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7
| sequence_name
stringlengths 4
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listlengths 1
348
| keywords
listlengths 1
8
| score
int64 1
2.35k
| offset_a
int64 -14,827
666,262,453B
| offset_b
int64 0
635M
⌀ | cross_references
listlengths 1
128
⌀ | former_ids
listlengths 1
3
⌀ | author
stringlengths 7
231
⌀ | timestamp
timestamp[us]date 1999-12-11 03:00:00
2025-07-19 00:40:46
| filename
stringlengths 29
29
| hash
stringlengths 32
32
|
|---|---|---|---|---|---|---|---|---|---|---|---|---|
A012101
|
Expansion of tan(arcsin(sinh(x))) (odd powers only).
|
[
"1",
"4",
"76",
"3424",
"277456",
"35345344",
"6504742336",
"1632531979264",
"535821754153216",
"222769351470429184",
"114411762387714436096",
"71132353206363509039104",
"52648938670226334981246976"
] |
[
"nonn"
] | 17 | 0 | 2 |
[
"A012101",
"A012571"
] | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2017-04-17T12:49:45 |
oeisdata/seq/A012/A012101.seq
|
e2e03855f6bd744aee4f9995e2935e7b
|
A012102
|
arctan(arcsin(sinh(x)))=x+4/5!*x^5+192/7!*x^7+9616/9!*x^9...
|
[
"1",
"0",
"4",
"192",
"9616",
"1115392",
"172350528",
"37703053312",
"10989042954496",
"4099556761067520",
"1910734175200936960",
"1087150572502335373312",
"741705342559787764715520",
"597689034047543849712812032"
] |
[
"nonn"
] | 6 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2014-07-13T12:04:50 |
oeisdata/seq/A012/A012102.seq
|
70be1755f9bd023bb38beea60ed8cc2a
|
A012103
|
cos(arcsin(sinh(x))) = 1-1/2!*x^2-7/4!*x^4-121/6!*x^6-5167/8!*x^8...
|
[
"1",
"-1",
"-7",
"-121",
"-5167",
"-410641",
"-51771127",
"-9466034761",
"-2365187249887",
"-773771636088481",
"-320901749327353447",
"-164490143309272987801",
"-102106049239499080993807",
"-75475990780239097513548721"
] |
[
"sign"
] | 10 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2017-05-28T14:53:40 |
oeisdata/seq/A012/A012103.seq
|
20b934c5eb600e09adfb60fb830319e3
|
A012104
|
sinh(arcsin(sinh(x)))=x+3/3!*x^3+41/5!*x^5+1403/7!*x^7+90641/9!*x^9...
|
[
"1",
"3",
"41",
"1403",
"90641",
"9578803",
"1504717241",
"329275068203",
"95780865239841",
"35749976635509603",
"16656470900685818441",
"9475632849374117143003",
"6463874923226439205813041",
"5208135569542179761157408403"
] |
[
"nonn"
] | 4 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:50:40 |
oeisdata/seq/A012/A012104.seq
|
4c99c44598410fdf8c37217bb631fce8
|
A012105
|
arcsinh(arcsin(sinh(x)))=x+1/3!*x^3+9/5!*x^5+337/7!*x^7+20433/9!*x^9...
|
[
"1",
"1",
"9",
"337",
"20433",
"2146497",
"334449049",
"72730741137",
"21072553238433",
"7839688801269505",
"3643403659959276585",
"2068430144100589034577",
"1408597220893698317848945",
"1133327555472108223412440257"
] |
[
"nonn"
] | 4 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:50:40 |
oeisdata/seq/A012/A012105.seq
|
43d2f98bf049453f52b78d2637d5aaff
|
A012106
|
tanh(arcsin(sinh(x)))=x-4/5!*x^5+80/7!*x^7+5456/9!*x^9+511360/11!*x^11...
|
[
"1",
"0",
"-4",
"80",
"5456",
"511360",
"83316416",
"18755459840",
"5535063173376",
"2088819464171520",
"981883326234254336",
"562564553455472742400",
"385997167840660261687296",
"312523332440480815021588480"
] |
[
"sign"
] | 4 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:50:40 |
oeisdata/seq/A012/A012106.seq
|
6fe718f0de4ab0f436bd208dc025ddf7
|
A012107
|
arctanh(arcsin(sinh(x)))=x+4/3!*x^3+84/5!*x^5+4432/7!*x^7+432144/9!*x^9...
|
[
"1",
"4",
"84",
"4432",
"432144",
"67336512",
"15330202432",
"4799825862912",
"1978228668612864",
"1038257514383795200",
"676117122084133770240",
"534973800492211106598912",
"505535479689176978173726720"
] |
[
"nonn"
] | 6 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2015-02-05T11:50:35 |
oeisdata/seq/A012/A012107.seq
|
9750667043feebba869ef54601e618bf
|
A012108
|
cosh(arcsin(sinh(x)))=1+1/2!*x^2+9/4!*x^4+201/6!*x^6+9649/8!*x^8...
|
[
"1",
"1",
"9",
"201",
"9649",
"809201",
"105268089",
"19650225401",
"4982657935329",
"1648151554792801",
"689411371817131369",
"355814217290199455401",
"222111401946937825176209",
"164952387078229730219557201"
] |
[
"nonn"
] | 6 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2015-03-19T10:16:17 |
oeisdata/seq/A012/A012108.seq
|
92b0dbdcb6dad8e3e6aac4dddabb46c5
|
A012109
|
sec(arcsin(sinh(x)))=1+1/2!*x^2+13/4!*x^4+421/6!*x^6+26713/8!*x^8...
|
[
"1",
"1",
"13",
"421",
"26713",
"2794441",
"436186213",
"95033434861",
"27555582190513",
"10260037095841681",
"4771143086720391613",
"2710025439753915534901",
"1846296024220715321941513",
"1486014763274444231870834521"
] |
[
"nonn"
] | 18 | 0 | 3 |
[
"A012109",
"A012261"
] | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2017-05-06T00:28:03 |
oeisdata/seq/A012/A012109.seq
|
8df0ee888f0f405181a70dfd5bf57ecd
|
A012110
|
sech(arcsin(sinh(x)))=1-1/2!*x^2-3/4!*x^4-21/6!*x^6-1543/8!*x^8...
|
[
"1",
"-1",
"-3",
"-21",
"-1543",
"-139241",
"-17567883",
"-3247844861",
"-820544875023",
"-270409929116881",
"-112752402237298963",
"-58042577464009155301",
"-36153625550535244615703",
"-26800108152000698851560121"
] |
[
"sign"
] | 6 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2020-03-19T17:10:31 |
oeisdata/seq/A012/A012110.seq
|
04ee9b1257919eef1cf1cb6350796700
|
A012111
|
Expansion of e.g.f.: exp(arcsin(arcsinh(x)))=1+x+1/2!*x^2+1/3!*x^3+1/4!*x^4+9/5!*x^5...
|
[
"1",
"1",
"1",
"1",
"1",
"9",
"49",
"113",
"1",
"6993",
"83361",
"171777",
"-2206335",
"45264153",
"961321425",
"412458993",
"-96313079295",
"1241225427105",
"41773143339585",
"-81335384742015",
"-9493597481579775",
"102955176831541545",
"4967941000109596785"
] |
[
"sign"
] | 6 | 0 | 6 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2019-07-31T13:13:24 |
oeisdata/seq/A012/A012111.seq
|
02559b352a3ecf5d5e0d6ccf01d15370
|
A012112
|
arcsin(arcsin(arcsinh(x)))=x+1/3!*x^3+17/5!*x^5+337/7!*x^7+26081/9!*x^9...
|
[
"1",
"1",
"17",
"337",
"26081",
"1744865",
"309508209",
"45520971441",
"14262333206209",
"3762227031539905",
"1815125042343268305",
"760652468272079182097",
"519897554030667139338913",
"319124893510287714867264161"
] |
[
"nonn"
] | 4 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:50:40 |
oeisdata/seq/A012/A012112.seq
|
21554a292969c9c7239cdd7e9e2621d8
|
A012113
|
Expansion of e.g.f. tan(arcsin(arcsinh(x))) (odd powers only).
