ba86a754cb61920c
A012553
sech(sinh(x)*tan(x))=1-12/4!*x^4-360/6!*x^6-4592/8!*x^8...
[ "1", "0", "-12", "-360", "-4592", "866880", "144205248", "10276506240", "-1972062209792", "-1066588240250880", "-219129099375885312", "33054966279836497920", "54554661987210721497088", "24677742880461438548951040" ]
[ "sign" ]
4
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:50:53
oeisdata/seq/A012/A012553.seq
97814ebba3c0ab3df8ba4738c6dee0d9
A012554
exp(sinh(x)*arctan(x))=1+2/2!*x^2+8/4!*x^4+110/6!*x^6+520/8!*x^8...
[ "1", "2", "8", "110", "520", "80458", "-4654604", "820778478", "-157200016272", "41164154565906", "-13482969489167252", "5454988601609663734", "-2666562535164656750936", "1549911678027846498248986", "-1056435556882844258622185948", "834565745980558555804948223614" ]
[ "sign" ]
6
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2018-05-07T17:33:17
oeisdata/seq/A012/A012554.seq
d5b0b62e59aa8b579d503ac88ed616ef
A012555
sin(sinh(x)*arctan(x))=2/2!*x^2-4/4!*x^4-10/6!*x^6-1160/8!*x^8...
[ "2", "-4", "-10", "-1160", "25258", "861940", "-503620962", "179232404208", "-65782233424302", "27609266214439916", "-13506425126580217786", "7702534973614205704808", "-5093447847556265363925254", "3877832071517816281261654756" ]
[ "sign" ]
4
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:50:53
oeisdata/seq/A012/A012555.seq
98e2da7b0d408cc08f64a2f8389f4ba8
A012556
arcsin(sinh(x)*arctan(x))=2/2!*x^2-4/4!*x^4+230/6!*x^6-7880/8!*x^8...
[ "2", "-4", "230", "-7880", "922378", "-104579660", "22872643950", "-5494080273552", "1980593407445778", "-817099673512164244", "445251089168585478902", "-279905701143388803184984", "216483300093818109473976346" ]
[ "sign" ]
4
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:50:53
oeisdata/seq/A012/A012556.seq
398afc20ee7962698333c21871062011
A012557
tan(sinh(x)*arctan(x))=2/2!*x^2-4/4!*x^4+350/6!*x^6-11240/8!*x^8...
[ "2", "-4", "350", "-11240", "1461658", "-167279660", "35689423926", "-8594866078032", "2902777731046578", "-1163594305273709524", "584328120817240344206", "-346295976826690961613880", "244030359200524004600252746" ]
[ "sign" ]
6
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-03-01T10:18:44
oeisdata/seq/A012/A012557.seq
b033e1f6f4ef2b1377b3a0d66d59aca6
A012558
arctan(sinh(x)*arctan(x))=2/2!*x^2-4/4!*x^4-130/6!*x^6+2200/8!*x^8...
[ "0", "2", "-4", "-130", "2200", "393178", "-36230060", "-2241493098", "696842413488", "151155071419698", "-94998751466350804", "4870009119362109230", "9231493784347343489864", "1174397467642045406094346" ]
[ "sign" ]
6
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2016-11-28T19:46:33
oeisdata/seq/A012/A012558.seq
627df5aa5888e0e58360fa5578d048f3
A012559
cos(sinh(x)*arctan(x))=1-12/4!*x^4+120/6!*x^6-5040/8!*x^8...
[ "1", "0", "-12", "120", "-5040", "398400", "-42267456", "6511220352", "-1348919320320", "361546293368832", "-121866178161646592", "50449587034359175168", "-25164869672254098452480", "14886957060645519281602560" ]
[ "sign" ]
9
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-10-17T04:19:49
oeisdata/seq/A012/A012559.seq
c5ad63403e61989b9294508b0b1bd76c
A012560
sinh(sinh(x)*arctan(x))=2/2!*x^2-4/4!*x^4+230/6!*x^6-7880/8!*x^8...
[ "2", "-4", "230", "-7880", "680458", "-77968460", "12944005230", "-2852439671952", "810954585734418", "-288565474593329044", "125662055644822916342", "-65733137963856533872984", "40670869816508001470654746" ]
[ "sign" ]
4
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:50:53
oeisdata/seq/A012/A012560.seq
c509b1895d53e86c355f282459646576
A012561
tanh(sinh(x)*arctan(x))=2/2!*x^2-4/4!*x^4-130/6!*x^6+2200/8!*x^8...
