sequence_id
stringlengths 7
7
| sequence_name
stringlengths 4
573
| sequence
listlengths 1
348
| keywords
listlengths 1
8
| score
int64 1
2.35k
| offset_a
int64 -14,827
666,262,453B
| offset_b
int64 0
635M
⌀ | cross_references
listlengths 1
128
⌀ | former_ids
listlengths 1
3
⌀ | author
stringlengths 7
231
⌀ | timestamp
timestamp[us]date 1999-12-11 03:00:00
2025-07-19 00:40:46
| filename
stringlengths 29
29
| hash
stringlengths 32
32
|
|---|---|---|---|---|---|---|---|---|---|---|---|---|
A013101
|
Expansion of sec(arcsinh(x) + tan(x)) (coefficients of even powers only).
|
[
"1",
"4",
"88",
"5014",
"527624",
"89331514",
"22153827556",
"7576868616438",
"3416549387012336",
"1964348168375260594",
"1402481265951220466076",
"1217416473808119071396046",
"1262628491065344385303595816"
] |
[
"nonn"
] | 15 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2017-11-28T11:48:56 |
oeisdata/seq/A013/A013101.seq
|
3d747065d3a3d2ae8b306bb1638435a2
|
A013102
|
Expansion of e.g.f: sech(arcsinh(x)+tan(x)).
|
[
"1",
"-4",
"72",
"-3414",
"304696",
"-43757114",
"9229955724",
"-2685455642198",
"1030584093889104",
"-504321546504212914",
"306492028524272596724",
"-226465717137080425353646",
"199935485865217931345463224"
] |
[
"sign"
] | 12 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2024-12-10T05:45:07 |
oeisdata/seq/A013/A013102.seq
|
455d60a322a48fe7defaf78b61e46a4e
|
A013103
|
exp(arcsinh(x)+arctan(x))=1+2*x+4/2!*x^2+5/3!*x^3-8/4!*x^4-55/5!*x^5...
|
[
"1",
"2",
"4",
"5",
"-8",
"-55",
"70",
"1535",
"-920",
"-80695",
"-28550",
"6860075",
"10642900",
"-859242475",
"-2554095050",
"148907237375",
"685535422000",
"-34123911391375",
"-219648785612750",
"9992873727945875",
"84602550046787500"
] |
[
"sign"
] | 4 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:51:19 |
oeisdata/seq/A013/A013103.seq
|
c04d860972a7eaf40217a42410385e4a
|
A013104
|
sin(arcsinh(x)+arctan(x))=2*x-11/3!*x^3+185/5!*x^5-6785/7!*x^7...
|
[
"2",
"-11",
"185",
"-6785",
"438425",
"-44098925",
"6375156125",
"-1253044612625",
"321457635604625",
"-104323833636303125",
"41784590833455153125",
"-20245593926258507665625",
"11671970082146320158265625"
] |
[
"sign"
] | 4 | 0 | 1 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:51:19 |
oeisdata/seq/A013/A013104.seq
|
277e9e1509fd8a1c86ca51193783d5d6
|
A013105
|
E.g.f.: arcsin(arcsinh(x)+arctan(x)) = 2*x + 5/3!*x^3 + 201/5!*x^5 + 16767/7!*x^7 +...
|
[
"2",
"5",
"201",
"16767",
"2966985",
"843657003",
"360874106901",
"214962711675327",
"170540233765256817",
"173705883261260614803",
"220988408403985490684493",
"343398031722161543448485703",
"640041489411864479945549850537"
] |
[
"nonn"
] | 8 | 1 | 1 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-05-24T13:23:34 |
oeisdata/seq/A013/A013105.seq
|
e680fec7a95bdfed7bb45986e6969899
|
A013106
|
tan(arcsinh(x)+arctan(x))=2*x+13/3!*x^3+305/5!*x^5+15055/7!*x^7...
|
[
"2",
"13",
"305",
"15055",
"1273025",
"164517175",
"30146073425",
"7436961751375",
"2376178127194625",
"954639310366870375",
"470988100516584340625",
"279956419390270100749375",
"197317558974617657009890625"
] |
[
"nonn"
] | 7 | 0 | 1 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2015-02-07T06:19:45 |
oeisdata/seq/A013/A013106.seq
|
2c01ba71f027acd0e9698f6c9e1ad094
|
A013107
|
arctan(arcsinh(x)+arctan(x))=2*x-19/3!*x^3+1041/5!*x^5-141489/7!*x^7...
|
[
"2",
"-19",
"1041",
"-141489",
"35842401",
"-14587836921",
"8707393003617",
"-7166002987401489",
"7776862795242656577",
"-10760731866324884664297",
"18490186709158886988610113",
"-38627726709262739118225523137"
] |
[
"sign"
] | 6 | 0 | 1 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2016-11-29T08:30:28 |
oeisdata/seq/A013/A013107.seq
|
019050de4a740b6c2bf6a0028bfe9fdc
|
A013108
|
cos(arcsinh(x)+arctan(x))=1-4/2!*x^2+40/4!*x^4-1030/6!*x^6+51160/8!*x^8...
|
[
"1",
"-4",
"40",
"-1030",
"51160",
"-4176250",
"507867100",
"-86130937750",
"19429666282000",
"-5626346310003250",
"2034312191276462500",
"-898279284686285368750",
"475692945053706430375000",
"-297573010648301986578906250"
] |
[
"sign"
] | 6 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2013-04-26T18:10:44 |
oeisdata/seq/A013/A013108.seq
|
e5f0654cc60c843a1fd9f8ebe96423a0
|
A013109
|
arcsinh(arcsinh(x)+arctan(x))=2*x-11/3!*x^3+441/5!*x^5-48897/7!*x^7...
|
[
"2",
"-11",
"441",
"-48897",
"10711449",
"-3898352493",
"2124846180765",
"-1619764201737297",
"1645104402411921297",
"-2147066174256624128277",
"3501336873746919748187493",
"-6976563529004472877778185497"
] |
[
"sign"
] | 6 | 0 | 1 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2014-07-19T18:16:11 |
oeisdata/seq/A013/A013109.seq
|
26b723b07fa1667c5d5ccc2c49986c72
|
A013110
|
tanh(arcsinh(x)+arctan(x))=2*x-19/3!*x^3+785/5!*x^5-70705/7!*x^7...
|
[
"2",
"-19",
"785",
"-70705",
"11020385",
"-2631928825",
"892329853025",
"-407413940220625",
"240968321541442625",
"-179211927264110235625",
"163684517256281564050625",
"-180116677926822557970570625",
"235018935742557547408645390625"
] |
[
"sign"
] | 4 | 0 | 1 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:51:19 |
oeisdata/seq/A013/A013110.seq
|
7f97c33b5992b99ea0fdb388697d3df9
|
A013111
|
arctanh(arcsinh(x)+arctan(x))=2*x+13/3!*x^3+561/5!*x^5+58959/7!*x^7...
|
[
"2",
"13",
"561",
"58959",
"11644353",
"3689490231",
"1715357184849",
"1099472915829519",
"929329108531548417",
"1001522171480774224743",
"1340339793936610136490513",
"2180857643900986608848041983",
"4239717441519601414508854360257"
] |
[
"nonn"
] | 11 | 0 | 1 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2016-11-29T08:31:27 |
oeisdata/seq/A013/A013111.seq
|
2c39f41d07203831eb88a3ae24713807
|
A013112
|
cosh(arcsinh(x)+arctan(x))=1+4/2!*x^2-8/4!*x^4+70/6!*x^6-920/8!*x^8...
