Datasets:
christopher
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oeis

Dataset card Data Studio Files
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2
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stringlengths
7
7
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4
573
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1
348
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score
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2.35k
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int64
-14,827
666,262,453B
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635M
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cross_references
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timestamp
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1999-12-11 03:00:00
2025-07-19 00:40:46
filename
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29
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32
32
A012701
arctan(arctanh(x)*log(x+1))=2/2!*x^2-3/3!*x^3+16/4!*x^4-50/5!*x^5...
[ "0", "0", "2", "-3", "16", "-50", "128", "756", "-20064", "298656", "-3561408", "38990160", "-310756800", "467943840", "66887172480", "-2183463747360", "51505489029120", "-1001091175633920", "15963926463621120", "-153477175865587200" ]
[ "sign" ]
6
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2016-11-28T19:53:04
oeisdata/seq/A012/A012701.seq
e147c8dac550202bcfc672a34fd66020
A012702
Expansion of e.g.f.: cos(arctanh(x)*log(x+1))=1-12/4!*x^4+60/5!*x^5-570/6!*x^6+3780/7!*x^7...
[ "1", "0", "0", "0", "-12", "60", "-570", "3780", "-36288", "290304", "-3077160", "27976080", "-325364952", "3125330208", "-38076353952", "320524495200", "-3277240862208", "-12892686066816", "851147013155904", "-38579486635656576", "1000229709289596288" ]
[ "sign" ]
6
0
5
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2017-08-11T14:12:40
oeisdata/seq/A012/A012702.seq
1c643311e722d531f00802564bedfc94
A012703
Expansion of e.g.f.: sinh(arctanh(x)*log(x+1))=2/2!*x^2-3/3!*x^3+16/4!*x^4-50/5!*x^5...
[ "0", "0", "2", "-3", "16", "-50", "488", "-3024", "35376", "-313704", "4119552", "-46248840", "682997280", "-9209575440", "152505104880", "-2394128401560", "44145984906240", "-789552273397440", "16082343831221760", "-322420285049880960" ]
[ "sign" ]
6
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2018-05-03T16:38:19
oeisdata/seq/A012/A012703.seq
6b48656a6fe8149863b4ab69dec13025
A012704
arcsinh(arctanh(x)*log(x+1)) = 2/2!*x^2-3/3!*x^3+16/4!*x^4-50/5!*x^5...
[ "0", "0", "2", "-3", "16", "-50", "248", "-504", "-1584", "94536", "-1222848", "16675560", "-150260640", "1047505680", "12037737840", "-574519410360", "16243532175360", "-341049918471360", "6341386354483200", "-86729688288097920", "452837960565661440", "31661940854577882240", "-1682428415293547953920" ]
[ "sign" ]
9
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-02-28T14:46:11
oeisdata/seq/A012/A012704.seq
ca93d669c0a89dd6e206e4e5e904ad24
A012705
arctanh(arctanh(x)*log(x+1))=2/2!*x^2-3/3!*x^3+16/4!*x^4-50/5!*x^5...
[ "0", "0", "2", "-3", "16", "-50", "608", "-4284", "53856", "-517824", "7607232", "-100164240", "1728315840", "-28348912800", "556461697920", "-10888103691360", "242440897198080", "-5503830139207680", "137385752450058240", "-3536219373095508480" ]
[ "sign" ]
6
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2016-11-28T19:54:43
oeisdata/seq/A012/A012705.seq
d0a61eb8af310715aa8e747ab16b6a06
A012706
Expansion of e.g.f.: cosh(arctanh(x)*log(x+1)) = 1+12/4!*x^4-60/5!*x^5+570/6!*x^6...
[ "1", "0", "0", "0", "12", "-60", "570", "-3780", "39648", "-350784", "4337160", "-48488880", "695537832", "-9378296928", "153105187872", "-2408666551200", "44087009541888", "-790629339479424", "16037164063659456", "-322336133481089664", "7178495810797951872", "-159644799778176115200" ]
[ "sign" ]
12
0
5
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2017-12-02T11:18:29
oeisdata/seq/A012/A012706.seq
70802d9035fddfccd43c5e257369640f
A012707
Expansion of e.g.f.: sec(arctanh(x)*log(x+1))=1+12/4!*x^4-60/5!*x^5+570/6!*x^6-3780/7!*x^7...
[ "1", "0", "0", "0", "12", "-60", "570", "-3780", "46368", "-471744", "6857160", "-89514480", "1475800392", "-23440985568", "439465502112", "-8219543623200", "173360899246848", "-3717086730616704", "87324245398685376" ]
[ "sign" ]
6
0
5
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2021-06-20T11:49:34
oeisdata/seq/A012/A012707.seq
8a4b896ddd577a817ec07ec650b9520b
A012708
Expansion of e.g.f.: sech(arctanh(x)*log(x+1))=1-12/4!*x^4+60/5!*x^5-570/6!*x^6...
[ "1", "0", "0", "0", "-12", "60", "-570", "3780", "-29568", "169344", "-557160", "-13049520", "375064008", "-7823848032", "135678667488", "-2221166656800", "32120158935552", "-397914002426496", "2522488580207424", "61215640433391744" ]
[ "sign" ]
6
0
5
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2023-04-23T18:26:29
oeisdata/seq/A012/A012708.seq
e826e2af81ee0aafe0ce3098bb94ce78
A012709
exp(arctanh(x)*exp(x))=1+x+3/2!*x^2+12/3!*x^3+57/4!*x^4+340/5!*x^5...
[ "1", "1", "3", "12", "57", "340", "2305", "18186", "158977", "1560840", "16695553", "196272142", "2483596577", "34036624700", "497515462561", "7792454528002", "129248702613505", "2278494692749840", "42291311707716609", "828953188249846678" ]
[ "nonn" ]
10
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-11-21T12:46:01
oeisdata/seq/A012/A012709.seq
b6615bfe4bcb1e9e9976419196c8e9e4
A012710
Expansion of e.g.f. sin(arctanh(x) * exp(x)).
[ "0", "1", "2", "4", "0", "-60", "-680", "-5504", "-45696", "-356080", "-2998112", "-23985216", "-210124288", "-1616818112", "-13420660864", "-52229820928", "283969097728", "28575615328512", "648822348255744", "17074162547880960", "350789663754797056" ]
[ "sign" ]
9
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2019-06-07T17:54:20
oeisdata/seq/A012/A012710.seq
693f26da8e3c6983fb2502cd3c5a0583
A012711
Expansion of e.g.f. arcsin(arctanh(x) * exp(x)).
[ "0", "1", "2", "6", "24", "168", "1360", "14280", "170688", "2420096", "38403328", "687737600", "13562531840", "293985622656", "6920272523008", "176170136886016", "4816418604806144", "140839702493749248", "4384422821203968000" ]
[ "nonn" ]
7
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2018-07-24T19:04:25
oeisdata/seq/A012/A012711.seq
0f482c49e8c2d6cc92676faadcd3cfe6
A012712
E.g.f.: tan(arctanh(x)*exp(x)).