[ "2", "-4", "-130", "2200", "151258", "-9618860", "-546359658", "83826810288", "15550415673138", "-5684890840251604", "671714199027714350", "-198489523044256423096", "248879210344083276692746" ]
[ "sign" ]
6
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2023-04-01T12:55:29
oeisdata/seq/A012/A012561.seq
d5ba78a78c8460750bb3c012a65af32b
A012562
arctanh(sinh(x)*arctan(x)) = 2/2!*x^2 - 4/4!*x^4 + 350/6!*x^6 - 11240/8!*x^8 + ...
[ "0", "2", "-4", "350", "-11240", "1703578", "-193890860", "49492653366", "-12321392081232", "4919573673167538", "-2124948350723616724", "1246509899975408733326", "-820629733751515166342200", "671843179144303883329974346", "-622270861646882104886119580924" ]
[ "sign" ]
12
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2016-11-28T19:47:32
oeisdata/seq/A012/A012562.seq
459b852c54e1267dfbbea7e62075b259
A012563
cosh(sinh(x)*arctan(x))=1+12/4!*x^4-120/6!*x^6+8400/8!*x^8...
[ "1", "0", "12", "-120", "8400", "-600000", "73313856", "-12123226752", "2695239655680", "-769790431168512", "275082505104161792", "-120207067043213252608", "63066575428691877122048", "-39120958138480154972405760" ]
[ "sign" ]
4
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:50:53
oeisdata/seq/A012/A012563.seq
053d51d556ef2921eeed5d274fcc3275
A012564
sec(sinh(x)*arctan(x))=1+12/4!*x^4-120/6!*x^6+15120/8!*x^8...
[ "1", "0", "12", "-120", "15120", "-1003200", "175323456", "-30612097152", "8428742150400", "-2694273274447872", "1128666024421563392", "-559638290295925823488", "336992041752644836265984", "-237186459370976230365020160" ]
[ "sign" ]
6
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2019-07-04T12:54:41
oeisdata/seq/A012/A012564.seq
ea61e96531c00da575160f564367a269
A012565
sech(sinh(x)*arctan(x))=1-12/4!*x^4+120/6!*x^6+1680/8!*x^8...
[ "1", "0", "-12", "120", "1680", "-4800", "-20091456", "2552065152", "-264925689600", "68708953577472", "-29508519541947392", "12189637912025356288", "-5505843502429896863744", "3137663619884947867484160" ]
[ "sign" ]
4
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:50:53
oeisdata/seq/A012/A012565.seq
8bba5549a74fb0780d90574abafe13b9
A012566
arcsin(sinh(x)*cos(x))=x-1/3!*x^3-15/5!*x^5-201/7!*x^7+1025/9!*x^9...
[ "1", "-1", "-15", "-201", "1025", "505199", "45962865", "672778599", "-885967354495", "-245542561428001", "-22172563647911055", "14487811265589717399", "9628380148436165613185", "2365618724494349248126799" ]
[ "sign" ]
6
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2016-12-25T15:34:00
oeisdata/seq/A012/A012566.seq
d84b916cb03963ab99430958c4398303
A012567
E.g.f.: arctan(sinh(x)*cos(x)) = x - 4/3!*x^3 + 60/5!*x^5 - 2784/7!*x^7 + 225680/9!*x^9...
[ "1", "-4", "60", "-2784", "225680", "-29884864", "5784292800", "-1544557830144", "543835022577920", "-244140571254682624", "136105808837097815040", "-92250989686413124706304", "74707244097461420738908160" ]
[ "sign" ]
15
1
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-05-21T17:35:09
oeisdata/seq/A012/A012567.seq
0d9c50e4027583c4d0c5d0374d8a2fa9
A012568
arctanh(sinh(x)*cos(x))=x-20/5!*x^5-560/7!*x^7-7920/9!*x^9...
[ "1", "0", "-20", "-560", "-7920", "1034880", "172569280", "12339608320", "-1902800305920", "-1037015219466240", "-208832669083243520", "24402030281141555200", "43057075784745711636480", "18939654540025835056496640" ]
[ "sign" ]
9
0
3
[ "A009357", "A012568" ]
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2022-06-22T17:33:20
oeisdata/seq/A012/A012568.seq
06e83422d7dc5a3a40f2df776232d8aa
A012569
sec(sinh(x)*cos(x))=1+1/2!*x^2-3/4!*x^4-123/6!*x^6-455/8!*x^8...