|
[
"1",
"2",
"24",
"552",
"28032",
"1778688",
"212383872",
"25215328512",
"5734229114880",
"1029078328135680",
"410202091438571520",
"93624495716395745280",
"65377722614151010222080",
"15441784659337549573324800"
] |
[
"nonn"
] | 14 | 1 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2018-01-29T02:52:54 |
oeisdata/seq/A012/A012113.seq
|
bdfedff871daeef34378bb6d4916b74a
|
A012114
|
Expansion of e.g.f. arctan(arcsin(arcsinh(x))), odd powers only.
|
[
"1",
"-2",
"32",
"-1112",
"76544",
"-8132992",
"1287179904",
"-277075027200",
"78957666709504",
"-28538628272500736",
"12818361767117881344",
"-6984131400017632559104",
"4545914404919471492988928",
"-3480400203322521156596334592",
"3098206994542298409092871880704",
"-3171988840442245479109838621638656"
] |
[
"sign"
] | 11 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2017-03-09T16:54:17 |
oeisdata/seq/A012/A012114.seq
|
199ccd943fc2d8900dc72a347e154113
|
A012115
|
Expansion of e.g.f. of cos(arcsin(arcsinh(x))), even powers only.
|
[
"1",
"-1",
"1",
"-49",
"897",
"-96801",
"6803457",
"-1275363153",
"207592347393",
"-60889593787713",
"17888210916886017",
"-7679611833095218545",
"3530100224793651058305",
"-2109645360096014314212705",
"1387893136694794953345211905",
"-1109191050707015380265790041745",
"984063632341385922413073350925825"
] |
[
"sign"
] | 12 | 0 | 4 |
[
"A012115",
"A012248"
] | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2017-04-12T18:16:27 |
oeisdata/seq/A012/A012115.seq
|
4aca2f703f83fd13527f2ff7a89ee5fe
|
A012116
|
sinh(arcsin(arcsinh(x)))=x+1/3!*x^3+9/5!*x^5+113/7!*x^7+6993/9!*x^9...
|
[
"1",
"1",
"9",
"113",
"6993",
"171777",
"45264153",
"412458993",
"1241225427105",
"-81335384742015",
"102955176831541545",
"-22142143528417205775",
"20775502075935299781105",
"-8945394343172069982368895"
] |
[
"sign"
] | 7 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2013-11-21T12:46:01 |
oeisdata/seq/A012/A012116.seq
|
645cd944b33fc3109876ea8248aa491c
|
A012117
|
arcsinh(arcsin(arcsinh(x)))=x-1/3!*x^3+17/5!*x^5-449/7!*x^7+30113/9!*x^9...
|
[
"1",
"-1",
"17",
"-449",
"30113",
"-2761793",
"415351089",
"-81370683393",
"21955730621249",
"-7408485122203009",
"3161408870916725841",
"-1630838373598845388097",
"1013685573603673847917793",
"-741353146138643571687256001"
] |
[
"sign"
] | 6 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2017-08-07T12:37:15 |
oeisdata/seq/A012/A012117.seq
|
cd0f41beda7c45bac6347b278c806fd9
|
A012118
|
tanh(arcsin(arcsinh(x)))=x-2/3!*x^3+24/5!*x^5-664/7!*x^7+36096/9!*x^9...
|
[
"1",
"-2",
"24",
"-664",
"36096",
"-3054336",
"389859456",
"-67637286144",
"15712242647040",
"-4624447960903680",
"1704772464238264320",
"-762137182003035340800",
"409146648871581200056320",
"-258451658825083238747013120"
] |
[
"sign"
] | 7 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2013-11-21T12:46:01 |
oeisdata/seq/A012/A012118.seq
|
7a2d1039412cbc50671511c7e4f9569d
|
A012119
|
arctanh(arcsin(arcsinh(x)))=x+2/3!*x^3+32/5!*x^5+1000/7!*x^7+68480/9!*x^9...
|
[
"1",
"2",
"32",
"1000",
"68480",
"6561664",
"1023602304",
"201257787648",
"56084851257344",
"18730102842232832",
"8177799266538749952",
"4153222601561664323584",
"2616197218964411007008768",
"1879040755111699467662589952"
] |
[
"nonn"
] | 7 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2015-02-05T11:54:20 |
oeisdata/seq/A012/A012119.seq
|
4639dd5b72ad78a83af259d60d6e8e07
|
A012120
|
cosh(arcsin(arcsinh(x)))=1+1/2!*x^2+1/4!*x^4+49/6!*x^6+1/8!*x^8...
|
[
"1",
"1",
"1",
"49",
"1",
"83361",
"-2206335",
"961321425",
"-96313079295",
"41773143339585",
"-9493597481579775",
"4967941000109596785",
"-1991874953215606007295",
"1319075774798596975837665",
"-807077677117010238256087935"
] |
[
"sign"
] | 6 | 0 | 4 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2013-11-22T13:16:39 |
oeisdata/seq/A012/A012120.seq
|
82b84fc073199f78e990f606f771e7f4
|
A012121
|
sec(arcsin(arcsinh(x)))=1+1/2!*x^2+5/4!*x^4+109/6!*x^6+3177/8!*x^8...
|
[
"1",
"1",
"5",
"109",
"3177",
"227961",
"15773229",
"2521786149",
"294715261521",
"91106569198449",
"14283819393505749",
"8353531761471301725",
"1366332291998753348025",
"1671117489759750577634025",
"171277162439935833445571325",
"660477991317304143815464418325"
] |
[
"nonn"
] | 6 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2017-10-09T11:15:09 |
oeisdata/seq/A012/A012121.seq
|
6540c242ed520939b2dde723ffef3fff
|
A012122
|
sech(arcsin(arcsinh(x)))=1-1/2!*x^2+5/4!*x^4-109/6!*x^6+4073/8!*x^8...
|
[
"1",
"-1",
"5",
"-109",
"4073",
"-295161",
"30105261",
"-4622444709",
"920180967249",
"-244553774342769",
"80285311139524821",
"-32887829518696856925",
"16096767138947015536185",
"-9423401435342942243589225"
] |
[
"sign"
] | 6 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2016-03-19T14:10:24 |
oeisdata/seq/A012/A012122.seq
|
52b60e18a998428adb1e5e825751374b
|
A012123
|
E.g.f.: exp(arcsin(tanh(x))).
|
[
"1",
"1",
"1",
"0",
"-3",
"-4",
"21",
"80",
"-263",
"-2224",
"4841",
"88960",
"-99723",
"-4942144",
"-199939",
"366928640",
"501445617",
"-35219691264",
"-101818966319",
"4251941253120",
"19731909099757",
"-631113275843584",
"-4192563651606299",
"113005305852006400",
"1009030667701246697"
] |
[
"sign"
] | 32 | 0 | 5 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2017-05-22T12:59:41 |
oeisdata/seq/A012/A012123.seq
|
6fb13a3de8ef786c454bbeee11f64a33
|
A012124
|
arcsin(arcsin(tanh(x)))=x+4/5!*x^5+24/7!*x^7+1744/9!*x^9+61504/11!*x^11...
|
[
"1",
"0",
"4",
"24",
"1744",
"61504",
"6700992",
"632723584",
"106726576384",
"19137224693760",
"4819549055104000",
"1376115921056118784",
"493566558620424622080",
"203121814961910275620864",
"99267625002820837091098624"
] |
[
"nonn"
] | 4 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:50:41 |
oeisdata/seq/A012/A012124.seq
|
a421b41b742833a36f6db8e1129da5f0
|
A012125
|
Expansion of x/ (1-4*x+16*x^2)^(3/2).