[ "0", "1", "2", "7", "36", "285", "2470", "25891", "304584", "4116473", "61307338", "1011045759", "18130445036", "353222430613", "7401849057902", "166375042595867", "3987022624401808", "101564702642995953", "2738893925584229778", "77978462505905882103", "2336771614133464558516", "73533230212519134743821" ]
[ "nonn" ]
21
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-02-05T11:29:35
oeisdata/seq/A012/A012712.seq
09609091e3b64b0bd77a805400da7d3a
A012713
E.g.f.: arctan(arctanh(x)*exp(x))=x+2/2!*x^2+3/3!*x^3-12/4!*x^4-147/5!*x^5...
[ "0", "1", "2", "3", "-12", "-147", "-890", "63", "76776", "1130489", "6587338", "-92728933", "-3395342500", "-47724446811", "-11416580786", "18058083754519", "494993369091536", "5229048665015409", "-122759838344591214", "-7368934381520578637" ]
[ "sign" ]
8
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-12-07T05:09:02
oeisdata/seq/A012/A012713.seq
5b78a7b0371ac0a9dbc3f8bd2933cf3f
A012714
E.g.f.: cos(arctanh(x)*exp(x))=1-1/2!*x^2-6/3!*x^3-31/4!*x^4-140/5!*x^5...
[ "1", "0", "-1", "-6", "-31", "-140", "-625", "-2170", "-2623", "96072", "1642975", "23520882", "295668001", "3935469564", "50912723823", "723034935870", "10169862858113", "159490471907856", "2472265829827775", "43176564012771434" ]
[ "sign" ]
6
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-01-15T16:53:35
oeisdata/seq/A012/A012714.seq
8b430427a127de7f103769194f9e9d79
A012715
Expansion of e.g.f. sinh(arctanh(x) * exp(x)).
[ "0", "1", "2", "6", "24", "160", "1120", "9296", "79744", "791232", "8303488", "98662784", "1234416128", "17090231808", "247660907520", "3911062116352", "64395491606528", "1142963925405696", "21081499860049920", "415641154415091712" ]
[ "nonn" ]
7
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2018-07-24T19:20:36
oeisdata/seq/A012/A012715.seq
b2f9d74fb59fefde3cca591f2b119c51
A012716
arcsinh(arctanh(x)*exp(x))=x+2/2!*x^2+4/3!*x^3-52/5!*x^5-440/6!*x^6...
[ "0", "1", "2", "4", "0", "-52", "-440", "-968", "20160", "407248", "3393568", "-7743232", "-873283840", "-15700243392", "-92423547008", "3404251259008", "126748437358592", "1959254285705472", "-9945595116842496", "-1499843474292945920" ]
[ "sign" ]
14
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-11-21T12:46:01
oeisdata/seq/A012/A012716.seq
f93592a467c788e535154c3b1532a23e
A012717
arctanh(arctanh(x)*exp(x))=x+2/2!*x^2+7/3!*x^3+36/4!*x^4+293/5!*x^5...
[ "0", "1", "2", "7", "36", "293", "2710", "31099", "408072", "6199465", "105183658", "1990233551", "41337728300", "937722749325", "23029648705726", "609300643351555", "17268619403747600", "522102791124578001", "16771008730706230098" ]
[ "nonn" ]
10
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2016-11-28T19:56:00
oeisdata/seq/A012/A012717.seq
3c44080ddc3686276aca2530bddd4827
A012718
cosh(arctanh(x)*exp(x))=1+1/2!*x^2+6/3!*x^3+33/4!*x^4+180/5!*x^5...
[ "1", "0", "1", "6", "33", "180", "1185", "8890", "79233", "769608", "8392065", "97609358", "1249180449", "16946392892", "249854555041", "3881392411650", "64853211006977", "1135530767344144", "21209811847666689", "413312033834754966" ]
[ "nonn" ]
6
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-05-15T05:32:37
oeisdata/seq/A012/A012718.seq
d6cf21bdb8d1cbcd312bc3610fa2665a
A012719
sec(arctanh(x)*exp(x))=1+1/2!*x^2+6/3!*x^3+37/4!*x^4+260/5!*x^5...
[ "1", "0", "1", "6", "37", "260", "2365", "24850", "301033", "4051848", "60901145", "1003420638", "18072389069", "352027414284", "7390186076949", "166110699895530", "3983896292586577", "101488729722338064", "2737830394817774257" ]
[ "nonn" ]
4
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:05
oeisdata/seq/A012/A012719.seq
631985aebbd0c27cbe2f40df7b2c864f
A012720
sech(arctanh(x)*exp(x))=1-1/2!*x^2-6/3!*x^3-27/4!*x^4-60/5!*x^5...
[ "1", "0", "-1", "-6", "-27", "-60", "435", "8750", "84777", "475272", "-2114745", "-106313438", "-1794336819", "-17317361204", "18165128891", "5261034602070", "135408683857873", "2003263412796176", "6167034429608463", "-699433926727865526" ]
[ "sign" ]
6
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-10-07T14:55:26
oeisdata/seq/A012/A012720.seq
c31d2edc410f65d3c5dc084a8101edcf
A012721
exp(arctanh(x)*sin(x))=1+2/2!*x^2+16/4!*x^4+350/6!*x^6+16280/8!*x^8...
[ "1", "2", "16", "350", "16280", "1280458", "151282316", "25067231982", "5547679327632", "1580745016902930", "563647979697490836", "245869122688036168950", "128799713392548410995032", "79791827954988156443060506" ]
[ "nonn" ]
8
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-10-24T12:01:56
oeisdata/seq/A012/A012721.seq
ae10072a01cc6a10565e37bdc218dded
A012722
arcsinh(arctanh(x)*sin(x))=2/2!*x^2+4/4!*x^4-10/6!*x^6+1160/8!*x^8...
[ "2", "4", "-10", "1160", "267178", "25749260", "1675836318", "292637394192", "163260945099858", "64904840292491284", "19017877552509443654", "7018293499345186438552", "5539610614858975449636346" ]
[ "sign" ]
6
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-06-16T12:10:07
oeisdata/seq/A012/A012722.seq
c7e2d866044e4d7ad6b3c54e89295b4d
A012723
exp(arctanh(x)*arcsin(x))=1+2/2!*x^2+24/4!*x^4+718/6!*x^6+40040/8!*x^8...
[ "1", "2", "24", "718", "40040", "3586122", "470928612", "85257985902", "20354196606768", "6195953068191762", "2342416197502447932", "1076777305129376444790", "591474826398069745456200", "382625479333794154176056730" ]
[ "nonn" ]
4
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:06
oeisdata/seq/A012/A012723.seq
187dae74da62d94a9218550e244b26f2
A012724
sinh(arctanh(x)*arcsin(x))=2/2!*x^2+12/4!*x^4+358/6!*x^6+19992/8!*x^8...