|
[
"1",
"4",
"-8",
"70",
"-920",
"-28550",
"10642900",
"-2554095050",
"685535422000",
"-219648785612750",
"84602550046787500",
"-38917136125065331250",
"21166653214210218325000",
"-13470291608750677967093750"
] |
[
"sign"
] | 6 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-11-27T09:03:04 |
oeisdata/seq/A013/A013112.seq
|
1f6c02cfd0bc0243f34264c19bd73c39
|
A013113
|
sec(arcsinh(x)+arctan(x))=1+4/2!*x^2+56/4!*x^4+1990/6!*x^6...
|
[
"1",
"4",
"56",
"1990",
"130280",
"13814650",
"2137954100",
"457685029750",
"128915903246000",
"46370152422675250",
"20689120752785127500",
"11232151174947132868750",
"7281395066161326989645000",
"5560840304175437693730906250"
] |
[
"nonn"
] | 6 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2024-12-05T15:12:07 |
oeisdata/seq/A013/A013113.seq
|
c3a637db5591716abcbf720e6c90dfa7
|
A013114
|
sech(arcsinh(x)+arctan(x))=1-4/2!*x^2+104/4!*x^4-6790/6!*x^6...
|
[
"1",
"-4",
"104",
"-6790",
"827480",
"-162019450",
"46518314300",
"-18413421592150",
"9610889961530000",
"-6395770003655763250",
"5285420552751908562500",
"-5310341702734086669088750",
"6374725468204682712703775000"
] |
[
"sign"
] | 6 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2020-03-21T14:48:13 |
oeisdata/seq/A013/A013114.seq
|
d7871c3d4419eb2461d472ce76fb14b7
|
A013115
|
log(arcsinh(x)+cos(x)) = x-2/2!*x^2+4/3!*x^3-16/4!*x^4+88/5!*x^5...
|
[
"0",
"1",
"-2",
"4",
"-16",
"88",
"-560",
"4184",
"-37952",
"398848",
"-4613632",
"58835456",
"-835257344",
"12993783424",
"-217535518720",
"3911934210560",
"-75654182936576",
"1562951627091968",
"-34235182359642112",
"793328025614454784"
] |
[
"sign"
] | 10 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2013-11-01T15:26:23 |
oeisdata/seq/A013/A013115.seq
|
68f2703f7db5d256b77ff23664553474
|
A013116
|
exp(arcsinh(x)+sinh(x))=1+2*x+4/2!*x^2+8/3!*x^3+16/4!*x^4+42/5!*x^5...
|
[
"1",
"2",
"4",
"8",
"16",
"42",
"184",
"744",
"1152",
"-558",
"99744",
"924904",
"-5133696",
"-83024966",
"906195840",
"14896602184",
"-171321409536",
"-3277450732382",
"44275226644992",
"942900995465032",
"-14354506519279616",
"-338298547449554102"
] |
[
"sign"
] | 9 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2013-11-01T14:16:23 |
oeisdata/seq/A013/A013116.seq
|
90d8751507d2ea2c556df28befdc8861
|
A013117
|
exp(tanh(x)+log(x+1))=1+2*x+3/2!*x^2+2/3!*x^3-11/4!*x^4-38/5!*x^5...
|
[
"1",
"2",
"3",
"2",
"-11",
"-38",
"79",
"954",
"137",
"-33582",
"-96741",
"1555666",
"10865661",
"-86780822",
"-1244836953",
"4930566346",
"162614558865",
"-100938990558",
"-24583330322637",
"-71145784216286",
"4265463634593925",
"30382485085757818"
] |
[
"sign"
] | 4 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:51:19 |
oeisdata/seq/A013/A013117.seq
|
c98b17c15eed28aa758eae1ca06aaa0c
|
A013118
|
Expansion of e.g.f. sin(tanh(x) + log(x+1)).
|
[
"0",
"2",
"-1",
"-8",
"18",
"42",
"15",
"-3460",
"16492",
"16890",
"286155",
"-12520400",
"99727254",
"-271849550",
"6922105827",
"-197946213020",
"2348657908440",
"-19619328534222",
"396132741200439",
"-9735975917400728",
"156971908263615450",
"-2248810586848724102",
"48167349073405076823",
"-1170896255906195317300"
] |
[
"sign"
] | 11 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2018-07-31T09:59:27 |
oeisdata/seq/A013/A013118.seq
|
2abc5f020475fd43eebf0615be5700cd
|
A013119
|
E.g.f. arcsin(tanh(x)+log(x+1)) = 2*x - 1/2!*x^2 + 8/3!*x^3 - 30/4!*x^4 +- ...
|
[
"0",
"2",
"-1",
"8",
"-30",
"358",
"-2655",
"41428",
"-511980",
"9864538",
"-171757845",
"3961279808",
"-88981176570",
"2406642164782",
"-65936688564747",
"2056690243987468",
"-66255959470897560",
"2349481394958302898",
"-86780043600660006633"
] |
[
"sign"
] | 14 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2013-11-21T12:46:02 |
oeisdata/seq/A013/A013119.seq
|
3dac6e797f1eb743e8054b0ff9a729c2
|
A013120
|
Expansion of e.g.f. tan(tanh(x) + log(x+1)).
|
[
"0",
"2",
"-1",
"16",
"-54",
"612",
"-4710",
"57944",
"-683144",
"10015344",
"-154359720",
"2701047424",
"-50673755088",
"1040194570144",
"-22870244075952",
"540441764640064",
"-13599312731310720",
"363949691199176448",
"-10307618997050443392"
] |
[
"sign"
] | 9 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2022-07-22T18:33:09 |
oeisdata/seq/A013/A013120.seq
|
2108dd5c9f3aaaeae2ec1e2150c48058
|
A013121
|
Expansion of e.g.f. arctan(tanh(x) + log(x+1)).
|
[
"0",
"2",
"-1",
"-16",
"42",
"748",
"-5130",
"-80792",
"1139880",
"15089632",
"-401063040",
"-3986514112",
"203199458880",
"1170901443424",
"-139120136531376",
"-67846807312832",
"122712218206730880",
"-762584236008814848"
] |
[
"sign"
] | 9 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2018-07-31T18:38:27 |
oeisdata/seq/A013/A013121.seq
|
99d7358016164193f99a86295f59fa25
|
A013122
|
cos(tanh(x)+log(x+1))=1-4/2!*x^2+6/3!*x^3+13/4!*x^4-20/5!*x^5...
|
[
"1",
"0",
"-4",
"6",
"13",
"-20",
"-454",
"1302",
"13213",
"-57528",
"-566304",
"1146750",
"83953137",
"-715819260",
"590760166",
"-61357519650",
"2337988853657",
"-32573393982320",
"362267655859524",
"-8238027536343882",
"209882071249912757"
] |
[
"sign"
] | 4 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:51:19 |
oeisdata/seq/A013/A013122.seq
|
d266c06a627df6027f2bc642d5574af3
|
A013123
|
Expansion of e.g.f. sinh(tanh(x) + log(x+1)).