[ "1", "1", "-3", "-123", "-455", "162889", "7941813", "-647037363", "-141890950799", "176381997457", "4580546025413229", "624311846901265941", "-219756895048343473751", "-104610854473143576793127" ]
[ "sign" ]
6
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2021-12-29T12:12:30
oeisdata/seq/A012/A012569.seq
cb6bfdc3634b6db8bebe6229b6a7224f
A012570
sech(sinh(x)*cos(x))=1-1/2!*x^2+13/4!*x^4-277/6!*x^6+12185/8!*x^8...
[ "1", "-1", "13", "-277", "12185", "-840489", "84759717", "-11842313277", "2175505004849", "-510170676389457", "148514509335632701", "-52567147994554822501", "22230968162996350213321", "-11070593880057710100740473" ]
[ "sign" ]
6
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2021-07-28T19:21:59
oeisdata/seq/A012/A012570.seq
788b6a53c85fd4dfe1134902e80fe4ba
A012571
Expansion of arcsin(sinh(x)*sinh(x)).
[ "0", "2", "8", "152", "6848", "554912", "70690688", "13009484672", "3265063958528", "1071643508306432", "445538702940858368", "228823524775428872192", "142264706412727018078208", "105297877340452669962493952" ]
[ "nonn" ]
13
0
2
[ "A012101", "A012571" ]
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2017-02-16T03:20:30
oeisdata/seq/A012/A012571.seq
063a518cbcdb1b5e31d99c2295b270bf
A012572
exp(arcsinh(x)*log(x+1))=1+2/2!*x^2-3/3!*x^3+16/4!*x^4-80/5!*x^5...
[ "1", "0", "2", "-3", "16", "-80", "488", "-3339", "26472", "-241128", "2416002", "-26168835", "310984452", "-4057771068", "56774212350", "-841821751575", "13356966503088", "-227284196307984", "4085254725230514", "-76911822855270819" ]
[ "sign" ]
8
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-10-31T04:40:45
oeisdata/seq/A012/A012572.seq
a744ce02eeb880b14eea1f5599e535a2
A012573
Expansion of e.g.f. sin(arcsinh(x) * log(x+1)).
[ "0", "0", "2", "-3", "4", "-20", "38", "441", "-4776", "34056", "-368838", "5189085", "-61808100", "666424980", "-8929309170", "147346759665", "-2283822093840", "33140217608400", "-562702300383630", "11332944235915965", "-219113911766658060" ]
[ "sign" ]
15
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2018-07-20T03:11:46
oeisdata/seq/A012/A012573.seq
d4669008368357513d4af7223f331935
A012574
Expansion of e.g.f.: arcsin(arcsinh(x)*log(x+1)).
[ "0", "0", "2", "-3", "4", "-20", "278", "-2079", "12024", "-102024", "1526202", "-21144915", "254194620", "-3422013660", "60148579710", "-1146224919735", "21194144971440", "-407432463085200", "8837992445168370", "-209438776595814435", "5103026808528257460", "-128021892811081933860" ]
[ "sign" ]
11
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-07-17T18:26:15
oeisdata/seq/A012/A012574.seq
4def9b6be34655d2b393675a0c46900a
A012575
tan(arcsinh(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", "398", "-3339", "20424", "-170064", "2564442", "-36806715", "452112780", "-6050016180", "103580488230", "-1918670093235", "34463159406480", "-644382830011200", "13519192507361970", "-305019253676537235" ]
[ "sign" ]
8
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-02-02T18:20:17
oeisdata/seq/A012/A012575.seq
135c1ac11b22bcfa7cde114caab0ca70
A012576
Expansion of e.g.f. arctan(arcsinh(x) * log(x+1)).
[ "0", "0", "2", "-3", "4", "-20", "-82", "1701", "-13176", "102096", "-499878", "-4097115", "139441740", "-2543404500", "36360855750", "-325904118435", "-572181239280", "111107478652800", "-3446722823542350", "73786652661818925" ]
[ "sign" ]
8
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2018-07-20T03:11:54
oeisdata/seq/A012/A012576.seq
86db4014763a783341e5a6c10c0fe45b
A012577
cos(arcsinh(x)*log(x+1))=1-12/4!*x^4+60/5!*x^5-210/6!*x^6+1260/7!*x^7...