|
[
"0",
"1",
"6",
"6",
"-100",
"-570",
"-588",
"8092",
"45432",
"47430",
"-607420",
"-3385932",
"-3557112",
"43868188",
"243513480",
"256815480",
"-3094459408",
"-17130508218",
"-18113603868",
"214848211780",
"1187079671400",
"1257576694836",
"-14747640408424",
"-81367084566264",
"-86322262278000",
"1003635505135900"
] |
[
"sign"
] | 27 | 0 | 3 |
[
"A012125",
"A025175"
] | null |
Wouter Meeussen
| 2021-05-07T16:54:47 |
oeisdata/seq/A012/A012125.seq
|
a9c47942fde479f073873f9672a7b484
|
A012126
|
arctan(arcsin(tanh(x)))=x-3/3!*x^3+49/5!*x^5-1971/7!*x^7+147457/9!*x^9...
|
[
"1",
"-3",
"49",
"-1971",
"147457",
"-17712131",
"3119521521",
"-757475512691",
"242537719364737",
"-99014166389423235",
"50196880291533920305",
"-30939568726951088808371",
"22784988607303653453394305"
] |
[
"sign"
] | 4 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:50:41 |
oeisdata/seq/A012/A012126.seq
|
2e77c01aa6e7aa5b0abba2e636d7d9b2
|
A012127
|
sinh(arcsin(tanh(x)))=x-4/5!*x^5+80/7!*x^7-2224/9!*x^9+88960/11!*x^11...
|
[
"1",
"0",
"-4",
"80",
"-2224",
"88960",
"-4942144",
"366928640",
"-35219691264",
"4251941253120",
"-631113275843584",
"113005305852006400",
"-24021321751206703104",
"5979261710118927892480"
] |
[
"sign"
] | 6 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2019-08-08T15:48:39 |
oeisdata/seq/A012/A012127.seq
|
2556608620d81770bcfbdda60bf89266
|
A012128
|
arcsinh(arcsin(tanh(x)))=x-2/3!*x^3+24/5!*x^5-776/7!*x^7+49536/9!*x^9...
|
[
"1",
"-2",
"24",
"-776",
"49536",
"-5271936",
"842846848",
"-188826614016",
"56431158829056",
"-21687384462233600",
"10419278733341491200",
"-6118220781221123260416",
"4311116228906909580820480",
"-3590017073187013127497383936"
] |
[
"sign"
] | 6 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2021-08-03T19:48:19 |
oeisdata/seq/A012/A012128.seq
|
64f367fef4ab17759c51a50b5eca0316
|
A012129
|
tanh(arcsin(tanh(x)))=x-3/3!*x^3+41/5!*x^5-1243/7!*x^7+65681/9!*x^9...
|
[
"1",
"-3",
"41",
"-1243",
"65681",
"-5335283",
"616216121",
"-95919970123",
"19349625251361",
"-4909180152449763",
"1529770153928451401",
"-574346328696763158203",
"255703860384773029976241",
"-133196988269151890206719443"
] |
[
"sign"
] | 6 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2022-06-23T10:15:39 |
oeisdata/seq/A012/A012129.seq
|
22f333af742d924e10e8b942228f42d0
|
A012130
|
arctanh(arcsin(tanh(x)))=x+1/3!*x^3+9/5!*x^5+169/7!*x^7+6513/9!*x^9...
|
[
"1",
"1",
"9",
"169",
"6513",
"382449",
"33949369",
"4083320409",
"654225568353",
"132856897394785",
"33620948951783145",
"10322993203249787529",
"3791611637554126839505",
"1638719968206448148183889"
] |
[
"nonn"
] | 7 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2015-02-05T11:56:38 |
oeisdata/seq/A012/A012130.seq
|
09b3e13c29203425c54268f39da41c6a
|
A012131
|
cosh(arcsin(tanh(x)))=1+1/2!*x^2-3/4!*x^4+21/6!*x^6-263/8!*x^8...
|
[
"1",
"1",
"-3",
"21",
"-263",
"4841",
"-99723",
"-199939",
"501445617",
"-101818966319",
"19731909099757",
"-4192563651606299",
"1009030667701246697",
"-277080625752723191879",
"86724157841631252590437",
"-30813037783471577493355059",
"12363651257099764677344554977"
] |
[
"sign"
] | 10 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2015-03-08T17:52:11 |
oeisdata/seq/A012/A012131.seq
|
4abd19557cdb508eef61b05e49ce518b
|
A012132
|
Numbers z such that x*(x+1) + y*(y+1) = z*(z+1) is solvable in positive integers x,y.
|
[
"3",
"6",
"8",
"10",
"11",
"13",
"15",
"16",
"18",
"20",
"21",
"23",
"26",
"27",
"28",
"31",
"33",
"36",
"37",
"38",
"40",
"41",
"43",
"44",
"45",
"46",
"48",
"49",
"51",
"52",
"53",
"54",
"55",
"56",
"57",
"58",
"59",
"61",
"62",
"63",
"64",
"66",
"67",
"68",
"71",
"73",
"74",
"75",
"76",
"77",
"78",
"80",
"81",
"83",
"86",
"88",
"89",
"91",
"92",
"93"
] |
[
"nonn"
] | 85 | 1 | 1 |
[
"A000217",
"A001108",
"A001652",
"A012132",
"A027861",
"A047219",
"A098790",
"A115598",
"A124124",
"A166080",
"A212160",
"A212161"
] | null |
Sander van Rijnswou (sander(AT)win.tue.nl)
| 2023-12-30T03:06:32 |
oeisdata/seq/A012/A012132.seq
|
ac49631e70dac3599f3a0929319e0024
|
A012133
|
sech(arcsin(tanh(x)))=1-1/2!*x^2+9/4!*x^4-201/6!*x^6+8369/8!*x^8...
|
[
"1",
"-1",
"9",
"-201",
"8369",
"-559601",
"54852729",
"-7411089401",
"1320161221089",
"-299803443573601",
"84543945702681449",
"-28984920596097196201",
"11872728882101557841809",
"-5726623333843769342341201"
] |
[
"sign"
] | 6 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2022-09-21T14:57:40 |
oeisdata/seq/A012/A012133.seq
|
9b6ffc073f4fb60dab147bf180cc166a
|
A012134
|
exp(arcsin(arctanh(x)))=1+x+1/2!*x^2+4/3!*x^3+13/4!*x^4+84/5!*x^5...
|
[
"1",
"1",
"1",
"4",
"13",
"84",
"469",
"4208",
"33433",
"386064",
"3984681",
"56523072",
"718210725",
"12121690944",
"183013440765",
"3589856932608",
"62801454477105",
"1406019035808000",
"27970921286867025",
"704535958463063040"
] |
[
"nonn"
] | 7 | 0 | 4 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2013-11-21T12:46:01 |
oeisdata/seq/A012/A012134.seq
|
210e74e715602f0012a976171e913fb1
|
A012135
|
arcsin(arcsin(arctanh(x)))=x+4/3!*x^3+92/5!*x^5+5272/7!*x^7+567440/9!*x^9...
|
[
"1",
"4",
"92",
"5272",
"567440",
"98979200",
"25530690624",
"9147312168576",
"4349983363258624",
"2652517304182955008",
"2018610268528861424640",
"1875904660571518053251072",
"2091013498538531655993561088"
] |
[
"nonn"
] | 6 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2019-03-22T17:15:07 |
oeisdata/seq/A012/A012135.seq
|
b30463b69d698617ac012114373bfc45
|
A012136
|
Expansion of e.g.f. tan(arcsin(arctanh(x))) (odd powers only).
|
[
"1",
"5",
"129",
"7797",
"848481",
"145041093",
"35799178401",
"12045448529397",
"5298881528389185",
"2952169020073027845",
"2031522244065649876545",
"1692164698229362361298165",
"1677876856826199251515980705"
] |
[
"nonn"
] | 14 | 1 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2024-05-08T05:13:03 |
oeisdata/seq/A012/A012136.seq
|
73a3fdf5961abca7470246825b33a712
|
A012137
|
arctan(arcsin(arctanh(x))) = x + (1/3!)*x^3 + (17/5!)*x^5 + (673/7!)*x^7 + (54305/9!)*x^9 + ...