|
[
"0",
"2",
"-1",
"8",
"-30",
"102",
"-735",
"6036",
"-43372",
"366666",
"-3909645",
"43735936",
"-509688234",
"6614683246",
"-93752033739",
"1403126034316",
"-22351107663000",
"380878785320338",
"-6864318972384345",
"130206659362724728"
] |
[
"sign"
] | 7 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2018-07-31T18:43:43 |
oeisdata/seq/A013/A013123.seq
|
0d17f2709c5207ee7b398e8c8ab9fac0
|
A013124
|
Expansion of e.g.f. arcsinh(tanh(x) + log(x+1)).
|
[
"0",
"2",
"-1",
"-8",
"18",
"298",
"-1905",
"-25412",
"350700",
"4095754",
"-108856125",
"-940845072",
"49635561030",
"233977315570",
"-31129149144093",
"12883816215268",
"25437319822551000",
"-179134252641817006",
"-25989451309294893657"
] |
[
"sign"
] | 7 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2018-07-31T18:43:51 |
oeisdata/seq/A013/A013124.seq
|
15a74ed454ddf09f92709ba2525054dc
|
A013125
|
Expansion of E.g.f.: tanh(tanh(x)+log(x+1))=2*x-1/2!*x^2-16/3!*x^3+42/4!*x^4+492/5!*x^5...
|
[
"0",
"2",
"-1",
"-16",
"42",
"492",
"-3210",
"-30168",
"404264",
"2783952",
"-75206520",
"-292604288",
"19217701008",
"3111794272",
"-6389076941520",
"29520888356032",
"2643629755167360",
"-29037077579992832",
"-1307061634619873664"
] |
[
"sign"
] | 6 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2018-05-27T11:06:22 |
oeisdata/seq/A013/A013125.seq
|
0f8183e6c37e0f653c50e1ae433d1174
|
A013126
|
cosh(tanh(x)+log(x+1))=1+4/2!*x^2-6/3!*x^3+19/4!*x^4-140/5!*x^5...
|
[
"1",
"0",
"4",
"-6",
"19",
"-140",
"814",
"-5082",
"43509",
"-400248",
"3812904",
"-42180270",
"520553895",
"-6701464068",
"92507196786",
"-1398195467970",
"22513722221865",
"-380979724310896",
"6839735642061708",
"-130277805146941014"
] |
[
"sign"
] | 4 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:51:19 |
oeisdata/seq/A013/A013126.seq
|
49ba0b35909b8dbed194989fee599a60
|
A013127
|
Expansion of e.g.f.: sec(tanh(x)+log(x+1))=1+4/2!*x^2-6/3!*x^3+83/4!*x^4-460/5!*x^5...
|
[
"1",
"0",
"4",
"-6",
"83",
"-460",
"5374",
"-52962",
"711833",
"-9731160",
"156311784",
"-2676262710",
"50867352939",
"-1037096208564",
"22896291533210",
"-539916293280210",
"13603842760270129",
"-363832977079307248",
"10308592491205055532"
] |
[
"sign"
] | 6 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2023-02-27T10:52:14 |
oeisdata/seq/A013/A013127.seq
|
5f484e343d8991e0caad29fc7dc96095
|
A013128
|
Expansion of e.g.f.: sech(tanh(x)+log(x+1))=1-4/2!*x^2+6/3!*x^3+77/4!*x^4-340/5!*x^5...
|
[
"1",
"0",
"-4",
"6",
"77",
"-340",
"-3574",
"34062",
"278337",
"-5275800",
"-28795584",
"1159543110",
"2472700941",
"-340042014156",
"704790251070",
"126778070956110",
"-958235638366239",
"-57637006798322672",
"866891599173180708"
] |
[
"sign"
] | 6 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2018-07-11T12:07:25 |
oeisdata/seq/A013/A013128.seq
|
c1a2fddaf2480bb0df1b55fc7d1f2336
|
A013129
|
Expansion of e.g.f.: exp(tanh(x)+sin(x))=1+2*x+4/2!*x^2+5/3!*x^3-8/4!*x^4-71/5!*x^5...
|
[
"1",
"2",
"4",
"5",
"-8",
"-71",
"-122",
"863",
"5352",
"-11207",
"-239494",
"-103541",
"14203028",
"49174077",
"-1067540778",
"-8312033249",
"94081990576",
"1398228044113",
"-8737926966734",
"-258914411211565",
"612930093492268",
"53899233359866405"
] |
[
"sign"
] | 6 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2022-06-22T10:10:52 |
oeisdata/seq/A013/A013129.seq
|
94ca45947ce157eb6fd54730f49944c2
|
A013130
|
arcsin(tanh(x)+sin(x))=2*x+5/3!*x^3+185/5!*x^5+16095/7!*x^7...
|
[
"2",
"5",
"185",
"16095",
"2778425",
"787492235",
"333091515965",
"196604887454175",
"154421803574964305",
"155738815364225864915",
"196154237311733664577445",
"301759169017942105204192455",
"556786733540782098106300699385"
] |
[
"nonn"
] | 4 | 0 | 1 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:51:20 |
oeisdata/seq/A013/A013130.seq
|
38d84539e5c8ac35cbffd977346fb791
|
A013131
|
Expansion of e.g.f.: exp(tanh(x)+arcsin(x))=1+2*x+4/2!*x^2+7/3!*x^3+8/4!*x^4+17/5!*x^5...
|
[
"1",
"2",
"4",
"7",
"8",
"17",
"214",
"1761",
"8632",
"38969",
"381754",
"5371821",
"56522540",
"533244077",
"6087452310",
"95701880241",
"1458087413200",
"21713687902033",
"333863833250482",
"6101409790911765",
"114840891055289940",
"2263678163011472213"
] |
[
"nonn"
] | 6 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2015-03-04T17:56:26 |
oeisdata/seq/A013/A013131.seq
|
125ae67abcdf73c97f41a59efe265767
|
A013132
|
sin(tanh(x)+arcsin(x))=2*x-9/3!*x^3+97/5!*x^5-2975/7!*x^7...
|
[
"2",
"-9",
"97",
"-2975",
"114217",
"-8693355",
"641356549",
"-99659748575",
"10015783072433",
"-3322983000373651",
"246472578957172573",
"-288961675751112506727",
"-23857648902841926624247"
] |
[
"sign"
] | 4 | 0 | 1 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:51:20 |
oeisdata/seq/A013/A013132.seq
|
9876753cd50922b1c1e0f6a59a141945
|
A013133
|
exp(tanh(x)+tan(x))=1+2*x+4/2!*x^2+8/3!*x^3+16/4!*x^4+64/5!*x^5...
|
[
"1",
"2",
"4",
"8",
"16",
"64",
"448",
"2816",
"14592",
"80896",
"705536",
"7278592",
"65245184",
"532070400",
"5385535488",
"71008190464",
"910402060288",
"10323887915008",
"124371776831488",
"1895043049717760",
"30930578556583936"
] |
[
"nonn"
] | 4 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:51:20 |
oeisdata/seq/A013/A013133.seq
|
c95adb46b96ae9a46db933e6f851d454
|
A013134
|
sin(tanh(x)+tan(x))=2*x-8/3!*x^3+64/5!*x^5-2816/7!*x^7+80896/9!*x^9...