[ "2", "12", "358", "19992", "1791882", "235396260", "42624803310", "10177141489200", "3098164254001170", "1171315364214109500", "538446859100064311670", "295771765211446451586120", "191335531681410403898936730" ]
[ "nonn" ]
6
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-08-30T20:20:37
oeisdata/seq/A012/A012724.seq
094fc4387e47a14446df1cf1e046c7f9
A012725
Expansion of e.g.f. exp(arctanh(x)*tan(x)) (even powers only).
[ "1", "2", "28", "920", "54416", "5056288", "678865856", "124425704832", "29873423298816", "9104340085891584", "3435702339713424384", "1573394503700675106816", "859935938676055185002496", "553085284375423405752918016" ]
[ "nonn" ]
22
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2023-08-08T04:48:53
oeisdata/seq/A012/A012725.seq
03761f8d734ce7bb96aeafedc30bc1d4
A012726
arctanh(arctanh(x)*tan(x))=2/2!*x^2+16/4!*x^4+560/6!*x^6+39296/8!*x^8...
[ "0", "2", "16", "560", "39296", "4768768", "881315840", "230827284480", "81324940394496", "37097190468747264", "21272100905987080192", "14977571327515946909696", "12703902924309766749552640", "12776509288228175937154318336" ]
[ "nonn" ]
10
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-02-05T09:47:33
oeisdata/seq/A012/A012726.seq
8a172daac7d3560e739cd76b7d50767d
A012727
exp(arctanh(x)*arctan(x))=1+2/2!*x^2+12/4!*x^4+328/6!*x^6+13328/8!*x^8...
[ "1", "2", "12", "328", "13328", "1160352", "123701952", "22207125120", "4532782825728", "1380071532433920", "459909185638812672", "212375023941305272320", "104929881035116227072000", "68350141067274779587092480" ]
[ "nonn" ]
6
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2016-11-28T19:59:02
oeisdata/seq/A012/A012727.seq
4145384375fb3922e71ef4ae6cef18c7
A012728
sin(arctanh(x)*arctan(x))=2/2!*x^2+88/6!*x^6+112032/10!*x^10...
[ "2", "88", "112032", "339519360", "-45065746337280", "-13641523340876605440", "-5909672857101969499054080", "-4213934311138261721595771125760" ]
[ "sign" ]
7
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2016-11-28T20:02:01
oeisdata/seq/A012/A012728.seq
31c188b3fcde1181f9e999709b687b30
A012729
arcsin(arctanh(x)*arctan(x))=2/2!*x^2+328/6!*x^6+1402272/10!*x^10...
[ "2", "328", "1402272", "34476662400", "2862572968849920", "606547177566513039360", "275433333396552433711226880", "237761902453820639998996848476160" ]
[ "nonn" ]
6
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2016-11-28T20:03:25
oeisdata/seq/A012/A012729.seq
fce667b596a52a451881089ec86ecc81
A012730
tan(arctanh(x)*arctan(x))=2/2!*x^2+448/6!*x^6+2138112/10!*x^10...
[ "2", "448", "2138112", "53551718400", "4262315839979520", "826978943730607718400", "331594807758028302723317760", "245412719115132295441404238233600", "308745457206861968420290988707864903680", "620129923454446057412994114512456319793889280" ]
[ "nonn" ]
6
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-09-24T14:42:39
oeisdata/seq/A012/A012730.seq
ccd607c9824bde4fc4e56172ddaf83f3
A012731
arctan(arctanh(x)*arctan(x))=2/2!*x^2-32/6!*x^6+283392/10!*x^10...
[ "2", "-32", "283392", "1121740800", "157951397068800", "14184297129466920960", "5248874425245870210416640", "2544005109030684773416383283200" ]
[ "sign" ]
7
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2016-11-28T20:05:58
oeisdata/seq/A012/A012731.seq
bdd361cdce69ca2cc74daf37343f0b3e
A012732
cos(arctanh(x)*arctan(x)) = 1-12/4!*x^4-9968/8!*x^8-77575872/12!*x^12...
[ "1", "-12", "-9968", "-77575872", "-2494079278848", "-227607911866125312", "-47454799045677121597440", "-19613396255307422099013550080", "-14538029942147907114791552602275840" ]
[ "sign" ]
7
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2016-11-28T20:36:33
oeisdata/seq/A012/A012732.seq
455575cf6c12e11e02373642973d52f7
A012733
arcsinh(arctanh(x)*arctan(x))=2/2!*x^2+88/6!*x^6+353952/10!*x^10...
[ "2", "88", "353952", "4859875200", "286589256061440", "38349390501320693760", "11520524205295446001950720", "6360705742909296331970308177920" ]
[ "nonn" ]
6
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-04-12T18:24:10
oeisdata/seq/A012/A012733.seq
5f198f0917a24846eee0a3b735670625
A012734
arctanh(arctanh(x)*arctan(x))=2/2!*x^2+448/6!*x^6+2380032/10!*x^10...
[ "2", "448", "2380032", "69695846400", "6697099792220160", "1606188416621920911360", "810882197441673837894696960", "766865924510666637669136261447680" ]
[ "nonn" ]
6
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2016-11-28T20:40:53
oeisdata/seq/A012/A012734.seq
c04c1d9039a5f9aef19a3b5b0c1264d4
A012735
cosh(arctanh(x)*arctan(x)) = 1+12/4!*x^4+13328/8!*x^8+123701952/12!*x^12...
[ "1", "12", "13328", "123701952", "4532782825728", "459909185638812672", "104929881035116227072000", "46932023772320615610531102720", "37335044041745321283133064572108800", "49122678379677747841112058639072413614080", "101040224553048123974208287067140687061807267840" ]
[ "nonn" ]
10
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2014-05-31T13:22:11
oeisdata/seq/A012/A012735.seq
0e38af061bc7a1f18de814ed82a09e82
A012736
sec(arctanh(x)*arctan(x)) = 1+12/4!*x^4+20048/8!*x^8+255870912/12!*x^12...
[ "1", "12", "20048", "255870912", "12348478073088", "1607757077354376192", "462465118290965584465920", "257450488580368515571587072000", "252414780430562625969597955397713920" ]
[ "nonn" ]
7
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2016-08-17T12:50:30
oeisdata/seq/A012/A012736.seq
85b3d4a21ba4924072dd07bf0f6a1ea3
A012737
sech(arctanh(x)*arctan(x))=1-12/4!*x^4-3248/8!*x^8-25240512/12!*x^12...
[ "1", "-12", "-3248", "-25240512", "-722745554688", "-61363036297915392", "-12105663188188359045120", "-4791193110632356981925068800" ]
[ "sign" ]
7
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2016-11-28T20:45:06
oeisdata/seq/A012/A012737.seq
c072f8babe9ef7bf2e28e23545721163
A012738
exp(arctanh(x)*cos(x)) = 1+x+1/2!*x^2-3/4!*x^4+45/6!*x^6+504/7!*x^7...