|
[
"1",
"1",
"17",
"673",
"54305",
"7334273",
"1497501873",
"430436005665",
"165573876222529",
"82074493484054017",
"50922938856050558289",
"38644611846710150572193",
"35205379514991276523808353",
"37909794281251146499011279233"
] |
[
"nonn"
] | 9 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2020-01-18T19:50:59 |
oeisdata/seq/A012/A012137.seq
|
ee5282a40bcb180f57aa6949a9aebb34
|
A012138
|
cos(arcsin(arctanh(x)))=1-1/2!*x^2-11/4!*x^4-349/6!*x^6-22455/8!*x^8...
|
[
"1",
"-1",
"-11",
"-349",
"-22455",
"-2465241",
"-416217603",
"-100729124469",
"-33198564667887",
"-14328891118054449",
"-7852649782447649403",
"-5329635152693662625805",
"-4388960085492355649955495"
] |
[
"sign"
] | 5 | 0 | 3 |
[
"A012138",
"A012251"
] | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:50:41 |
oeisdata/seq/A012/A012138.seq
|
d83cede26f94a8573e54197d28b7a003
|
A012139
|
sinh(arcsin(arctanh(x)))=x+4/3!*x^3+84/5!*x^5+4208/7!*x^7+386064/9!*x^9...
|
[
"1",
"4",
"84",
"4208",
"386064",
"56523072",
"12121690944",
"3589856932608",
"1406019035808000",
"704535958463063040",
"439949357001315947520",
"335139715537167259791360",
"305989012726577998256148480"
] |
[
"nonn"
] | 4 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:50:41 |
oeisdata/seq/A012/A012139.seq
|
bf4eb94b86690872f5d9167de711071a
|
A012140
|
arcsinh(arcsin(arctanh(x)))=x+2/3!*x^3+32/5!*x^5+1336/7!*x^7...
|
[
"1",
"2",
"32",
"1336",
"108800",
"14701312",
"2986596480",
"852635258112",
"325714440802304",
"160437668874481664",
"98998538588401238016",
"74780329820590921056256",
"67860526461080359727955968",
"72835853250644384064569933824"
] |
[
"nonn"
] | 6 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2023-01-09T18:38:20 |
oeisdata/seq/A012/A012140.seq
|
f1aa0e8863daffca482ba7234cbc44f4
|
A012141
|
tanh(arcsin(arctanh(x)))=x+1/3!*x^3+9/5!*x^5+281/7!*x^7+20913/9!*x^9...
|
[
"1",
"1",
"9",
"281",
"20913",
"2869329",
"613734393",
"185272366761",
"74333015297505",
"38107181118565665",
"24270343990842570345",
"18795056467624757017785",
"17394205995630055629900945",
"18964089582659357000823035505"
] |
[
"nonn"
] | 7 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2013-11-21T12:46:01 |
oeisdata/seq/A012/A012141.seq
|
38be9887437d006e9bb65f840f72f55c
|
A012142
|
Expansion of e.g.f. arctanh(arcsin(arctanh(x))), odd powers only.
|
[
"1",
"5",
"137",
"9085",
"1107665",
"215251189",
"61040810841",
"23787478734573",
"12195876997744289",
"7959108767371738085",
"6442333032874852024617",
"6333998826435424439107165",
"7435387461759207059826574193",
"10272314131487696006461656792277",
"16499075087858185014891901869790713"
] |
[
"nonn"
] | 16 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2018-08-19T02:50:33 |
oeisdata/seq/A012/A012142.seq
|
2ca52899e03a71f0f1701f616f8b6c4c
|
A012143
|
cosh(arcsin(arctanh(x)))=1+1/2!*x^2+13/4!*x^4+469/6!*x^6+33433/8!*x^8...
|
[
"1",
"1",
"13",
"469",
"33433",
"3984681",
"718210725",
"183013440765",
"62801454477105",
"27970921286867025",
"15708198897246520125",
"10866653910101298549285",
"9083998201236955132833225",
"9030162506735790711308044665"
] |
[
"nonn"
] | 4 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:50:41 |
oeisdata/seq/A012/A012143.seq
|
d5ff86d550fd78ddf84c6518c3e40aed
|
A012144
|
sec(arcsin(arctanh(x)))=1+1/2!*x^2+17/4!*x^4+769/6!*x^6+66849/8!*x^8...
|
[
"1",
"1",
"17",
"769",
"66849",
"9506241",
"2007271089",
"589807203777",
"230194642564161",
"115219444193968257",
"71962921603647030609",
"54865853223458268869505",
"50151129904368572197783905",
"54139213630083955379966633025"
] |
[
"nonn"
] | 6 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2022-06-22T15:35:25 |
oeisdata/seq/A012/A012144.seq
|
cc633c92512526664137f4c46aadbadc
|
A012145
|
sech(arcsin(arctanh(x)))=1-1/2!*x^2-7/4!*x^4-169/6!*x^6-9199/8!*x^8...
|
[
"1",
"-1",
"-7",
"-169",
"-9199",
"-915441",
"-146524599",
"-34565815257",
"-11286151088991",
"-4868161148587617",
"-2677533017865604839",
"-1826930427561513127305",
"-1513046625847449915823695",
"-1494316021415982844933350225"
] |
[
"sign"
] | 6 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2022-05-05T18:28:09 |
oeisdata/seq/A012/A012145.seq
|
7627a7c6938e83a0a299187d24c95c52
|
A012146
|
arcsin(tan(sin(x)))=x+2/3!*x^3+16/5!*x^5+440/7!*x^7+27904/9!*x^9...
|
[
"1",
"2",
"16",
"440",
"27904",
"2850176",
"425017984",
"88153419008",
"24337836937216",
"8628418353065984",
"3819956976511713280",
"2065506026582536355840",
"1339535792840983753424896",
"1026285196477087825278599168"
] |
[
"nonn"
] | 6 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2019-05-13T13:21:25 |
oeisdata/seq/A012/A012146.seq
|
0a1d27a40b6247ba3423f8c15b84faf2
|
A012147
|
arctanh(tan(sin(x)))=x+3/3!*x^3+41/5!*x^5+1467/7!*x^7+100625/9!*x^9...
|
[
"1",
"3",
"41",
"1467",
"100625",
"11103155",
"1795927225",
"400540116971",
"117802787966241",
"44174901566136419",
"20571101104110689353",
"11646565567973048707867",
"7878351005250269762378801",
"6275481526065593121954975251"
] |
[
"nonn"
] | 7 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2015-02-05T12:04:47 |
oeisdata/seq/A012/A012147.seq
|
a261bd7f6b57ee52b70a0742895d01f8
|
A012148
|
sec(tan(sin(x)))=1+1/2!*x^2+9/4!*x^4+153/6!*x^6+4337/8!*x^8...
|
[
"1",
"1",
"9",
"153",
"4337",
"188049",
"11533497",
"947095529",
"100391885153",
"13337306468001",
"2164609458010345",
"420395208704497849",
"96150102074339268945",
"25560738902667056074801",
"7807205800461246020523161",
"2710746396065167779192263433",
"1059485323408621763305666629825"
] |
[
"nonn"
] | 7 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2013-11-21T12:46:01 |
oeisdata/seq/A012/A012148.seq
|
7f43f606783764e1de9ae3051a56e219
|
A012149
|
sech(tan(sin(x)))=1-1/2!*x^2+1/4!*x^4+47/6!*x^6-447/8!*x^8...