|
[
"2",
"-8",
"64",
"-2816",
"80896",
"-7278592",
"532070400",
"-71008190464",
"10323887915008",
"-1895043049717760",
"458133970106712064",
"-113313946829854867456",
"40093022675430493126656",
"-13211730725723035930722304"
] |
[
"sign"
] | 6 | 0 | 1 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2015-11-25T10:01:21 |
oeisdata/seq/A013/A013134.seq
|
fed0ac687e20b22af8b136f49db22d68
|
A013135
|
arcsin(tanh(x)+tan(x))=2*x+8/3!*x^3+320/5!*x^5+31488/7!*x^7...
|
[
"2",
"8",
"320",
"31488",
"6241280",
"2048135168",
"1005768458240",
"690254567374848",
"630909848433459200",
"740848367450511638528",
"1086821026187766828892160",
"1947858113799053357202014208",
"4187952101776996175279418245120"
] |
[
"nonn"
] | 4 | 0 | 1 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:51:20 |
oeisdata/seq/A013/A013135.seq
|
ac6b205733b16e77eb73cc37257637d3
|
A013136
|
tan(tanh(x)+tan(x))=2*x+16/3!*x^3+544/5!*x^5+40192/7!*x^7...
|
[
"2",
"16",
"544",
"40192",
"5111296",
"994586624",
"274584084480",
"102058445570048",
"49134745327894528",
"29743376752794664960",
"22111413979264501940224",
"19803614205698007369777152",
"21031646806008885489451401216"
] |
[
"nonn"
] | 9 | 0 | 1 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2015-02-07T06:26:35 |
oeisdata/seq/A013/A013136.seq
|
51ab1b2fd74a6b0826fe45f426ac308f
|
A013137
|
arctan(tanh(x)+tan(x))=2*x-16/3!*x^3+800/5!*x^5-97536/7!*x^7...
|
[
"2",
"-16",
"800",
"-97536",
"22208000",
"-8125689856",
"4360566579200",
"-3226435003416576",
"3148058338141798400",
"-3916271639106285469696",
"6050134274987713730969600",
"-11363591103950667093393801216"
] |
[
"sign"
] | 4 | 0 | 1 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:51:20 |
oeisdata/seq/A013/A013137.seq
|
64920e5f52e6cea0201e65832f7e0450
|
A013138
|
cos(tanh(x)+tan(x))=1-4/2!*x^2+16/4!*x^4-448/6!*x^6+14592/8!*x^8...
|
[
"1",
"-4",
"16",
"-448",
"14592",
"-705536",
"65245184",
"-5385535488",
"910402060288",
"-124371776831488",
"30930578556583936",
"-6638266678020931584",
"2186545615284171964416",
"-694382737827711997181952"
] |
[
"sign"
] | 6 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2024-09-21T17:12:56 |
oeisdata/seq/A013/A013138.seq
|
4d7366ff8faff4647eef459caa21763a
|
A013139
|
sec(tanh(x)+tan(x))=1+4/2!*x^2+80/4!*x^4+4288/6!*x^6+426240/8!*x^8...
|
[
"1",
"4",
"80",
"4288",
"426240",
"67920896",
"15873495040",
"5113806962688",
"2172417489305600",
"1176644688113041408",
"791421023406538096640",
"647183647775891247857664",
"632330839348840678513704960"
] |
[
"nonn"
] | 6 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2023-02-21T11:33:02 |
oeisdata/seq/A013/A013139.seq
|
1e80da0c8e0da3550cb9a624f35eefd6
|
A013140
|
exp(tanh(x)+arctan(x))=1+2*x+4/2!*x^2+4/3!*x^3-16/4!*x^4-88/5!*x^5...
|
[
"1",
"2",
"4",
"4",
"-16",
"-88",
"64",
"2496",
"4096",
"-106624",
"-480896",
"6875136",
"54717440",
"-673392640",
"-7775895552",
"99550288896",
"1454255472640",
"-21279326830592",
"-360442602684416",
"6159283224084480",
"116460747215831040"
] |
[
"sign"
] | 4 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:51:20 |
oeisdata/seq/A013/A013140.seq
|
c546f7bcc60440b87b65de97a2eb98ad
|
A013141
|
sin(tanh(x)+arctan(x))=2*x-12/3!*x^3+232/5!*x^5-8960/7!*x^7...
|
[
"2",
"-12",
"232",
"-8960",
"580480",
"-57192960",
"8028368896",
"-1530617461760",
"381866595811328",
"-120993556601405440",
"47505188434021777408",
"-22644967739703901421568",
"12882783407125570011004928"
] |
[
"sign"
] | 6 | 0 | 1 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2018-05-11T13:57:05 |
oeisdata/seq/A013/A013141.seq
|
a3cb22eeb30f99e39d868d7bc4ee4548
|
A013142
|
arcsin(tanh(x)+arctan(x))=2*x+4/3!*x^3+168/5!*x^5+13248/7!*x^7...
|
[
"2",
"4",
"168",
"13248",
"2226048",
"599902208",
"243130652672",
"137141067373568",
"103018549675327488",
"99335294756500832256",
"119626550900969898049536",
"175950984763936427137433600",
"310396731889156481163306991616"
] |
[
"nonn"
] | 6 | 0 | 1 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2014-12-16T17:14:01 |
oeisdata/seq/A013/A013142.seq
|
b1dedc518c41b1387286c701a39ee786
|
A013143
|
tan(tanh(x)+arctan(x))=2*x+12/3!*x^3+232/5!*x^5+9184/7!*x^7...
|
[
"2",
"12",
"232",
"9184",
"628864",
"65666304",
"9724490752",
"1938995759104",
"500703018057728",
"162578867050250240",
"64828188125105225728",
"31143422445257665019904",
"17740655235950956739821568"
] |
[
"nonn"
] | 8 | 0 | 1 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2015-02-07T06:40:53 |
oeisdata/seq/A013/A013143.seq
|
40a833e39624d1f81c178dfb454645cd
|
A013144
|
arctan(tanh(x)+arctan(x))=2*x-20/3!*x^3+1128/5!*x^5-158112/7!*x^7...
|
[
"2",
"-20",
"1128",
"-158112",
"41334912",
"-17364051712",
"10697958401024",
"-9087507664709632",
"10179531541621604352",
"-14538540850131730563072",
"25785525466844174964228096",
"-55601885971190702384095952896"
] |
[
"sign"
] | 6 | 0 | 1 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2016-11-29T08:33:06 |
oeisdata/seq/A013/A013144.seq
|
95bdc4e2ada2f07694b1ea447a90c8c3
|
A013145
|
E.g.f.: cos(tanh(x)+arctan(x))=1-4/2!*x^2+48/4!*x^4-1344/6!*x^6+68096/8!*x^8...
|
[
"1",
"-4",
"48",
"-1344",
"68096",
"-5489024",
"649853952",
"-106867367936",
"23404867387392",
"-6602987646386176",
"2335532843551916032",
"-1012790947054260453376",
"528471932766276016930816",
"-326628755754313262527676416",
"235945768815569189548314329088"
] |
[
"sign"
] | 6 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-08-28T13:11:47 |
oeisdata/seq/A013/A013145.seq
|
2f2183f0c465ea2794e0266e6b9a2120
|
A013146
|
sinh(tanh(x)+arctan(x))=2*x+4/3!*x^3-88/5!*x^5+2496/7!*x^7...