[ "1", "1", "1", "0", "-3", "0", "45", "504", "2457", "24384", "161625", "2375296", "20549397", "338479232", "3457938757", "64501554688", "772773915313", "16130341302272", "221864504883633", "5112670099460096", "79479234590193325", "2003580047549120512" ]
[ "sign" ]
8
0
5
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-10-24T16:18:29
oeisdata/seq/A012/A012738.seq
444063e6787592df31a5553bc6d2e66a
A012739
sin(arctanh(x)*cos(x))=x-2/3!*x^3+20/5!*x^5-16/7!*x^7+14096/9!*x^9...
[ "1", "-2", "20", "-16", "14096", "887456", "126998976", "21834514688", "5067177011456", "1485621376751104", "540527763829711872", "238770291840873000960", "125924968135743519723520", "78156500138405011699867648" ]
[ "sign" ]
6
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-11-04T17:02:29
oeisdata/seq/A012/A012739.seq
1211ead54f441cddd845e1d68860df09
A012740
arcsin(arctanh(x)*cos(x))=x+8/5!*x^5+448/7!*x^7+32384/9!*x^9...
[ "1", "0", "8", "448", "32384", "3363712", "498146816", "101255683072", "27100382101504", "9228615461568512", "3895169435932917760", "1996505925721071157248", "1222138138975234336751616", "880971359478741744513712128" ]
[ "nonn" ]
4
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:07
oeisdata/seq/A012/A012740.seq
f4f55f269439914411d096b1cbfc8d66
A012741
tan(arctanh(x)*cos(x))=x+1/3!*x^3+5/5!*x^5+509/7!*x^7+44393/9!*x^9...
[ "1", "1", "5", "509", "44393", "4436441", "630529965", "126873147413", "33552906028625", "11170776120292657", "4582643056340650197", "2275243986686803354029", "1344475182597566546716345", "932197702028175163027746313" ]
[ "nonn" ]
9
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-02-07T03:32:23
oeisdata/seq/A012/A012741.seq
7c417237d5b70d2d650f7c0b92719342
A012742
arctan(arctanh(x)*cos(x))=x-3/3!*x^3+53/5!*x^5-1799/7!*x^7...
[ "1", "-3", "53", "-1799", "154985", "-16589771", "3172731677", "-721614303695", "241340829836497", "-94965599172723859", "49224836859318783493", "-29702702631352493918103", "22109389701103652762325561" ]
[ "sign" ]
6
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-11-05T03:56:34
oeisdata/seq/A012/A012742.seq
47ec9aa693abeec0e21bb158b5a73c09
A012743
cos(arctanh(x)*cos(x))=1-1/2!*x^2+5/4!*x^4-85/6!*x^6-887/8!*x^8...
[ "1", "-1", "5", "-85", "-887", "-145865", "-14963507", "-2554796829", "-556819358703", "-157094249035537", "-55286734778859115", "-23786315258989816933", "-12282781149659030865767", "-7498816363839210619416025" ]
[ "sign" ]
4
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:07
oeisdata/seq/A012/A012743.seq
1d255e58b6bbbe4313f7f0f097338850
A012744
sinh(arctanh(x)*cos(x))=x+504/7!*x^7+24384/9!*x^9+2375296/11!*x^11...
[ "1", "0", "0", "504", "24384", "2375296", "338479232", "64501554688", "16130341302272", "5112670099460096", "2003580047549120512", "951418445045046378496", "538352433444301745848320", "357916525207050277213175808" ]
[ "nonn", "easy" ]
8
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-11-21T12:46:01
oeisdata/seq/A012/A012744.seq
fb189d338faeef99f8badc7c82095470
A012745
arcsinh(arctanh(x)*cos(x))=x-2/3!*x^3+28/5!*x^5-520/7!*x^7+59728/9!*x^9...
[ "1", "-2", "28", "-520", "59728", "-3842720", "963273920", "-151564390016", "60786495498496", "-18563464667034112", "10709479914780654592", "-5442000735745663911936", "4284121800522638439469056", "-3262273090906052050909765632" ]
[ "sign" ]
10
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-02-04T17:46:22
oeisdata/seq/A012/A012745.seq
c446a16753cbeb02a6f277a8c13284ee
A012746
arctanh(arctanh(x)*cos(x)) = x+1/3!*x^3+13/5!*x^5+677/7!*x^7+54937/9!*x^9...
[ "1", "1", "13", "677", "54937", "6248713", "988579109", "212756765101", "60179200959793", "21632158018229009", "9619077100099258429", "5182270736688171740085", "3326876613520624630798281", "2509818428217896837411045913", "2198676694008933148388904662357", "2213672191262297018716557756353725" ]
[ "nonn" ]
13
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2016-05-20T06:09:34
oeisdata/seq/A012/A012746.seq
f10881594ca6966c8904d6387f73ef64
A012747
cosh(arctanh(x)*cos(x))=1+1/2!*x^2-3/4!*x^4+45/6!*x^6+2457/8!*x^8...
[ "1", "1", "-3", "45", "2457", "161625", "20549397", "3457938757", "772773915313", "221864504883633", "79479234590193325", "34768359140993612893", "18241340561609524790601", "11306811847252896133698825" ]
[ "sign" ]
6
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2022-07-07T11:43:34
oeisdata/seq/A012/A012747.seq
fb4fd3191029d6b93d9949b33ba55ab3
A012748
Expansion of e.g.f. sec(arctanh(x)*cos(x)), only even powers.
[ "1", "1", "1", "25", "3617", "340145", "40490657", "7034559753", "1668333374913", "504856533178465", "189500285350524865", "86696156445549770233", "47524548345395009982689", "30739504895562596416971025", "23162222253680333719652996449", "20112913566033287819336502367465", "19939158697176271310635403636418945" ]
[ "nonn" ]
15
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2024-06-21T14:35:07
oeisdata/seq/A012/A012748.seq
712d3f479a87469524a9aebfd619d339
A012749
sech(arctanh(x)*cos(x))=1-1/2!*x^2+9/4!*x^4-225/6!*x^6+6993/8!*x^8...
[ "1", "-1", "9", "-225", "6993", "-592545", "38019993", "-7568120833", "704958936737", "-307874830583745", "28902473366214185", "-31727751790145150113", "1072204316646061940721", "-7192967681050724533661025" ]
[ "sign" ]
4
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:07
oeisdata/seq/A012/A012749.seq
61184a3228ed2fed3016f19a8e8928fe
A012750
exp(arctanh(x)*sinh(x)) = 1+2/2!*x^2+24/4!*x^4+670/6!*x^6+34664/8!*x^8...
[ "1", "2", "24", "670", "34664", "2889898", "355793636", "60839374622", "13810040271408", "4019737531147986", "1460034627147106108", "647382654230985522694", "344160751932393939417288", "216083913094173247176675386" ]
[ "nonn" ]
9
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-10-24T16:21:32
oeisdata/seq/A012/A012750.seq
59429817b4bde973bccc47df8f1fd80b
A012751
tan(arctanh(x)*sinh(x))=2/2!*x^2+12/4!*x^4+430/6!*x^6+27384/8!*x^8...