|
[
"1",
"-1",
"1",
"47",
"-447",
"-31649",
"1241153",
"94750991",
"-10593064063",
"-734072274241",
"217167723689345",
"9078987118530031",
"-9048136095510326335",
"132977311200029875999",
"677245929952843206843329"
] |
[
"sign"
] | 6 | 0 | 4 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2016-09-16T17:55:35 |
oeisdata/seq/A012/A012149.seq
|
013be98db76c0cef9c57c1f928b196cf
|
A012150
|
Expansion of e.g.f. exp(tan(arcsin(x))).
|
[
"1",
"1",
"1",
"4",
"13",
"76",
"421",
"3256",
"25369",
"245008",
"2449801",
"28441216",
"346065061",
"4700478784",
"67243537453",
"1047088053376",
"17192488230961",
"302112622479616",
"5593309059948049",
"109527844826856448",
"2255588021494237501"
] |
[
"nonn"
] | 38 | 0 | 4 |
[
"A012150",
"A012194",
"A088009",
"A111959",
"A190863"
] | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2024-06-08T09:32:51 |
oeisdata/seq/A012/A012150.seq
|
5627575710c9ba00f4d7fdb6eb60cd49
|
A012151
|
arcsin(tan(tan(x)))=x+5/3!*x^3+121/5!*x^5+7013/7!*x^7+760465/9!*x^9...
|
[
"1",
"5",
"121",
"7013",
"760465",
"134832389",
"35777541385",
"13330794123941",
"6648498133614241",
"4277423006885663237",
"3448604325132908471833",
"3404386999104410323462373",
"4038035818558270717884559921"
] |
[
"nonn"
] | 4 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:50:41 |
oeisdata/seq/A012/A012151.seq
|
401d3eb7494c5b1541690cd43ac56330
|
A012152
|
arctanh(tan(tan(x)))=x+6/3!*x^3+176/5!*x^5+12240/7!*x^7...
|
[
"1",
"6",
"176",
"12240",
"1561088",
"318007808",
"94807748608",
"38942692972544",
"21088169713729536",
"14558790290337431552",
"12481351528273319821312",
"13009249833253480856289280",
"16200881782506627598590672896"
] |
[
"nonn"
] | 7 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2015-02-05T12:11:45 |
oeisdata/seq/A012/A012152.seq
|
c8e84977e68256046b6e070406f2fb48
|
A012153
|
sec(tan(tan(x)))=1+1/2!*x^2+21/4!*x^4+1053/6!*x^6+96905/8!*x^8...
|
[
"1",
"1",
"21",
"1053",
"96905",
"14216409",
"3045819741",
"897606889013",
"348348521840273",
"172224469448231985",
"105685328498514238501",
"78822199814116989651661",
"70223663543654715642543129",
"73659278933239564262294052361"
] |
[
"nonn"
] | 6 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2021-06-19T10:00:03 |
oeisdata/seq/A012/A012153.seq
|
cf4457497ac5be9810d57aa1f0e99244
|
A012154
|
sech(tan(tan(x))) = 1-1/2!*x^2-11/4!*x^4-253/6!*x^6-9015/8!*x^8 ... .
|
[
"1",
"-1",
"-11",
"-253",
"-9015",
"-362009",
"2294909",
"7143505067",
"2709263596817",
"958529947538255",
"359564035447469189",
"146418020203030157779",
"64393370639942123229401",
"29924760789755403918019639"
] |
[
"sign"
] | 8 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2023-09-15T15:04:45 |
oeisdata/seq/A012/A012154.seq
|
93dbad5205c38015a331c35b1e5b20c2
|
A012155
|
E.g.f.: arcsin(tan(sinh(x))) (odd powers only).
|
[
"1",
"4",
"76",
"3592",
"325648",
"49088128",
"11155494208",
"3566506418560",
"1525463139748096",
"840688518856539136",
"579910469070833277952",
"489338149015716318963712",
"495775150805105569019662336"
] |
[
"nonn"
] | 23 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2015-06-28T10:28:03 |
oeisdata/seq/A012/A012155.seq
|
5b1697f5c649a668b045b144cf61db1b
|
A012156
|
arctanh(tan(sinh(x)))=x+5/3!*x^3+121/5!*x^5+7069/7!*x^7+763057/9!*x^9...
|
[
"1",
"5",
"121",
"7069",
"763057",
"132103157",
"33527321257",
"11731117858573",
"5412661283979361",
"3184128808387236581",
"2326120405922560979929",
"2066008261961436163683709",
"2192446490036211173903631121"
] |
[
"nonn"
] | 12 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2015-02-05T12:18:03 |
oeisdata/seq/A012/A012156.seq
|
46773d898639f2dd4abbb86d6e1f4971
|
A012157
|
sec(tan(sinh(x)))=1+1/2!*x^2+17/4!*x^4+673/6!*x^6+48929/8!*x^8...
|
[
"1",
"1",
"17",
"673",
"48929",
"5673089",
"961574833",
"224363899425",
"68975480890433",
"27023130631305217",
"13143522467110047569",
"7770835407698957687457",
"5488724780305016514749281",
"4564763996367746354642156161"
] |
[
"nonn"
] | 7 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-03-30T16:45:52 |
oeisdata/seq/A012/A012157.seq
|
b94cb256842a2d5cc99b988e6b081ca3
|
A012158
|
sech(tan(sinh(x)))=1-1/2!*x^2-7/4!*x^4-73/6!*x^6-239/8!*x^8...
|
[
"1",
"-1",
"-7",
"-73",
"-239",
"95311",
"12793417",
"1502683335",
"172513245857",
"17253776069663",
"455220048522521",
"-596864160295290537",
"-305119961556198266191",
"-109834061252143977404561"
] |
[
"sign"
] | 12 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2024-11-18T13:23:57 |
oeisdata/seq/A012/A012158.seq
|
07eb3d4236a390cc6d519bb427ba9a3d
|
A012159
|
E.g.f.: exp(tan(arcsinh(x))).
|
[
"1",
"1",
"1",
"2",
"5",
"16",
"61",
"216",
"937",
"6400",
"41881",
"125696",
"259181",
"18156672",
"225924245",
"-930421504",
"-25529526319",
"394852151296",
"8376428366257",
"-97538559528960",
"-2542034772205739",
"37824762737852416"
] |
[
"sign"
] | 17 | 0 | 4 |
[
"A012159",
"A012167"
] | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2013-10-30T09:37:21 |
oeisdata/seq/A012/A012159.seq
|
d27b6b6718ff469a70a823bc2b1077c1
|
A012160
|
sin(tan(arcsinh(x)))=x-4/5!*x^5-136/7!*x^7+272/9!*x^9-222016/11!*x^11...
|
[
"1",
"0",
"-4",
"-136",
"272",
"-222016",
"21267520",
"-3836913536",
"874251520256",
"-254117293340672",
"92635637659667456",
"-41075111126460016640",
"21845766688887149694976",
"-13711633858766326011314176"
] |
[
"sign"
] | 6 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2022-04-22T15:34:09 |
oeisdata/seq/A012/A012160.seq
|
74c019a8fb3ef995330a98c349277e9a
|
A012161
|
arcsin(tan(arcsinh(x)))=x+2/3!*x^3+24/5!*x^5+720/7!*x^7+48000/9!*x^9...
|
[
"1",
"2",
"24",
"720",
"48000",
"4896000",
"804480000",
"175037491200",
"53010886656000",
"19962353688576000",
"9637819435745280000",
"5576675932580413440000",
"3929711821948633743360000",
"3235566861687414718464000000"
] |
[
"nonn"
] | 4 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:50:42 |
oeisdata/seq/A012/A012161.seq
|
91bee3dc5f84476d98a9295765292cd4
|
A012162
|
tan(tan(arcsinh(x)))=x+3/3!*x^3+41/5!*x^5+1187/7!*x^7+62129/9!*x^9...