[ "1", "0", "0", "0", "-12", "60", "-210", "1260", "-11088", "78624", "-476520", "4469520", "-59173752", "609811488", "-4917756480", "63884751840", "-1229990362368", "16261478914944", "-136911418778304", "2226347294914944", "-65132012907161472" ]
[ "sign" ]
4
0
5
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:50:53
oeisdata/seq/A012/A012577.seq
3739423976d8941e57cee7723cfaa2a8
A012578
Expansion of e.g.f. arcsinh(arcsinh(x) * log(x+1)).
[ "0", "0", "2", "-3", "4", "-20", "38", "441", "-4776", "34056", "-126918", "-1463715", "44636700", "-890330220", "13954992270", "-144155651535", "517645374960", "19331453038800", "-757391766234510", "18491125497187005", "-311747885279029260" ]
[ "sign" ]
8
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2018-07-20T03:12:02
oeisdata/seq/A012/A012578.seq
f99f98c6b46b086cd41e4b7eb224c9f9
A012579
Expansion of e.g.f. tanh(arcsinh(x) * log(x+1)).
[ "0", "0", "2", "-3", "4", "-20", "-82", "1701", "-13176", "102096", "-741798", "2555685", "32996940", "-986649300", "17351145030", "-237817720035", "2593221000720", "-18017408438400", "-162521065585230", "10623453347243565", "-281538871670714220", "5556579737347871820", "-89014595698012503330", "977317781020921150965" ]
[ "sign" ]
10
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2018-07-20T03:12:42
oeisdata/seq/A012/A012579.seq
246439f3ab563ebd8813448b03d5068c
A012580
arctanh(arcsinh(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", "398", "-3339", "20424", "-170064", "2806362", "-43459515", "558557580", "-7606771380", "138088561830", "-2820420542835", "55165236001680", "-1086992549563200", "24100477113093810", "-594762006770251155" ]
[ "sign" ]
8
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-10-31T05:24:20
oeisdata/seq/A012/A012580.seq
8d0c6a0a560c68dd2364223ed293ab58
A012581
cosh(arcsinh(x)*log(x+1))=1+12/4!*x^4-60/5!*x^5+210/6!*x^6...
[ "1", "0", "0", "0", "12", "-60", "210", "-1260", "14448", "-139104", "1131720", "-11676720", "163234632", "-2192512608", "27259115520", "-393931268640", "6898028418048", "-119527801113984", "1985315996055744", "-36767841202329984" ]
[ "sign" ]
7
0
5
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-02-04T14:31:49
oeisdata/seq/A012/A012581.seq
107b88f48de279456fa1b18bb5fe6bb7
A012582
sec(arcsinh(x)*log(x+1))=1+12/4!*x^4-60/5!*x^5+210/6!*x^6-1260/7!*x^7...
[ "1", "0", "0", "0", "12", "-60", "210", "-1260", "21168", "-260064", "2442120", "-26091120", "411273192", "-6914670048", "106449907200", "-1707861486240", "32324814763008", "-667333358292864", "13774375825919424", "-293275396792404864" ]
[ "sign" ]
4
0
5
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:50:53
oeisdata/seq/A012/A012582.seq
9a90aa79c7f09b62222d3440cc97da6b
A012583
Expansion of e.g.f.: sech(arcsinh(x)*log(x+1))=1-12/4!*x^4+60/5!*x^5-210/6!*x^6...
[ "1", "0", "0", "0", "-12", "60", "-210", "1260", "-4368", "-42336", "833880", "-9944880", "109031208", "-998835552", "5256888000", "57628902240", "-2552409700608", "53611141985664", "-880205240332224", "12318269451041664", "-115115298914746752" ]
[ "sign" ]
6
0
5
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2023-02-20T10:55:30
oeisdata/seq/A012/A012583.seq
7786b28c7008cb536b600fa379c2c694
A012584
exp(arcsinh(x)*exp(x))=1+x+3/2!*x^2+9/3!*x^3+33/4!*x^4+145/5!*x^5...
[ "1", "1", "3", "9", "33", "145", "715", "3801", "21889", "140001", "974803", "6947017", "50720417", "421135793", "3950147227", "33562929817", "240061039105", "2672302901185", "45695167547043", "388308372326665", "-1858226878271967", "9709607588675537" ]
[ "sign" ]
8
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-10-31T05:23:43
oeisdata/seq/A012/A012584.seq
f676d6d3776427eaea200f563dc42a2e
A012585
sin(arcsinh(x)*exp(x)) = x+2/2!*x^2+1/3!*x^3-12/4!*x^4-75/5!*x^5...