[ "0", "2", "12", "430", "27384", "2844538", "444855620", "96566466022", "27798112443248", "10239758940342642", "4695120560496345596", "2621628020059813754526", "1751011006876497963996520", "1378272807335260827405511146" ]
[ "nonn" ]
8
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-02-06T10:33:05
oeisdata/seq/A012/A012751.seq
2813f8dd8ccfdaa2f41a1fad75d22517
A012752
exp(arctanh(x)*arcsinh(x)) = 1+2/2!*x^2+16/4!*x^4+398/6!*x^6+18072/8!*x^8...
[ "1", "2", "16", "398", "18072", "1465962", "169054092", "28688618814", "6235376638608", "1810793539845714", "636329871517885332", "282006422882452989030", "145933818284739352119000", "91644646853849910546846330" ]
[ "nonn" ]
9
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-10-24T16:22:08
oeisdata/seq/A012/A012752.seq
41b66c867becbcf091d2a8c06ee01723
A012753
tan(arctanh(x)*arcsinh(x))=2/2!*x^2+4/4!*x^4+398/6!*x^6+10344/8!*x^8...
[ "0", "2", "4", "398", "10344", "1808442", "161718060", "45246852870", "8895239749200", "3696108480038130", "1280274899653919700", "747254995555318476030", "400947704397371982315960", "314940075899759001168711210" ]
[ "nonn" ]
8
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-02-06T10:49:16
oeisdata/seq/A012/A012753.seq
5417582b31a9e527b02af1ab12b5d3b9
A012754
exp(arctanh(x)*tanh(x)) = 1+2/2!*x^2+12/4!*x^4+280/6!*x^6+13328/8!*x^8...
[ "1", "2", "12", "280", "13328", "1016608", "120249536", "19735743872", "4349101334784", "1233253332705792", "437938810884459520", "190333673674118699008", "99369086035110941036544", "61369835997419856216006656" ]
[ "nonn" ]
11
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-11-21T12:46:01
oeisdata/seq/A012/A012754.seq
ff0bd337bb615f74a30863be5c78ebd7
A012755
tan(arctanh(x)*tanh(x))=2/2!*x^2+400/6!*x^6+2688/8!*x^8...
[ "0", "2", "0", "400", "2688", "1631488", "60938240", "35243972608", "3826154307584", "2477263324839936", "571708399442198528", "435722170330996801536", "177081722613295659089920", "162107313371111569999527936" ]
[ "nonn" ]
8
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-02-06T11:10:13
oeisdata/seq/A012/A012755.seq
4e330709ab6ad2fff10363447f04483d
A012756
exp(arctanh(x)*arctanh(x))=1+2/2!*x^2+28/4!*x^4+968/6!*x^6+61584/8!*x^8...
[ "1", "2", "28", "968", "61584", "6221472", "912779712", "183144253056", "48126940270848", "16031131073204736", "6598147635721116672", "3287285755024478177280", "1949289186179973455646720", "1356446896562442205265633280" ]
[ "nonn" ]
8
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-02-08T07:34:54
oeisdata/seq/A012/A012756.seq
5f4d845f202fff0d4a49804f43cba7ef
A012757
tan(arctanh(x)^2) = 2/2!*x^2 + 16/4!*x^4 + 608/6!*x^6 + 43776/8!*x^8 + ...
[ "0", "2", "16", "608", "43776", "5248512", "937297920", "232869949440", "76704079872000", "32321764442112000", "16950418888812134400", "10823130351189900656640", "8265103101463254238494720", "7437225349735123409814159360" ]
[ "nonn" ]
11
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-02-06T11:15:02
oeisdata/seq/A012/A012757.seq
67a3cddbe6b2450e8e07fb0c9d34054c
A012758
Expansion of e.g.f. arcsin(cosh(x) * log(x+1)).
[ "0", "1", "-1", "6", "-18", "123", "-855", "8610", "-92540", "1220765", "-17627085", "291506270", "-5265113502", "105134332743", "-2272750891411", "53258927842666", "-1338863892701400", "36033888424535961", "-1032074699069841561" ]
[ "sign" ]
13
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2018-07-25T04:09:30
oeisdata/seq/A012/A012758.seq
ac283d30fe42877b2caa77cc831b541e
A012759
Expansion of e.g.f.: arctan(cosh(x)*log(x+1))=x-1/2!*x^2+3/3!*x^3-57/5!*x^5+405/6!*x^6...
[ "0", "1", "-1", "3", "0", "-57", "405", "-1827", "-4424", "223541", "-2901285", "19263167", "121524216", "-6372341445", "112206095729", "-915357416711", "-12418256340720", "674275623382473", "-14438518400518281", "129951850481453275" ]
[ "sign" ]
8
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2014-01-06T17:08:52
oeisdata/seq/A012/A012759.seq
9d22cd98f165e6356917a35ef698d30c
A012760
Expansion of e.g.f. arcsinh(cosh(x) * log(x+1)).
[ "0", "1", "-1", "4", "-6", "-7", "135", "-968", "1764", "58669", "-1068885", "10920908", "-41078730", "-1105690419", "31085174939", "-413045671712", "692738905320", "126897371107929", "-3901725279332361", "61836650105641300", "-52537696659319150" ]
[ "sign" ]
10
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2018-07-27T04:35:31
oeisdata/seq/A012/A012760.seq
073b6080d1f988001c841fc26338c245
A012761
Expansion of e.g.f. arctanh(cosh(x) * log(x+1)).
[ "0", "1", "-1", "7", "-24", "203", "-1575", "17869", "-208152", "2978653", "-45883485", "806530811", "-15347080848", "321642878919", "-7260372461251", "177107309744065", "-4619185786492560", "128667734086725657", "-3805156334531373561" ]
[ "sign" ]
10
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2018-07-27T04:35:36
oeisdata/seq/A012/A012761.seq
df5e8790001a9bf0155a8fe74ad72373
A012762
Expansion of e.g.f.: sec(cosh(x)*log(x+1))=1+1/2!*x^2-3/3!*x^3+28/4!*x^4-160/5!*x^5...
[ "1", "0", "1", "-3", "28", "-160", "1510", "-13860", "162188", "-2015928", "28741220", "-442050620", "7490417768", "-136676535840", "2694128185424", "-56789020808520", "1278027412615632", "-30539597036104512", "772903901239459408" ]
[ "sign" ]
6
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2018-06-27T18:51:43
oeisdata/seq/A012/A012762.seq
d5045a494a668d9d5feca0cd83d03f62
A012763
Expansion of e.g.f.: sech(cosh(x)*log(x+1))=1-1/2!*x^2+3/3!*x^3-18/4!*x^4+60/5!*x^5...