|
[
"1",
"3",
"41",
"1187",
"62129",
"4782467",
"547167193",
"80119022947",
"16118331113441",
"3804780451118851",
"1198259782941477641",
"411098266056364045603",
"189240360206280390564241",
"87405020278156979563746947"
] |
[
"sign"
] | 10 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2015-02-06T16:30:09 |
oeisdata/seq/A012/A012162.seq
|
9150383255c286f40d10e94e24b487fe
|
A012163
|
cos(tan(arcsinh(x)))=1-1/2!*x^2-3/4!*x^4-21/6!*x^6+185/8!*x^8...
|
[
"1",
"-1",
"-3",
"-21",
"185",
"-9641",
"1668021",
"-192801597",
"42064398961",
"-10576096455505",
"3476312353756781",
"-1396500495046819941",
"679259896835809126697",
"-392775363671591649764601"
] |
[
"sign"
] | 4 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:50:42 |
oeisdata/seq/A012/A012163.seq
|
959e6bf6bac10a3c5c415752819ec423
|
A012164
|
sinh(tan(arcsinh(x))) = x+2/3!*x^3+16/5!*x^5+216/7!*x^7+6400/9!*x^9...
|
[
"1",
"2",
"16",
"216",
"6400",
"125696",
"18156672",
"-930421504",
"394852151296",
"-97538559528960",
"37824762737852416",
"-16526000392804139008",
"8864261701679059992576",
"-5567468507542446595047424"
] |
[
"sign"
] | 9 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2013-10-30T17:07:15 |
oeisdata/seq/A012/A012164.seq
|
7d0b1f6c7332eec7be85e2ebdc23095f
|
A012165
|
tanh(tan(arcsinh(x)))=x-1/3!*x^3+1/5!*x^5-57/7!*x^7+4513/9!*x^9...
|
[
"1",
"-1",
"1",
"-57",
"4513",
"-362737",
"43685409",
"-7472568937",
"1694762362561",
"-492370173816033",
"178467092014537921",
"-78960125273223620761",
"41880334808869380979041",
"-26232480244560931030777297"
] |
[
"sign"
] | 9 | 0 | 4 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2015-02-03T08:44:40 |
oeisdata/seq/A012/A012165.seq
|
2c0923fcba84f82bffc6104ef79645aa
|
A012166
|
arctanh(tan(arcsinh(x))) = x+3/3!*x^3+49/5!*x^5+1915/7!*x^7+143905/9!*x^9...
|
[
"1",
"3",
"49",
"1915",
"143905",
"17011475",
"2994791825",
"719040113675",
"229441987074625",
"92824148885459875",
"46824601078366320625",
"28633111489683067566875",
"20964654070778933185750625",
"18047023186844734022903421875"
] |
[
"nonn"
] | 9 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2013-10-30T17:10:15 |
oeisdata/seq/A012/A012166.seq
|
8cf842e437567550344ec6c4660ed43f
|
A012167
|
cosh(tan(arcsinh(x)))=1+1/2!*x^2+5/4!*x^4+61/6!*x^6+937/8!*x^8...
|
[
"1",
"1",
"5",
"61",
"937",
"41881",
"259181",
"225924245",
"-25529526319",
"8376428366257",
"-2542034772205739",
"1049519923013252461",
"-506849756298097166215",
"294020276106503596553801",
"-199395048123852155910464323"
] |
[
"sign"
] | 6 | 0 | 3 |
[
"A012159",
"A012167"
] | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2020-08-25T18:25:46 |
oeisdata/seq/A012/A012167.seq
|
6b6adb2cf12d670c9e305a6d2599025d
|
A012168
|
sec(tan(arcsinh(x)))=1+1/2!*x^2+9/4!*x^4+201/6!*x^6+7921/8!*x^8...
|
[
"1",
"1",
"9",
"201",
"7921",
"524081",
"48396345",
"6493605561",
"1082018699105",
"246352273609441",
"64161902428428265",
"22422522791742857001",
"8300517886009938036049",
"4196071192877342442444561"
] |
[
"nonn"
] | 6 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2017-04-24T15:13:43 |
oeisdata/seq/A012/A012168.seq
|
5ce0225a4ad8a37222f9a24fc5555d3c
|
A012169
|
sech(tan(arcsinh(x)))=1-1/2!*x^2+1/4!*x^4-1/6!*x^6+449/8!*x^8...
|
[
"1",
"-1",
"1",
"-1",
"449",
"-31681",
"3077185",
"-445157441",
"87981830785",
"-22627780368001",
"7353703042163585",
"-2948527179059299201",
"1429774747400938052161",
"-824792570907860638058561",
"558247886671770078618138049"
] |
[
"sign"
] | 4 | 0 | 5 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:50:42 |
oeisdata/seq/A012/A012169.seq
|
71cf313fd45bc485bc5a42140be5bbab
|
A012170
|
arcsin(tan(tanh(x)))=x+1/3!*x^3+1/5!*x^5+169/7!*x^7+5857/9!*x^9...
|
[
"1",
"1",
"1",
"169",
"5857",
"365905",
"48069217",
"6592812217",
"1367546003521",
"352618786733473",
"113088877092468289",
"44682599178075094729",
"21050259388599343979041",
"11746444483256346415750897"
] |
[
"nonn"
] | 6 | 0 | 4 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2016-09-24T12:04:21 |
oeisdata/seq/A012/A012170.seq
|
51901f360db647ba64160a69cf0dbd92
|
A012171
|
arctanh(tan(tanh(x)))=x+2/3!*x^3+16/5!*x^5+496/7!*x^7+24064/9!*x^9...
|
[
"1",
"2",
"16",
"496",
"24064",
"1908224",
"227958784",
"36620830720",
"7865201852416",
"2142236553248768",
"725477781101608960",
"298762982193334583296",
"146937839959786186080256",
"85124605007437662078894080"
] |
[
"nonn"
] | 9 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2015-02-05T15:09:06 |
oeisdata/seq/A012/A012171.seq
|
b8f74c048a0da9ca8476e0cc7239abd6
|
A012172
|
sec(tan(tanh(x)))=1+1/2!*x^2+5/4!*x^4+13/6!*x^6+41/8!*x^8...
|
[
"1",
"1",
"5",
"13",
"41",
"1529",
"-168851",
"14151621",
"-1169749807",
"65719458673",
"5735813087573",
"-3489760303917315",
"1000904582588332537",
"-229661980583327166359",
"41111046331054702141117",
"-2494708337718975104154187",
"-2794803495926284988945714271"
] |
[
"sign"
] | 6 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2013-10-15T19:59:19 |
oeisdata/seq/A012/A012172.seq
|
ce02394dfa10b025646696fa09ae1c2e
|
A012173
|
sech(tan(tanh(x)))=1-1/2!*x^2+5/4!*x^4-13/6!*x^6-1751/8!*x^8...
|
[
"1",
"-1",
"5",
"-13",
"-1751",
"132871",
"-6935699",
"5067579",
"89435340497",
"-21076246089073",
"3055142025663317",
"13219661379785475",
"-235907327725301640967",
"116095997487821991940759",
"-33017130566183943274793027",
"-532247345346868679322284213",
"8810833241719412871344351850401"
] |
[
"sign"
] | 6 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2015-01-15T17:00:39 |
oeisdata/seq/A012/A012173.seq
|
9558544530cf93a0b6e7057516df7def
|
A012174
|
Expansion of e.g.f.: exp(tan(arctanh(x)))=1+x+1/2!*x^2+5/3!*x^3+17/4!*x^4+121/5!*x^5...
|
[
"1",
"1",
"1",
"5",
"17",
"121",
"721",
"6621",
"56545",
"636337",
"7062241",
"94260341",
"1283497841",
"19853570985",
"319471153457",
"5628171840461",
"104260273696961",
"2063430523313761",
"43168502192389825",
"949149114720943077"
] |
[
"nonn"
] | 6 | 0 | 4 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2016-12-27T19:24:46 |
oeisdata/seq/A012/A012174.seq
|
be7826da1d2430c9aa63002856e14774
|
A012175
|
sin(tan(arctanh(x)))=x+3/3!*x^3+41/5!*x^5+1019/7!*x^7+12305/9!*x^9...