|
[
"2",
"4",
"-88",
"2496",
"-106624",
"6875136",
"-673392640",
"99550288896",
"-21279326830592",
"6159283224084480",
"-2276409633583071232",
"1031635526526543462400",
"-558671488143239984709632",
"355396466132997594824048640"
] |
[
"sign"
] | 6 | 0 | 1 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2024-11-17T12:49:53 |
oeisdata/seq/A013/A013146.seq
|
8abcf7274a8bb3c10ec12b9292f813d0
|
A013147
|
arcsinh(tanh(x)+arctan(x))=2*x-12/3!*x^3+488/5!*x^5-55552/7!*x^7...
|
[
"2",
"-12",
"488",
"-55552",
"12546944",
"-4711567872",
"2650074624000",
"-2084720933010432",
"2185097305985613824",
"-2943182792681798926336",
"4953485656236312191369216",
"-10186669183126638973192372224"
] |
[
"sign"
] | 6 | 0 | 1 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2015-06-17T15:38:20 |
oeisdata/seq/A013/A013147.seq
|
900cf2a71248892e6a8a8250236ec55b
|
A013148
|
tanh(tanh(x)+arctan(x))=2*x-20/3!*x^3+872/5!*x^5-82848/7!*x^7...
|
[
"2",
"-20",
"872",
"-82848",
"13615232",
"-3427600128",
"1224824628224",
"-589372636243968",
"367372633732907008",
"-287938978919399424000",
"277156456747324043952128",
"-321405895510495023427223552"
] |
[
"sign"
] | 6 | 0 | 1 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2025-03-21T18:48:49 |
oeisdata/seq/A013/A013148.seq
|
4a9466f3c02b48a5e7ab673ebd5adaad
|
A013149
|
cosh(tanh(x)+arctan(x))=1+4/2!*x^2-16/4!*x^4+64/6!*x^6+4096/8!*x^8...
|
[
"1",
"4",
"-16",
"64",
"4096",
"-480896",
"54717440",
"-7775895552",
"1454255472640",
"-360442602684416",
"116460747215831040",
"-47685470462142971904",
"24020257118743960748032",
"-14514884376044102613991424"
] |
[
"sign"
] | 6 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2021-12-13T16:32:17 |
oeisdata/seq/A013/A013149.seq
|
58b99e2b0e8061303e2d962e03a49825
|
A013150
|
sec(tanh(x)+arctan(x))=1+4/2!*x^2+48/4!*x^4+1344/6!*x^6+71680/8!*x^8...
|
[
"1",
"4",
"48",
"1344",
"71680",
"6134144",
"766639104",
"132845576192",
"30189756186624",
"8791995173601280",
"3164834039610834944",
"1391075516277863612416",
"727593505575051704926208",
"449845963881833812549697536"
] |
[
"nonn"
] | 6 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2024-01-17T14:50:05 |
oeisdata/seq/A013/A013150.seq
|
8b124d4ed2be871acc13e8d7839eb495
|
A013151
|
sech(tanh(x)+arctan(x))=1-4/2!*x^2+112/4!*x^4-7744/6!*x^6...
|
[
"1",
"-4",
"112",
"-7744",
"995840",
"-205558144",
"62203595776",
"-25948859891712",
"14273513699311616",
"-10010170584339742720",
"8717845696617764192256",
"-9230668213290446763196416",
"11677592409577212192402440192"
] |
[
"sign"
] | 4 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:51:21 |
oeisdata/seq/A013/A013151.seq
|
9297856e784009d0d52bfa920e674d6f
|
A013152
|
E.g.f.: log(tanh(x)+cos(x))=x-2/2!*x^2+3/3!*x^3-12/4!*x^4+65/5!*x^5...
|
[
"0",
"1",
"-2",
"3",
"-12",
"65",
"-392",
"2723",
"-23072",
"226785",
"-2475392",
"29857443",
"-397554432",
"5785047905",
"-91112993792",
"1544546456963",
"-28059800686592",
"543833037679425",
"-11198270349934592",
"244141035610073283"
] |
[
"sign"
] | 11 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-07-21T11:26:47 |
oeisdata/seq/A013/A013152.seq
|
70b33754888657b2f414e374f27a37bc
|
A013153
|
Expansion of e.g.f.: exp(tanh(x)+sinh(x))=1+2*x+4/2!*x^2+7/3!*x^3+8/4!*x^4+9/5!*x^5...
|
[
"1",
"2",
"4",
"7",
"8",
"9",
"118",
"865",
"1912",
"-12375",
"-53094",
"848621",
"7487532",
"-34580971",
"-722809274",
"1631142593",
"92118225104",
"100600927153",
"-13286089862286",
"-62231815768555",
"2227449108601940",
"20774283625070381"
] |
[
"sign"
] | 6 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2019-04-29T08:14:18 |
oeisdata/seq/A013/A013153.seq
|
aae84b4e68f325d7a7c42177ef80f5d8
|
A013154
|
exp(tanh(x)+arcsinh(x)) = 1+2*x+4/2!*x^2+5/3!*x^3-8/4!*x^4-63/5!*x^5...
|
[
"1",
"2",
"4",
"5",
"-8",
"-63",
"-26",
"1311",
"4008",
"-40503",
"-288486",
"1746571",
"23670420",
"-107820971",
"-2395713498",
"11358568591",
"304636017840",
"-2325027955727",
"-49472656345230",
"758733754118995",
"10516377983584300"
] |
[
"sign"
] | 13 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2013-11-01T18:48:14 |
oeisdata/seq/A013/A013154.seq
|
90e9e64094ea6c2133ea1c207bfcd204
|
A013155
|
Expansion of e.g.f. exp(arctanh(x)+log(x+1)).
|
[
"1",
"2",
"3",
"6",
"21",
"90",
"495",
"3150",
"23625",
"198450",
"1885275",
"19646550",
"225935325",
"2809456650",
"37927664775",
"547844046750",
"8491582724625",
"139700231921250",
"2444754058621875",
"45123174910563750",
"879901910755993125",
"18004146789314936250",
"387089155970271129375",
"8696002899239114208750"
] |
[
"nonn"
] | 18 | 0 | 2 |
[
"A013155",
"A079484"
] | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2024-01-05T14:49:31 |
oeisdata/seq/A013/A013155.seq
|
92fee3c55e9770c4a05eff4fa7e68376
|
A013156
|
sin(arctanh(x) + log(x+1)) = 2*x - 1/2!*x^2 - 4/3!*x^3 + 18/4!*x^4 - 110/5!*x^5 + ...
|
[
"0",
"2",
"-1",
"-4",
"18",
"-110",
"495",
"-3560",
"19180",
"-175670",
"1060875",
"-12405100",
"74505750",
"-1145912950",
"5007404675",
"-121546204000",
"-249464553000",
"-9910138520750",
"-387578487479625",
"2249416271459500",
"-229283516527763750"
] |
[
"sign"
] | 9 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2013-04-20T13:21:00 |
oeisdata/seq/A013/A013156.seq
|
135115c2ed12148fc3712e25b649acc1
|
A013157
|
Expansion of e.g.f.: arcsin(arctanh(x)+log(x+1))=2*x-1/2!*x^2+12/3!*x^3-30/4!*x^4+526/5!*x^5...