[ "1", "2", "1", "-12", "-75", "-290", "-779", "-504", "21353", "309658", "2312649", "4942652", "-30773795", "551161910", "5842489277", "-202099628912", "-2781070598703", "37094805544626", "667109649353745", "-13372667222408444", "-244753093572037115", "5558587672503819534", "110344062209219143685" ]
[ "sign" ]
13
1
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-10-30T12:53:05
oeisdata/seq/A012/A012585.seq
14369304661cdbf58688d2f84adcddc2
A012586
arcsin(arcsinh(x)*exp(x))=x+2/2!*x^2+3/3!*x^3+12/4!*x^4+93/5!*x^5...
[ "1", "2", "3", "12", "93", "670", "5775", "66360", "866201", "12368218", "199321595", "3586550660", "70423787445", "1499367858742", "34522135846471", "854378102311664", "22596634681576113", "636104718523145010", "18994369965270547315" ]
[ "nonn" ]
7
1
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-04-04T11:37:46
oeisdata/seq/A012/A012586.seq
232fd24e338aa83f93d751c6bedfff30
A012587
E.g.f.: tan(arcsinh(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", "1240", "10456", "112896", "1316816", "16378528", "229634304", "3569726336", "59315089600", "1055150016128", "20254767489152", "415619313491968", "9028238025838848", "207506148418183680", "5043727679716764672" ]
[ "nonn" ]
17
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-02-06T09:17:10
oeisdata/seq/A012/A012587.seq
14cc16f0c5087ca96ed9a284b45ab17c
A012588
Expansion of e.g.f. arctan(arcsinh(x) * exp(x)).
[ "0", "1", "2", "0", "-24", "-132", "40", "8568", "83328", "-44272", "-13222112", "-182425408", "173064320", "53699598912", "947897491840", "-1462598830976", "-450248068501504", "-9631043314112256", "21880384337367552", "6765800654464927744", "169339160025954805760", "-532061075701090923520", "-165698959735673781516288" ]
[ "sign" ]
12
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2018-07-20T03:12:56
oeisdata/seq/A012/A012588.seq
1734c477da5a2461f5a335f9eb94b2b4
A012589
cos(arcsinh(x)*exp(x))=1-1/2!*x^2-6/3!*x^3-19/4!*x^4-20/5!*x^5...
[ "1", "0", "-1", "-6", "-19", "-20", "155", "1190", "6617", "44664", "208375", "-904398", "-18752699", "-19097052", "694693779", "-17424099810", "-291885915727", "3147952642416", "73814350009583", "-859299092152342", "-22448554968159587" ]
[ "sign" ]
8
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-10-31T09:47:59
oeisdata/seq/A012/A012589.seq
2e57726f4e06c7c740639ebfcb7ab98f
A012590
Expansion of e.g.f. arcsinh(arcsinh(x) * exp(x)).
[ "0", "1", "2", "1", "-12", "-67", "-50", "2917", "31752", "49849", "-3711302", "-59694967", "-115031620", "13336031733", "273381245254", "558981564013", "-100703000514928", "-2505740944272783", "-5344180827839502", "1386297984879140881", "40546775857977524228", "85953748442906064173", "-31561185255306611700930" ]
[ "sign" ]
10
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2018-07-20T03:13:06
oeisdata/seq/A012/A012590.seq
e38b1a520d448415300ff847418c987e
A012591
tanh(arcsinh(x)*exp(x)) = x+2/2!*x^2-24/4!*x^4-140/5!*x^5-200/6!*x^6...
[ "0", "1", "2", "0", "-24", "-140", "-200", "5096", "63616", "282192", "-3220832", "-80931136", "-710613376", "3394272960", "211897855104", "3116854010752", "2173449924608", "-951933369204480", "-22125765748465152", "-140624117764880384" ]
[ "sign" ]
12
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-10-31T09:49:11
oeisdata/seq/A012/A012591.seq
0a8fcdea32e9890e2a69d91d5f7ffad6
A012592
arctanh(arcsinh(x)*exp(x))=x+2/2!*x^2+4/3!*x^3+24/4!*x^4+188/5!*x^5...