[ "1", "0", "-1", "3", "-18", "60", "-60", "-1890", "31472", "-319032", "2369280", "-6374280", "-209401368", "5594400240", "-90523285944", "1016295254520", "-3922383447232", "-184920315173888", "6878045401558272", "-151394798389814208" ]
[ "sign" ]
6
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2018-08-02T17:29:41
oeisdata/seq/A012/A012763.seq
74fdd0c46b8439555e62b44a0a2de43a
A012764
arcsin(cosh(x)*sin(x))=x+3/3!*x^3+25/5!*x^5+1043/7!*x^7+72465/9!*x^9...
[ "1", "3", "25", "1043", "72465", "8621283", "1524721705", "377210665523", "124306024835745", "52632893869133763", "27845178915137542585", "17999274225229924466003", "13958549668775664990210225", "12790824660557018843352942243" ]
[ "nonn" ]
6
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2019-12-14T16:19:48
oeisdata/seq/A012/A012764.seq
228d4d8d1e018dedebcadfa134050139
A012765
exp(cosh(x)*arcsin(x))=1+x+1/2!*x^2+5/3!*x^3+17/4!*x^4+65/5!*x^5...
[ "1", "1", "1", "5", "17", "65", "385", "2221", "15073", "119873", "1010945", "9786229", "101590513", "1171166529", "14396384769", "194493711517", "2765830859457", "42939774236801", "694784293696513", "12195226930738277", "221386930443511505" ]
[ "nonn" ]
4
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:08
oeisdata/seq/A012/A012765.seq
3e8657bf05e9c74471da0e75566ac120
A012766
sin(cosh(x)*arcsin(x))=x+3/3!*x^3-15/5!*x^5-1029/7!*x^7-46239/9!*x^9...
[ "1", "3", "-15", "-1029", "-46239", "-2582701", "-223494895", "-31551766453", "-6578644464703", "-1828823841664733", "-641975997431127503", "-276576165893943654373", "-143429494944516129401055", "-88139150252441009278574733", "-63329932634044318341466520239" ]
[ "sign" ]
6
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-11-18T20:58:46
oeisdata/seq/A012/A012766.seq
8b9748bf420eb5daf67a12d78109c7c3
A012767
E.g.f.: arctan(cosh(x)*tan(x))=x+3/3!*x^3-35/5!*x^5-1057/7!*x^7+59865/9!*x^9...
[ "1", "3", "-35", "-1057", "59865", "5446683", "-726781835", "-133713611977", "32440474082865", "10034804733270963", "-3854719922524818035", "-1800259494456990656497", "1004556790822666566963465" ]
[ "sign" ]
6
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-08-01T16:04:44
oeisdata/seq/A012/A012767.seq
560e7fb093030108ee8d3054364a7ac0
A012768
exp(cosh(x)*arctan(x))=1+x+1/2!*x^2+2/3!*x^3+5/4!*x^4+20/5!*x^5...
[ "1", "1", "1", "2", "5", "20", "85", "16", "-887", "14096", "145865", "-887456", "-14963507", "126998976", "2554796829", "-21834514688", "-556819358703", "5067177011456", "157094249035537", "-1485621376751104", "-55286734778859115" ]
[ "sign" ]
6
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-10-07T18:20:48
oeisdata/seq/A012/A012768.seq
e4c59428e7118d48e9374cca6f4ef796
A012769
tan(cosh(x)*arctan(x))=x+3/3!*x^3+45/5!*x^5+1071/7!*x^7+69177/9!*x^9...
[ "1", "3", "45", "1071", "69177", "3986939", "609782693", "60159520487", "18315680711153", "2425226987446387", "1432393396034388637", "194035475753231168543", "248503763037617443112745", "18849742079674987910368107" ]
[ "sign" ]
8
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-02-07T03:46:29
oeisdata/seq/A012/A012769.seq
8ac410cf0c76e2f61b4fd99e35eb3e98
A012770
-log(cosh(x)*cos(x))=-4/4!*x^4-544/8!*x^8-707584/12!*x^12...
[ "4", "544", "707584", "3807514624", "58177770225664", "2030847773013704704", "140503203207887919775744", "17427925514250338592341622784", "3597303386901777560143500698189824", "1166406649834620087886383283250988580864" ]
[ "nonn" ]
13
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-03-15T11:10:36
oeisdata/seq/A012/A012770.seq
5e8e997598630905a853230a81eb6c99
A012771
exp(cosh(x)*arcsinh(x))=1+x+1/2!*x^2+3/3!*x^3+9/4!*x^4+25/5!*x^5...
[ "1", "1", "1", "3", "9", "25", "105", "371", "1393", "11985", "71025", "-13981", "-898887", "45127017", "455252889", "-5553908333", "-75822681503", "1415759895841", "21366754787169", "-404022487469117", "-7036035942040855", "148035510590478137" ]
[ "sign" ]
8
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-11-01T10:05:32
oeisdata/seq/A012/A012771.seq
4084b4db94982b62f667e6eea89028e6
A012772
Take every 5th term of Padovan sequence A000931, beginning with the sixth term.
[ "1", "3", "12", "49", "200", "816", "3329", "13581", "55405", "226030", "922111", "3761840", "15346786", "62608681", "255418101", "1042002567", "4250949112", "17342153393", "70748973084", "288627200960", "1177482265857", "4803651498529", "19596955630177" ]
[ "nonn", "easy", "changed" ]
23
0
2
[ "A012772", "A012781" ]
null
N. J. A. Sloane
2025-07-08T02:47:03
oeisdata/seq/A012/A012772.seq
409e4ab19b0eefe90a1fce23b8707c85
A012773
exp(cosh(x)*arctanh(x)) = 1+x+1/2!*x^2+6/3!*x^3+21/4!*x^4+100/5!*x^5...
[ "1", "1", "1", "6", "21", "100", "645", "4256", "34153", "302352", "2966505", "32245664", "380114493", "4879093440", "67244074989", "996485811712", "15717842398417", "264232448010496", "4694489063253585", "88283645811756544", "1744673430747688805" ]
[ "nonn" ]
9
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-10-24T16:23:02
oeisdata/seq/A012/A012773.seq
f79c37f1e317825164ce0ba8b8798a5c
A012774
Expansion of e.g.f. arcsin(sec(x) * log(x+1)).
[ "0", "1", "-1", "6", "-18", "143", "-915", "9730", "-100940", "1376357", "-19680165", "332019710", "-6000731022", "121502892067", "-2640899177735", "62588297762666", "-1585329875795640", "43101529687518377", "-1245060181757058633" ]
[ "sign" ]
9
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2018-07-27T04:35:59
oeisdata/seq/A012/A012774.seq
581e56c67c11566624d8e723865bcb7a
A012775
E.g.f.: arctan(sec(x)*log(x+1)) = x - 1/2!*x^2 + 3/3!*x^3 - 37/5!*x^5 + 345/6!*x^6 - ...