|
[
"0",
"2",
"-1",
"12",
"-30",
"526",
"-3135",
"65912",
"-693868",
"16780042",
"-263534805",
"7241447268",
"-153049925754",
"4746451931334",
"-126285481689003",
"4393248761465712",
"-140634651688634520",
"5453436399167044242",
"-203461284207097440873"
] |
[
"sign"
] | 6 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2018-05-20T11:40:23 |
oeisdata/seq/A013/A013157.seq
|
3f06f5270acf05bc6cd9cb731e6e4b93
|
A013158
|
Expansion of e.g.f. tan(arctanh(x) + log(x+1)).
|
[
"0",
"2",
"-1",
"20",
"-54",
"940",
"-5670",
"101440",
"-1011080",
"19618000",
"-276748200",
"5948856800",
"-108391285200",
"2598850748000",
"-57723908897200",
"1543071734672000",
"-40212272774544000",
"1193617208821024000"
] |
[
"sign"
] | 9 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2019-12-12T13:30:41 |
oeisdata/seq/A013/A013158.seq
|
29ea0e95116e90d57472f42fbfa79f50
|
A013159
|
arctan(arctanh(x)+log(x+1))=2*x-1/2!*x^2-12/3!*x^3+42/4!*x^4+436/5!*x^5...
|
[
"0",
"2",
"-1",
"-12",
"42",
"436",
"-4170",
"-32704",
"751016",
"3283072",
"-209162880",
"86913024",
"81648502848",
"-575015877024",
"-41409311392176",
"689874309603456",
"25412078270229120",
"-812967446932685568",
"-17148064731893670528"
] |
[
"sign"
] | 6 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2016-11-29T08:37:19 |
oeisdata/seq/A013/A013159.seq
|
b05b48cc5f42dac0d833ce047c98dc2f
|
A013160
|
cos(arctanh(x)+log(x+1))=1-4/2!*x^2+6/3!*x^3-19/4!*x^4+20/5!*x^5...
|
[
"1",
"0",
"-4",
"6",
"-19",
"20",
"-70",
"-1050",
"7645",
"-125640",
"1074400",
"-15186050",
"154663825",
"-2302431300",
"27387957350",
"-445100087250",
"6069674521625",
"-108269831098000",
"1666530849522500",
"-32533793834402250"
] |
[
"sign"
] | 4 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:51:21 |
oeisdata/seq/A013/A013160.seq
|
a2d7757464e7bde5841ca2dec1859696
|
A013161
|
Expansion of e.g.f. sinh(arctanh(x) + log(x+1)).
|
[
"0",
"2",
"-1",
"12",
"-30",
"270",
"-1215",
"12600",
"-81900",
"992250",
"-8434125",
"117879300",
"-1237732650",
"19666196550",
"-245827456875",
"4382752374000",
"-63549909423000",
"1257302087291250",
"-20745484440305625",
"451231749105637500"
] |
[
"sign"
] | 9 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2024-02-01T17:52:48 |
oeisdata/seq/A013/A013161.seq
|
ead6911bc6640c71e773c4b535dd21b2
|
A013162
|
Expansion of e.g.f. arcsinh(arctanh(x) + log(x+1)).
|
[
"0",
"2",
"-1",
"-4",
"18",
"146",
"-1425",
"-7592",
"210028",
"559322",
"-50827005",
"106120692",
"17584275654",
"-154934766198",
"-8006009893245",
"152561646167328",
"4407064919207640",
"-159846661630850958",
"-2597264235213998553"
] |
[
"sign"
] | 9 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2025-03-28T15:35:44 |
oeisdata/seq/A013/A013162.seq
|
5df36c0099f2dd1a0ef68c96720837b4
|
A013163
|
Expansion of e.g.f.: arctanh(arctanh(x)+log(x+1))=2*x-1/2!*x^2+20/3!*x^3-54/4!*x^4...
|
[
"0",
"2",
"-1",
"20",
"-54",
"1196",
"-7590",
"183424",
"-2024456",
"53868512",
"-879522480",
"25940060736",
"-567297596448",
"18589297654560",
"-510176264397072",
"18555679255219584",
"-611191404598032000",
"24595483932280127232"
] |
[
"sign"
] | 11 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2016-10-04T11:29:37 |
oeisdata/seq/A013/A013163.seq
|
e87fb6bd9e7dc2370093177074921368
|
A013164
|
cosh(arctanh(x)+log(x+1))=1+4/2!*x^2-6/3!*x^3+51/4!*x^4-180/5!*x^5...
|
[
"1",
"0",
"4",
"-6",
"51",
"-180",
"1710",
"-9450",
"105525",
"-793800",
"10319400",
"-98232750",
"1463667975",
"-16856739900",
"283755121650",
"-3834908327250",
"72041492147625",
"-1117601855370000",
"23190238498927500",
"-406108574195073750"
] |
[
"sign"
] | 4 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:51:21 |
oeisdata/seq/A013/A013164.seq
|
8ede827b736f84d4ab00a0e578a07363
|
A013165
|
sec(arctanh(x)+log(x+1))=1+4/2!*x^2-6/3!*x^3+115/4!*x^4-500/5!*x^5...
|
[
"1",
"0",
"4",
"-6",
"115",
"-500",
"8830",
"-70770",
"1316825",
"-15886440",
"324218600",
"-5249917750",
"119185529675",
"-2412502361100",
"61104527105050",
"-1476059511449250",
"41607421213320625",
"-1162370434739930000"
] |
[
"sign"
] | 4 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:51:21 |
oeisdata/seq/A013/A013165.seq
|
460ee7d711a7bd8a1c44557b2324b0f5
|
A013166
|
Expansion of e.g.f.: sech(arctanh(x)+log(x+1))=1-4/2!*x^2+6/3!*x^3+45/4!*x^4-300/5!*x^5...
|
[
"1",
"0",
"-4",
"6",
"45",
"-300",
"-630",
"18270",
"-44415",
"-1428840",
"13608000",
"106964550",
"-3044747475",
"2748645900",
"674525001150",
"-6848689097250",
"-138141621993375",
"3761985048822000",
"12387014410270500",
"-1765001060909336250"
] |
[
"sign"
] | 6 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2019-01-10T12:08:37 |
oeisdata/seq/A013/A013166.seq
|
a5f5ae53e1a259962caa5ab4b493f7b0
|
A013167
|
Expansion of e.g.f. log(arctanh(x) + exp(x)).
|
[
"0",
"2",
"-3",
"13",
"-74",
"573",
"-5414",
"61787",
"-817144",
"12374569",
"-210429994",
"3978169039",
"-82685370668",
"1875127830925",
"-46061020851390",
"1218540977107971",
"-34537657596434704",
"1044190509028339409",
"-33542143648555416402"
] |
[
"sign"
] | 7 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2018-07-31T22:34:17 |
oeisdata/seq/A013/A013167.seq
|
370ca5ac4e6f42eb4e00f0bd297aad8a
|
A013168
|
exp(arctanh(x)+sin(x))=1+2*x+4/2!*x^2+9/3!*x^3+24/4!*x^4+97/5!*x^5...