|
[
"1",
"3",
"41",
"1019",
"12305",
"-7478221",
"-3005647943",
"-1143787246421",
"-494108406644959",
"-250135591701350045",
"-148735005859748997559",
"-103273288933359010564517",
"-83050756624193183081902799"
] |
[
"sign"
] | 6 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2015-02-07T18:32:42 |
oeisdata/seq/A012/A012175.seq
|
d18d7caef307ab15ed0763c818a7ff3d
|
A012176
|
arcsin(tan(arctanh(x)))=x+5/3!*x^3+129/5!*x^5+7965/7!*x^7+910785/9!*x^9...
|
[
"1",
"5",
"129",
"7965",
"910785",
"168520725",
"46302986625",
"17780913886125",
"9118678334858625",
"6027946461936745125",
"4993688347647511370625",
"5067155718588449670088125",
"6180682927872411162068450625"
] |
[
"nonn"
] | 7 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2013-11-21T12:46:01 |
oeisdata/seq/A012/A012176.seq
|
8bf471533ea6f8b2a8b2d760fbebc1bc
|
A012177
|
tan(tan(arctanh(x)))=x+6/3!*x^3+176/5!*x^5+11792/7!*x^7...
|
[
"1",
"6",
"176",
"11792",
"1399808",
"258010112",
"68048472064",
"24288413734912",
"11265869660880896",
"6584336654436794368",
"4732528038730841194496",
"4101916559962554300891136",
"4218542156655644369974460416"
] |
[
"nonn"
] | 8 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2015-02-06T16:46:11 |
oeisdata/seq/A012/A012177.seq
|
c385499c6b90d10305fbe321ff671bb6
|
A012178
|
cos(tan(arctanh(x)))=1-1/2!*x^2-15/4!*x^4-561/6!*x^6-38623/8!*x^8...
|
[
"1",
"-1",
"-15",
"-561",
"-38623",
"-4206881",
"-661302639",
"-140958927825",
"-38921417469119",
"-13433349471318337",
"-5625858245527551439",
"-2783882722627688439921",
"-1585166024021465157765535"
] |
[
"sign"
] | 6 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2014-06-17T15:54:32 |
oeisdata/seq/A012/A012178.seq
|
85381e8f20842e3cca2992d942830c61
|
A012179
|
sinh(tan(arctanh(x)))=x+5/3!*x^3+121/5!*x^5+6621/7!*x^7+636337/9!*x^9...
|
[
"1",
"5",
"121",
"6621",
"636337",
"94260341",
"19853570985",
"5628171840461",
"2063430523313761",
"949149114720943077",
"534861693803619166681",
"362197405161801586405565",
"290099119826974859032451601"
] |
[
"nonn"
] | 4 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:50:42 |
oeisdata/seq/A012/A012179.seq
|
19f8be93d8bb0033748765f68eafb8d9
|
A012180
|
tanh(tan(arctanh(x)))=x+2/3!*x^3+16/5!*x^5+48/7!*x^7-29696/9!*x^9...
|
[
"1",
"2",
"16",
"48",
"-29696",
"-6049792",
"-1262426112",
"-308569372672",
"-89297625350144",
"-30123113337716736",
"-11520007513318621184",
"-4775431672418431664128",
"-1952929261585732032528384",
"-545214673336986589066166272"
] |
[
"sign"
] | 6 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2023-09-06T19:45:33 |
oeisdata/seq/A012/A012180.seq
|
68e1c50e0da769da1d61245f652693c8
|
A012181
|
arctanh(tan(arctanh(x))) = x + (6/3!)*x^3 + (184/5!)*x^5 + 13360/7!*x^7 + ...
|
[
"1",
"6",
"184",
"13360",
"1770880",
"373587200",
"115086003200",
"48784879769600",
"27245388132352000",
"19392357120188416000",
"17137521906875269120000",
"18411376349575875461120000",
"23632217190341837269237760000",
"35718167409293109428879360000000"
] |
[
"nonn"
] | 11 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2018-08-17T22:32:49 |
oeisdata/seq/A012/A012181.seq
|
aaa8c2ea304b89c12886fd350a52e66e
|
A012182
|
cosh(tan(arctanh(x)))=1+1/2!*x^2+17/4!*x^4+721/6!*x^6+56545/8!*x^8...
|
[
"1",
"1",
"17",
"721",
"56545",
"7062241",
"1283497841",
"319471153457",
"104260273696961",
"43168502192389825",
"22100367268731836881",
"13703484478282258062481",
"10117607255517016666964897",
"8769262856125733251376413601"
] |
[
"nonn"
] | 6 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2015-03-21T16:43:46 |
oeisdata/seq/A012/A012182.seq
|
468d7f10ea8d2069d70370156424f661
|
A012183
|
sec(tan(arctanh(x)))=1+1/2!*x^2+21/4!*x^4+1101/6!*x^6+107209/8!*x^8...
|
[
"1",
"1",
"21",
"1101",
"107209",
"16711481",
"3810146205",
"1195529025861",
"494050576455185",
"260086639760540401",
"169928807728242392485",
"134924876918419856397501",
"127963083862513681084495321"
] |
[
"nonn"
] | 4 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:50:42 |
oeisdata/seq/A012/A012183.seq
|
b3ed139b4ff0c1cd27203b68358a105e
|
A012184
|
sech(tan(arctanh(x)))=1-1/2!*x^2-11/4!*x^4-301/6!*x^6-14839/8!*x^8...
|
[
"1",
"-1",
"-11",
"-301",
"-14839",
"-1109881",
"-110852675",
"-12696026981",
"-1044878845295",
"344502726652559",
"397767671438223365",
"311149018395487011299",
"242840543036206414510489",
"203578596149994366707196439",
"187397387863859771967571124941",
"190632732651754400283645304176299"
] |
[
"sign"
] | 10 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2014-07-23T03:23:47 |
oeisdata/seq/A012/A012184.seq
|
85def2064c7d5d2e6d1dd15987f47161
|
A012185
|
Expansion of e.g.f.: exp(arctan(sin(x)))=1+x+1/2!*x^2-2/3!*x^3-11/4!*x^4+16/5!*x^5...
|
[
"1",
"1",
"1",
"-2",
"-11",
"16",
"301",
"-272",
"-16631",
"256",
"1543801",
"1758208",
"-216765251",
"-549115904",
"42924800101",
"178127730688",
"-11404529749871",
"-68157333438464",
"3916428205369201",
"31349506823815168",
"-1688780438764074491"
] |
[
"sign"
] | 9 | 0 | 4 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2015-01-28T18:28:19 |
oeisdata/seq/A012/A012185.seq
|
f0ae539c6f6bba9884eb13e2c5db00ec
|
A012186
|
arcsin(arctan(sin(x)))=x-2/3!*x^3+24/5!*x^5-888/7!*x^7+60672/9!*x^9...
|
[
"1",
"-2",
"24",
"-888",
"60672",
"-6741888",
"1108807296",
"-252757302528",
"76277556436992",
"-29437978293841920",
"14141695133810196480",
"-8275095832054525329408",
"5794473015450853604229120"
] |
[
"sign"
] | 4 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:50:42 |
oeisdata/seq/A012/A012186.seq
|
9bf0492b2dcbcf32919289adc581cad0
|
A012187
|
arctan(arctan(sin(x)))=x-5/3!*x^3+129/5!*x^5-8133/7!*x^7+941601/9!*x^9...
|
[
"1",
"-5",
"129",
"-8133",
"941601",
"-173748453",
"46802237793",
"-17335271239653",
"8453548403430081",
"-5250998394750249285",
"4048144275997010258625",
"-3792939800731791655328133",
"4245216299498829593948709345"
] |
[
"sign"
] | 6 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2015-02-09T13:30:26 |
oeisdata/seq/A012/A012187.seq
|
92f97857ca0b6336b9f3d3cdf2f9c0da
|
A012188
|
E.g.f. sinh(arctan(sin(x))) odd powers only.