[ "0", "1", "-1", "3", "0", "-37", "345", "-1967", "2296", "122093", "-2157165", "21241847", "-62837544", "-2704412921", "74329911565", "-1080320786971", "5480675823120", "220652162236409", "-8577532338045273", "168598543971458059", "-1306206271210775920", "-46736993299592412013" ]
[ "sign" ]
13
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2020-12-11T17:46:04
oeisdata/seq/A012/A012775.seq
3c0d65e4dd9aaa63c285eb42ca0e6d8b
A012776
Expansion of e.g.f. arcsinh(sec(x) * log(x+1)).
[ "0", "1", "-1", "4", "-6", "13", "75", "-688", "3444", "17701", "-627165", "8927708", "-77106810", "67688905", "13345186855", "-307791747352", "3673005693000", "5260749482825", "-1552250968018713", "45434699608017268", "-741230930507315470" ]
[ "sign" ]
10
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2018-07-25T04:07:54
oeisdata/seq/A012/A012776.seq
32014c836f829a1ba3a7bbc4892328f2
A012777
Expansion of e.g.f. arctanh(sec(x) * log(x+1)).
[ "0", "1", "-1", "7", "-24", "223", "-1635", "19409", "-221592", "3270325", "-50128965", "898512371", "-17140184688", "364328185843", "-8275583884295", "204221077642685", "-5369189766162960", "151121003206989833", "-4508710182336979593" ]
[ "sign" ]
11
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2018-07-27T04:36:06
oeisdata/seq/A012/A012777.seq
1c7e02708d0ebfa15760ee2255c7cd4b
A012778
Expansion of e.g.f. sec(sec(x)*log(x+1)).
[ "1", "0", "1", "-3", "28", "-160", "1630", "-14700", "180668", "-2227608", "32850740", "-507842060", "8829277928", "-162974579040", "3280768459280", "-70166399557800", "1609085392223312", "-39068177212368192", "1006531896581760976" ]
[ "sign" ]
17
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2019-01-22T08:35:04
oeisdata/seq/A012/A012778.seq
01b63f651c67e18a2c5b0a40e0199688
A012779
Expansion of e.g.f.: sech(sec(x)*log(x+1))=1-1/2!*x^2+3/3!*x^3-18/4!*x^4+60/5!*x^5...
[ "1", "0", "-1", "3", "-18", "60", "-180", "-1050", "24192", "-308952", "3131760", "-23742840", "62587272", "2606501040", "-75839636600", "1415140435800", "-20144425867712", "187207018203392", "730860552463104", "-93674690778135744" ]
[ "sign" ]
6
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2016-04-17T10:21:40
oeisdata/seq/A012/A012779.seq
49ed523c3b83f4b8b4115d80b8d7afb6
A012780
Expansion of e.g.f. arcsin(tan(x)) (odd powers only).
[ "1", "3", "45", "1743", "133305", "17089083", "3302755365", "896199578823", "324729845802225", "151401766241310963", "88276508686397289885", "62925559543228826845503", "53835082550295989275314345", "54438337988081689498005862443", "64228314189095958231926869651605" ]
[ "nonn" ]
15
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2022-09-02T09:46:02
oeisdata/seq/A012/A012780.seq
6c77bc148c97a3fdca0c395177d04168
A012781
Take every 5th term of Padovan sequence A000931, beginning with the second term.
[ "0", "1", "4", "16", "65", "265", "1081", "4410", "17991", "73396", "299426", "1221537", "4983377", "20330163", "82938844", "338356945", "1380359512", "5631308624", "22973462017", "93722435101", "382349636061", "1559831901918", "6363483400447", "25960439030624" ]
[ "nonn", "easy" ]
56
0
3
null
null
N. J. A. Sloane
2022-09-08T08:44:38
oeisdata/seq/A012/A012781.seq
3b636cc67f2f93ff4e3b402357464832
A012782
exp(sec(x)*arcsin(x))=1+x+1/2!*x^2+5/3!*x^3+17/4!*x^4+85/5!*x^5...
[ "1", "1", "1", "5", "17", "85", "505", "3201", "25153", "204905", "1945265", "19581949", "217998673", "2608398013", "33522871785", "463598293497", "6789373095937", "106484041306577", "1755926841763681", "30821112722260469", "566210591513987345" ]
[ "nonn" ]
4
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:08
oeisdata/seq/A012/A012782.seq
cd706ed9205dab1caaad0068527ab9ee
A012783
sin(sec(x)*arcsin(x))=x+3/3!*x^3+5/5!*x^5-889/7!*x^7-82167/9!*x^9...
[ "1", "3", "5", "-889", "-82167", "-7869301", "-906141171", "-128450716913", "-22562588189167", "-4955964959446253", "-1381444138161821675", "-495014642393801914473", "-227710892670360844819175", "-131704509800404485504904293" ]
[ "sign" ]
4
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:08
oeisdata/seq/A012/A012783.seq
31090194ae412d7499f531422d01bc1b
A012784
arcsin(sec(x)*arcsin(x))=x+5/3!*x^3+93/5!*x^5+4545/7!*x^7+443065/9!*x^9...
[ "1", "5", "93", "4545", "443065", "72439325", "17846988885", "6173626900441", "2852644920170097", "1696726612682937781", "1262481961197490093645", "1148731484660194718055025", "1254736888520332652127806761" ]
[ "nonn" ]
6
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2017-01-12T14:56:21
oeisdata/seq/A012/A012784.seq
b6db01405e27895bd9c1a8c5d5e04e91
A012785
tan(sec(x)*arcsin(x))=x+6/3!*x^3+140/5!*x^5+7616/7!*x^7+731856/9!*x^9...
[ "1", "6", "140", "7616", "731856", "108552224", "22943169600", "6543956234752", "2420812240335104", "1126850609820597760", "644442125440553221120", "444134934522130204704768", "363006744066808568769433600" ]
[ "nonn" ]
10
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-02-07T03:59:39
oeisdata/seq/A012/A012785.seq
c34a81cd0c736557adcc303992058a4f
A012786
arctan(sec(x)*arcsin(x))=x+2/3!*x^3-12/5!*x^5-432/7!*x^7+10000/9!*x^9...
[ "1", "2", "-12", "-432", "10000", "1500512", "-18269760", "-16350361856", "922523568384", "990634832194048", "92553699220882432", "-44373953423964778496", "9057208032779104423936", "25540436414796388855898112" ]
[ "sign" ]
4
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:08
oeisdata/seq/A012/A012786.seq
3a2358f0e4b362acdcf45ca53ba7a15e
A012787
cos(sec(x)*arcsin(x))=1-1/2!*x^2-15/4!*x^4-345/6!*x^6-11263/8!*x^8...
[ "1", "-1", "-15", "-345", "-11263", "-455025", "-16466703", "746021367", "480286325633", "150637957014303", "46203820378253425", "15313454320801213511", "5643895146092962507905", "2333857400234709586763695" ]
[ "sign" ]
6
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-05-26T10:14:54
oeisdata/seq/A012/A012787.seq
7bb5c528c138c5620477c68f3579375d
A012788
sinh(sec(x)*arcsin(x))=x+5/3!*x^3+85/5!*x^5+3201/7!*x^7+204905/9!*x^9...