|
[
"1",
"2",
"4",
"9",
"24",
"97",
"534",
"3647",
"27272",
"232345",
"2170874",
"22882827",
"260563908",
"3272680621",
"43811275382",
"637916495327",
"9816624434928",
"162606798592913",
"2827858695802930",
"52505736635681875",
"1018209224687676028"
] |
[
"nonn"
] | 9 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2013-10-24T17:01:32 |
oeisdata/seq/A013/A013168.seq
|
2018118b882ac7c37fe7b0d0c9639949
|
A013169
|
arcsin(arctanh(x)+sin(x))=2*x+9/3!*x^3+353/5!*x^5+36799/7!*x^7...
|
[
"2",
"9",
"353",
"36799",
"7537817",
"2561794059",
"1303341700269",
"927157598991519",
"878628923948350097",
"1069855675293079408723",
"1627609755057103980327221",
"3025319595854386788906432711",
"6746132863265524117134837248601"
] |
[
"nonn"
] | 6 | 0 | 1 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2014-09-14T09:24:18 |
oeisdata/seq/A013/A013169.seq
|
824ace5a317e822bc2af565a64d2d683
|
A013170
|
Expansion of e.g.f.: exp(arctanh(x)+arcsin(x)).
|
[
"1",
"2",
"4",
"11",
"40",
"185",
"1030",
"6785",
"51160",
"438425",
"4176250",
"44098925",
"507867100",
"6375156125",
"86130937750",
"1253044612625",
"19429666282000",
"321457635604625",
"5626346310003250",
"104323833636303125",
"2034312191276462500"
] |
[
"nonn"
] | 21 | 0 | 2 |
[
"A006228",
"A013170"
] | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2020-05-10T02:59:35 |
oeisdata/seq/A013/A013170.seq
|
b2fc70d47f1195b27cd48b07878464ad
|
A013171
|
sin(arctanh(x)+arcsin(x))=2*x-5/3!*x^3-55/5!*x^5-1535/7!*x^7...
|
[
"2",
"-5",
"-55",
"-1535",
"-80695",
"-6860075",
"-859242475",
"-148907237375",
"-34123911391375",
"-9992873727945875",
"-3640782796679981875",
"-1615246696514236394375",
"-857352190238672679484375"
] |
[
"sign"
] | 4 | 0 | 1 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:51:21 |
oeisdata/seq/A013/A013171.seq
|
dce7730aa5b2b5a4d6c1fb71b420cb61
|
A013172
|
exp(arctanh(x)+tan(x))=1+2*x+4/2!*x^2+12/3!*x^3+48/4!*x^4+232/5!*x^5...
|
[
"1",
"2",
"4",
"12",
"48",
"232",
"1344",
"8960",
"68096",
"580480",
"5489024",
"57192960",
"649853952",
"8028368896",
"106867367936",
"1530617461760",
"23404867387392",
"381866595811328",
"6602987646386176",
"120993556601405440"
] |
[
"nonn"
] | 8 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2013-10-24T17:01:22 |
oeisdata/seq/A013/A013172.seq
|
627cc1c39bfe62cddefe69eb60bd3468
|
A013173
|
arctan(arctanh(x)+tan(x))=2*x-12/3!*x^3+488/5!*x^5-48608/7!*x^7...
|
[
"2",
"-12",
"488",
"-48608",
"9080960",
"-2722798848",
"1197871592448",
"-726520846829568",
"581088281306562560",
"-592572418222512668672",
"750419972539476482195456",
"-1155381150026866713259671552",
"2125413346746653166067846742016"
] |
[
"sign"
] | 6 | 0 | 1 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2016-11-29T08:40:24 |
oeisdata/seq/A013/A013173.seq
|
1bdee994540486795abfcda148edf12f
|
A013174
|
exp(arctanh(x) + arctan(x)) = 1 + 2*x + 4/2!*x^2 + 8/3!*x^3 + 16/4!*x^4 + 80/5!*x^5 +...
|
[
"1",
"2",
"4",
"8",
"16",
"80",
"640",
"4160",
"21760",
"177920",
"2291200",
"25548800",
"223436800",
"2560563200",
"44438118400",
"702660608000",
"8725110784000",
"129295622144000",
"2796896567296000",
"57197188186112000",
"926039081943040000"
] |
[
"nonn"
] | 10 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2013-01-12T20:07:25 |
oeisdata/seq/A013/A013174.seq
|
c6ed20355ab86be764c83b4bd84a65eb
|
A013175
|
sin(arctanh(x)+arctan(x))=2*x-8/3!*x^3+80/5!*x^5-4160/7!*x^7...
|
[
"2",
"-8",
"80",
"-4160",
"177920",
"-25548800",
"2560563200",
"-702660608000",
"129295622144000",
"-57197188186112000",
"16886573106790400000",
"-10912577096233779200000",
"4743735379760119808000000"
] |
[
"sign"
] | 6 | 0 | 1 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2016-11-29T08:42:34 |
oeisdata/seq/A013/A013175.seq
|
c90223d3f8a6993fe9abec573c1cf5f2
|
A013176
|
arcsin(arctanh(x)+arctan(x))=2*x+8/3!*x^3+336/5!*x^5+32832/7!*x^7...
|
[
"2",
"8",
"336",
"32832",
"6596352",
"2172377088",
"1074790176768",
"742942875451392",
"684332863424888832",
"809904627202731540480",
"1197620189653593343131648",
"2163726873433446527375769600",
"4689766098958031240193965555712"
] |
[
"nonn"
] | 6 | 0 | 1 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2014-08-22T12:13:43 |
oeisdata/seq/A013/A013176.seq
|
7a2aa25652e80642ac35ad509b1cd727
|
A013177
|
tan(arctanh(x)+arctan(x))=2*x+16/3!*x^3+560/5!*x^5+42880/7!*x^7...
|
[
"2",
"16",
"560",
"42880",
"5692160",
"1158860800",
"335091660800",
"130514735104000",
"65860132462592000",
"41792278392537088000",
"32569972497977507840000",
"30580999289444580720640000",
"34048056335378925092864000000"
] |
[
"nonn"
] | 10 | 0 | 1 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2016-11-29T08:44:11 |
oeisdata/seq/A013/A013177.seq
|
7b4cb21d058595fa9550271bb1c4c9f7
|
A013178
|
arctan(arctanh(x)+arctan(x))=2*x-16/3!*x^3+816/5!*x^5-100224/7!*x^7...
|
[
"2",
"-16",
"816",
"-100224",
"23046912",
"-8501907456",
"4600667731968",
"-3432263151550464",
"3376634004034486272",
"-4235408050319799091200",
"6597340706535893925101568",
"-12493980287273651231218728960"
] |
[
"sign"
] | 6 | 0 | 1 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2016-11-29T08:46:29 |
oeisdata/seq/A013/A013178.seq
|
8484584670a0b9604809bc07755a5a7e
|
A013179
|
cos(arctanh(x)+arctan(x))=1-4/2!*x^2+16/4!*x^4-640/6!*x^6+21760/8!*x^8...