[ "0", "1", "2", "4", "24", "188", "1480", "14824", "182784", "2495632", "37988128", "649646336", "12226037120", "250202750016", "5549572352896", "132663174885760", "3396998634659840", "92768709569362176", "2691992696956801536" ]
[ "nonn" ]
8
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-10-24T10:38:19
oeisdata/seq/A012/A012592.seq
0a38fe890957b854f0e1d29c84f6499e
A012593
cosh(arcsinh(x)*exp(x))=1+1/2!*x^2+6/3!*x^3+21/4!*x^4+60/5!*x^5...
[ "1", "0", "1", "6", "21", "60", "285", "2170", "12873", "54936", "391065", "4881998", "33969309", "28359188", "826179445", "48496348290", "328705747217", "-5928717037136", "-26909518872399", "2320514677184022", "14213386673919397" ]
[ "sign" ]
8
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-10-31T10:30:26
oeisdata/seq/A012/A012593.seq
a9d139858e5b4573f8702fee0f680e3e
A012594
sec(arcsinh(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", "1225", "11410", "110353", "1260696", "16597745", "233501598", "3534940649", "58867014180", "1060745261433", "20315286728490", "414362268698017", "9016753267197744", "207836963025430369", "5046234392527982902" ]
[ "nonn" ]
4
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:02
oeisdata/seq/A012/A012594.seq
812ea48f9ee623e8649737a9d6114bc8
A012595
sech(arcsinh(x)*exp(x))=1-1/2!*x^2-6/3!*x^3-15/4!*x^4+60/5!*x^5...
[ "1", "0", "-1", "-6", "-15", "60", "975", "5390", "-10143", "-563976", "-5982945", "-9594398", "788690001", "14618418100", "85743956207", "-2026783258890", "-64627785960767", "-716881015039504", "7211897523161151", "458865700394648778" ]
[ "sign" ]
4
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:02
oeisdata/seq/A012/A012595.seq
7ea2cbb9ea68fa550c36235cd1d9a48b
A012596
exp(arcsinh(x)*sin(x))=1+2/2!*x^2+4/4!*x^4-40/6!*x^6-688/8!*x^8...
[ "1", "2", "4", "-40", "-688", "23968", "-1134784", "188393088", "-40676275968", "10688526352896", "-3523678949366784", "1431294964438824960", "-701609173130329731072", "408385401482058726547456" ]
[ "sign" ]
8
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-10-31T10:30:18
oeisdata/seq/A012/A012596.seq
9d17f7a052e7b79665e0ca57ff2fa83d
A012597
arcsinh(arcsinh(x)*sin(x))=2/2!*x^2-8/4!*x^4-40/6!*x^6+4352/8!*x^8...
[ "2", "-8", "-40", "4352", "8608", "-38439040", "4405714560", "425680207872", "-252920252235264", "-5528067305916416", "44468403610589394944", "-15834819953218036760576", "-5810504218823261839253504" ]
[ "sign" ]
4
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:02
oeisdata/seq/A012/A012597.seq
a1fb64bdce739534e7021036269dbba1
A012598
Expansion of e.g.f. exp(arcsinh(x)*arcsin(x)).
[ "1", "2", "12", "208", "6608", "438912", "38672832", "5956592640", "1035058952448", "288405058560000", "83042522104507392", "36519438671549890560", "15719007594987094364160", "10017433660808198506414080" ]
[ "nonn" ]
12
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2025-05-06T10:07:13
oeisdata/seq/A012/A012598.seq
4ae87b4e24e0e63d818efd11e979d463
A012599
sin(arcsinh(x)*arcsin(x))=2/2!*x^2-32/6!*x^6-4608/10!*x^10...
[ "2", "-32", "-4608", "129331200", "10853318000640", "1726305357602488320", "538535159720462065336320", "306551574237383273309735485440" ]
[ "sign" ]
5
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:02
oeisdata/seq/A012/A012599.seq
b568933a90f7806c12741786b999b627
A012600
E.g.f.: arcsin(arcsinh(x)*arcsin(x)) = 2/2!*x^2+208/6!*x^6+680832/10!*x^10...
[ "2", "208", "680832", "13382891520", "900036879360000", "154882202019677798400", "57048038229121314631188480", "39842938883822751996178291752960", "48329392241807199563371957327138652160", "95258638419599144345659651051786276479959040" ]
[ "nonn" ]
12
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-08-20T19:28:01
oeisdata/seq/A012/A012600.seq
ce6b5068912d618e229dc4b3b0d79d7b