[ "1", "5", "85", "3201", "204905", "19581949", "2608398013", "463598293497", "106484041306577", "30821112722260469", "11011429241275209765", "4772177089034491961201", "2471736193532210009786425", "1510365281819897595496029677" ]
[ "nonn" ]
6
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-06-07T16:49:16
oeisdata/seq/A012/A012788.seq
d27e794266f623b875349d6ca0932f7c
A012789
arcsinh(sec(x)*arcsin(x))=x+3/3!*x^3+13/5!*x^5+7/7!*x^7+5465/9!*x^9...
[ "1", "3", "13", "7", "5465", "978923", "85275045", "6907939183", "1989186790065", "849732569279059", "291378385380567613", "103124375038834822231", "54929709590807595546121", "39029092314830559489826107" ]
[ "nonn" ]
6
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2014-05-02T15:18:14
oeisdata/seq/A012/A012789.seq
e3d2b3a114a8cb44b374bfab7b9db38a
A012790
tanh(sec(x)*arcsin(x))=x+2/3!*x^3-20/5!*x^5-1104/7!*x^7-23728/9!*x^9...
[ "1", "2", "-20", "-1104", "-23728", "2048224", "394518592", "28921612032", "-3968669081344", "-2038929577444864", "-347998546570798080", "59058720637105172480", "67936182152875665510400", "22515279368057454566531072" ]
[ "sign" ]
4
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:08
oeisdata/seq/A012/A012790.seq
b2c05967074114e927858c7fb15241dd
A012791
arctanh(sec(x)*arcsin(x))=x+6/3!*x^3+148/5!*x^5+9184/7!*x^7...
[ "1", "6", "148", "9184", "1066640", "199000736", "54431471040", "20523724218880", "10203766053312768", "6467780044492713472", "5090997086675585360896", "4871968356294907783585792", "5570589015199967686042095616" ]
[ "nonn" ]
7
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-02-05T15:23:54
oeisdata/seq/A012/A012791.seq
35f5db11e8930c3a624511d0c7858f66
A012792
cosh(sec(x)*arcsin(x))=1+1/2!*x^2+17/4!*x^4+505/6!*x^6+25153/8!*x^8...
[ "1", "1", "17", "505", "25153", "1945265", "217998673", "33522871785", "6789373095937", "1755926841763681", "566210591513987345", "223294329140130622169", "105980484509441390341953", "59708382496464697426393105" ]
[ "nonn" ]
4
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:08
oeisdata/seq/A012/A012792.seq
6eb5f96cfc13ee4e2b602ea6b8452f6a
A012793
sec(sec(x)*arcsin(x))=1+1/2!*x^2+21/4!*x^4+885/6!*x^6+67753/8!*x^8...
[ "1", "1", "21", "885", "67753", "8319945", "1497879933", "371676224829", "121584750716497", "50703653565909009", "26255891609845966565", "16529283187035337691269", "12432784542297124704745209", "11011634249882125250110463705" ]
[ "nonn" ]
6
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-03-16T09:44:25
oeisdata/seq/A012/A012793.seq
00e3c76ae369a3802ca9ba66464d9f7a
A012794
sech(sec(x)*arcsin(x))=1-1/2!*x^2-11/4!*x^4-85/6!*x^6+4457/8!*x^8...
[ "1", "-1", "-11", "-85", "4457", "456055", "19404317", "-2130838749", "-709981721647", "-88561132771729", "8928572938556485", "8215826370826826011", "1643974395579178155321", "-777302111773052397223705", "-927256122029195944220743571", "-491644215408419904657774637165" ]
[ "sign" ]
6
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-03-25T16:27:20
oeisdata/seq/A012/A012794.seq
488ecd8e0e1edddc535d77c06baa0b60
A012795
arcsin(sec(x)*tan(x))=x+6/3!*x^3+120/5!*x^5+6216/7!*x^7+652800/9!*x^9...
[ "1", "6", "120", "6216", "652800", "115944576", "31101732480", "11717149191936", "5895158281052160", "3816842537847607296", "3090738173477544099840", "3060041827367678200774656", "3636490261219371329053163520" ]
[ "nonn" ]
6
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-07-18T14:08:52
oeisdata/seq/A012/A012795.seq
b05e19ed9ada8633193d2c10efb26577
A012796
arctan(sec(x)*tan(x))=x+3/3!*x^3-15/5!*x^5-1197/7!*x^7-255/9!*x^9...
[ "1", "3", "-15", "-1197", "-255", "5448003", "241437105", "-104019879597", "-17849464279935", "5108933510880003", "2525823613297136625", "-425245839735677809197", "-661733086487793705145215", "-4593026819719423131883197" ]
[ "sign" ]
6
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2017-05-22T18:30:39
oeisdata/seq/A012/A012796.seq
5a48179acc513bef339e04b1a89bf183
A012797
arcsinh(sec(x)*tan(x))=x+4/3!*x^3+20/5!*x^5-296/7!*x^7-13360/9!*x^9...
[ "1", "4", "20", "-296", "-13360", "1256704", "189575360", "-11506868096", "-7128426008320", "49808403426304", "682296985566233600", "90438749300061435904", "-128380014279650042490880", "-53104829106323270490423296" ]
[ "sign" ]
6
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2014-09-23T12:26:31
oeisdata/seq/A012/A012797.seq
05d6a1ba668ea1ae6fcde55ce2a96a0a
A012798
arctanh(sec(x)*tan(x))=x+7/3!*x^3+185/5!*x^5+12367/7!*x^7...
[ "1", "7", "185", "12367", "1558865", "316097527", "94003171145", "38543705698687", "20840298552277025", "14366953364916735847", "12299504390976449116505", "12801737583190675819689007", "15920156445351352463114729585" ]
[ "nonn" ]
7
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-02-05T15:29:34
oeisdata/seq/A012/A012798.seq
9775ad14f7081e525cff8f7ae0dbacbe
A012799
sec(sec(x)*tan(x))=1+1/2!*x^2+25/4!*x^4+1177/6!*x^6+98705/8!*x^8...
[ "1", "1", "25", "1177", "98705", "13250769", "2607761385", "707007382057", "252591724020385", "115013019820614177", "65019184411131252025", "44683093185748102178361", "36687179790948560158256945", "35468646820376578609567141873" ]
[ "nonn" ]
6
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2023-09-11T12:02:10
oeisdata/seq/A012/A012799.seq
e045d01b4265a575f764af8c56eb7faf
A012800
sech(sec(x)*tan(x))=1-1/2!*x^2-15/4!*x^4-177/6!*x^6+8225/8!*x^8...
[ "1", "-1", "-15", "-177", "8225", "1259231", "82092945", "-6743602257", "-3731314041535", "-658546620230977", "68462273756819505", "102601344100683911439", "37004621343746850934625", "-3605666448860960629195873" ]
[ "sign" ]
6
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2017-07-02T10:58:17
oeisdata/seq/A012/A012800.seq
2c5485fb7c7f416d8771f9d3d64f0cf1