|
[
"1",
"-2",
"16",
"-272",
"256",
"1758208",
"-549115904",
"178127730688",
"-68157333438464",
"31349506823815168",
"-17274394522483687424",
"11298666083444901019648",
"-8681212227186028691062784",
"7756335594110841587790512128"
] |
[
"sign"
] | 22 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2018-07-11T03:32:34 |
oeisdata/seq/A012/A012188.seq
|
dc2d78b1673f5e0f8c2481e98fc4166f
|
A012189
|
arcsinh(arctan(sin(x)))=x-4/3!*x^3+84/5!*x^5-4488/7!*x^7+450768/9!*x^9...
|
[
"1",
"-4",
"84",
"-4488",
"450768",
"-73573248",
"17815591104",
"-6013430329728",
"2703233646006528",
"-1562922378845445120",
"1130630051482809369600",
"-1000815673354945580034048",
"1064286361791704604763115520"
] |
[
"sign"
] | 6 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2013-04-20T07:55:39 |
oeisdata/seq/A012/A012189.seq
|
089c9bf68791ba38b771488aaa8cdd44
|
A012190
|
tanh(arctan(sin(x)))=x-5/3!*x^3+121/5!*x^5-6845/7!*x^7+690481/9!*x^9...
|
[
"1",
"-5",
"121",
"-6845",
"690481",
"-108594485",
"24502918441",
"-7495966306925",
"2984112329052001",
"-1498441322462840165",
"926096248873419539161",
"-690670275602276172370205",
"611502034169544516212107921"
] |
[
"sign"
] | 9 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2013-11-21T12:46:01 |
oeisdata/seq/A012/A012190.seq
|
22bc923e5e4bb5dab276f5206bf7c8eb
|
A012191
|
arctanh(arctan(sin(x))) = x - 1/3!*x^3 + 9/5!*x^5 - 393/7!*x^7 + 25329/9!*x^9 - ...
|
[
"1",
"-1",
"9",
"-393",
"25329",
"-2720433",
"438412857",
"-97949820153",
"29044709480289",
"-11037393803823585",
"5229024617702601705",
"-3021459365652314206953",
"2091487425283069032286545",
"-1708553607407338796161442193"
] |
[
"sign"
] | 7 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2018-01-15T15:10:53 |
oeisdata/seq/A012/A012191.seq
|
9ce447dcf31ccdb03a83a0a7ba6eb273
|
A012192
|
cosh(arctan(sin(x)))=1+1/2!*x^2-11/4!*x^4+301/6!*x^6-16631/8!*x^8...
|
[
"1",
"1",
"-11",
"301",
"-16631",
"1543801",
"-216765251",
"42924800101",
"-11404529749871",
"3916428205369201",
"-1688780438764074491",
"893492390128997891101",
"-569179458246274338443111",
"429766550332741063792045801"
] |
[
"sign"
] | 4 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:50:43 |
oeisdata/seq/A012/A012192.seq
|
22d86a8fa28f5adc0f57a59cf1926b62
|
A012193
|
sech(arctan(sin(x)))=1-1/2!*x^2+17/4!*x^4-721/6!*x^6+58337/8!*x^8...
|
[
"1",
"-1",
"17",
"-721",
"58337",
"-7657441",
"1482169457",
"-396854618161",
"140415423261377",
"-63432792091634881",
"35619694647751942097",
"-24334169873267896659601",
"19872330538404158435859617"
] |
[
"sign"
] | 6 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2018-06-06T15:11:27 |
oeisdata/seq/A012/A012193.seq
|
7e047d0521de11facd5801b67f39b487
|
A012194
|
exp(arctan(arcsin(x)))=1+x+1/2!*x^2-3/4!*x^4+4/5!*x^5+69/6!*x^6...
|
[
"1",
"1",
"1",
"0",
"-3",
"4",
"69",
"136",
"-1159",
"1744",
"115081",
"652864",
"-3250827",
"16365504",
"1156388557",
"12624963456",
"-12628752143",
"910310355200",
"42394317198097",
"735663001262080",
"2830775181039853",
"125940707707991040"
] |
[
"sign"
] | 4 | 0 | 5 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:50:43 |
oeisdata/seq/A012/A012194.seq
|
ad6c00f710681d179b7d894068905227
|
A012195
|
arcsin(arctan(arcsin(x)))=x+12/5!*x^5+80/7!*x^7+13776/9!*x^9...
|
[
"1",
"0",
"12",
"80",
"13776",
"566272",
"127692224",
"15090459904",
"4735792068864",
"1137376547676160",
"493601667145247744",
"198575926723414577152",
"116701919243205334355968",
"69932277446693762007433216"
] |
[
"nonn"
] | 4 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:50:43 |
oeisdata/seq/A012/A012195.seq
|
61bf8e48e60268f982142c3659fee1dc
|
A012196
|
arctan(arctan(arcsin(x)))=x-3/3!*x^3+57/5!*x^5-2419/7!*x^7+198801/9!*x^9...
|
[
"1",
"-3",
"57",
"-2419",
"198801",
"-25335395",
"4816346441",
"-1245230547347",
"427817295559329",
"-186336568593526211",
"101138532707457916121",
"-66575531182102753799603",
"52444802490227536269748273"
] |
[
"sign"
] | 6 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2015-03-15T10:20:04 |
oeisdata/seq/A012/A012196.seq
|
da4b66edab974cf1838fa2eeb29c205f
|
A012197
|
sinh(arctan(arcsin(x)))=x+4/5!*x^5+136/7!*x^7+1744/9!*x^9+652864/11!*x^11...
|
[
"1",
"0",
"4",
"136",
"1744",
"652864",
"16365504",
"12624963456",
"910310355200",
"735663001262080",
"125940707707991040",
"105433974790312437760",
"34875639805462923857920",
"32117899260249401371770880"
] |
[
"nonn"
] | 4 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:50:43 |
oeisdata/seq/A012/A012197.seq
|
49f26b29fc1150d23fc9b94f8a1b33e3
|
A012198
|
arcsinh(arctan(arcsin(x)))=x-2/3!*x^3+32/5!*x^5-1056/7!*x^7+77696/9!*x^9...
|
[
"1",
"-2",
"32",
"-1056",
"77696",
"-8411776",
"1476954112",
"-342658078720",
"110693077745664",
"-44684649940516864",
"23059986721115963392",
"-14340030701132323422208",
"10822861233504969629892608"
] |
[
"sign"
] | 6 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2013-11-28T12:48:08 |
oeisdata/seq/A012/A012198.seq
|
ee36de484b9fc136dff8fe8621418311
|
A012199
|
tanh(arctan(arcsin(x)))=x-3/3!*x^3+49/5!*x^5-1691/7!*x^7+108961/9!*x^9...
|
[
"1",
"-3",
"49",
"-1691",
"108961",
"-10415699",
"1476822801",
"-274051642731",
"68034310337345",
"-20698489943585315",
"7945165226724184305",
"-3587174193714146380475",
"1968139895275233488888545",
"-1234522114580149082237390195",
"916981332590411294370399470545"
] |
[
"sign"
] | 8 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2014-10-13T18:13:50 |
oeisdata/seq/A012/A012199.seq
|
1e98493714a35462c8799d2c7c69f50b
|
A012200
|
arctanh(arctan(arcsin(x))) = x + 1/3!*x^3 + 17/5!*x^5 + 393/7!*x^7 + 25601/9!*x^9 + ...
|
[
"1",
"1",
"17",
"393",
"25601",
"2044241",
"289407505",
"49702166681",
"12331304386689",
"3665631364571297",
"1415269826057944465",
"644290354204397460137",
"358377106160586506065793",
"231185244070754402809628657"
] |
[
"nonn"
] | 15 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2018-01-15T15:25:40 |
oeisdata/seq/A012/A012200.seq
|
8abe729637527ab0a74860247d1b6d44
|
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