|
[
"1",
"-4",
"16",
"-640",
"21760",
"-2291200",
"223436800",
"-44438118400",
"8725110784000",
"-2796896567296000",
"926039081943040000",
"-435519369139978240000",
"218626979887002419200000",
"-141711151230417633280000000"
] |
[
"sign"
] | 6 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2016-11-29T10:21:48 |
oeisdata/seq/A013/A013179.seq
|
a5f580a34d41bb5e1458904714f9cdf2
|
A013180
|
sec(arctanh(x)+arctan(x))=1+4/2!*x^2+80/4!*x^4+4480/6!*x^6...
|
[
"1",
"4",
"80",
"4480",
"462080",
"77248000",
"18902835200",
"6385348403200",
"2843287396352000",
"1614575957622784000",
"1138477316012441600000",
"976037590707833405440000",
"999765439694232249958400000"
] |
[
"nonn"
] | 6 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2016-11-29T10:22:50 |
oeisdata/seq/A013/A013180.seq
|
4cd749d0750d04e12849563f4eebeae0
|
A013181
|
Expansion of e.g.f.: log(arctanh(x)+cos(x)) = x-2/2!*x^2+7/3!*x^3-28/4!*x^4+193/5!*x^5...
|
[
"0",
"1",
"-2",
"7",
"-28",
"193",
"-1400",
"13319",
"-139424",
"1721281",
"-23379712",
"357281351",
"-5951323904",
"108706678273",
"-2142923081728",
"45591739883975",
"-1037606714249216",
"25211971076762753",
"-650452080060399616"
] |
[
"sign"
] | 6 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2016-01-12T15:05:12 |
oeisdata/seq/A013/A013181.seq
|
da94caaa516be202671bd64ad890df23
|
A013182
|
exp(arctanh(x)+sinh(x))=1+2*x+4/2!*x^2+11/3!*x^3+40/4!*x^4+177/5!*x^5...
|
[
"1",
"2",
"4",
"11",
"40",
"177",
"934",
"5889",
"42648",
"354825",
"3295194",
"34194349",
"387494364",
"4812801541",
"64310993478",
"929134537249",
"14291172086544",
"235303563551473",
"4092687247885554",
"75620298761841685",
"1467156197049970084"
] |
[
"nonn"
] | 10 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2013-11-21T12:46:02 |
oeisdata/seq/A013/A013182.seq
|
089135e882e1d1aeae631606f6a1ed8e
|
A013183
|
exp(arctanh(x)+arcsinh(x)) = 1+2*x+4/2!*x^2+9/3!*x^3+24/4!*x^4+105/5!*x^5...
|
[
"1",
"2",
"4",
"9",
"24",
"105",
"630",
"4095",
"27720",
"235305",
"2353050",
"24792075",
"267567300",
"3350672325",
"46909412550",
"682570263375",
"10103827734000",
"167108397080625",
"3007951147451250",
"55823919598321875",
"1049953727680357500"
] |
[
"nonn"
] | 12 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2013-10-24T17:17:10 |
oeisdata/seq/A013/A013183.seq
|
dd886dae2bdf0bca5d9fc664c752f9bf
|
A013184
|
exp(arctanh(x)+tanh(x)) = 1+2*x+4/2!*x^2+8/3!*x^3+16/4!*x^4+72/5!*x^5...
|
[
"1",
"2",
"4",
"8",
"16",
"72",
"544",
"3936",
"25344",
"193920",
"1920384",
"21876736",
"246359040",
"2967878656",
"39508168704",
"589063146496",
"9120978370560",
"149737853943808",
"2587275558617088",
"48291040167362560",
"939278027083448320"
] |
[
"nonn"
] | 10 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2013-10-24T17:16:09 |
oeisdata/seq/A013/A013184.seq
|
a0f667b9a679ddc36c51761cb161c37b
|
A013185
|
E.g.f.: log(cosh(x)+log(x+1)).
|
[
"0",
"1",
"-1",
"4",
"-19",
"113",
"-813",
"6921",
"-68290",
"766909",
"-9660965",
"134950693",
"-2070706988",
"34628733267",
"-626946816195",
"12218295424331",
"-255043813997776",
"5677409949583369",
"-134259854938074137"
] |
[
"sign"
] | 11 | 0 | 4 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2015-03-06T02:59:39 |
oeisdata/seq/A013/A013185.seq
|
c4e158e6f7a454c793fe1589d612770d
|
A013186
|
Expansion of e.g.f. log(cosh(x) + arcsin(x)).
|
[
"0",
"1",
"0",
"0",
"0",
"8",
"-48",
"392",
"-2240",
"20096",
"-147200",
"1754368",
"-16873472",
"241340032",
"-2769127424",
"44833033216",
"-593918959616",
"10840711614464",
"-164204798541824",
"3348758074142720",
"-57147730941444096"
] |
[
"sign"
] | 9 | 0 | 6 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2020-12-07T15:18:00 |
oeisdata/seq/A013/A013186.seq
|
0b3ba3806709b6ef66a5ac9912bed851
|
A013187
|
Expansion of e.g.f. log(cosh(x) + tan(x)).
|
[
"0",
"1",
"0",
"1",
"-4",
"25",
"-120",
"761",
"-5024",
"42065",
"-378240",
"3898321",
"-42905344",
"521329705",
"-6794511360",
"96017526281",
"-1448243646464",
"23356125062945",
"-399450070548480",
"7240133620964641",
"-138422733355024384"
] |
[
"sign"
] | 10 | 0 | 5 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2018-08-05T18:06:27 |
oeisdata/seq/A013/A013187.seq
|
a3e7a2a8e9ffdb6c61c42820876fbe14
|
A013188
|
E.g.f.: log(cosh(x)+arctan(x))=x-3/3!*x^3+12/4!*x^4-7/5!*x^5-168/6!*x^6...
|
[
"0",
"1",
"0",
"-3",
"12",
"-7",
"-168",
"917",
"-1568",
"-7183",
"198400",
"-3803987",
"27605248",
"316369129",
"-8352339968",
"40892465221",
"772060278784",
"-12655402122271",
"84749115129856",
"-1539257113273507",
"2576755050676224"
] |
[
"sign"
] | 6 | 0 | 4 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2013-03-12T18:29:22 |
oeisdata/seq/A013/A013188.seq
|
ef43abe66b3a16137d2c2ad33917ba07
|
A013189
|
All terms are squares and a(n) is length of n-th run.
|
[
"1",
"4",
"4",
"4",
"4",
"9",
"9",
"9",
"9",
"16",
"16",
"16",
"16",
"25",
"25",
"25",
"25",
"36",
"36",
"36",
"36",
"36",
"36",
"36",
"36",
"36",
"49",
"49",
"49",
"49",
"49",
"49",
"49",
"49",
"49",
"64",
"64",
"64",
"64",
"64",
"64",
"64",
"64",
"64",
"81",
"81",
"81",
"81",
"81",
"81",
"81",
"81",
"81",
"100",
"100",
"100",
"100",
"100",
"100",
"100",
"100",
"100",
"100",
"100",
"100",
"100",
"100"
] |
[
"nonn",
"easy"
] | 13 | 1 | 2 |
[
"A001462",
"A013189",
"A080605",
"A080606",
"A080607"
] | null |
James Propp
| 2015-04-04T02:40:34 |
oeisdata/seq/A013/A013189.seq
|
156f2a11d17ed5a8e01f61a456ad4f46
|
A013190
|
log(cosh(x)+arcsinh(x))=x-2/3!*x^3+8/4!*x^4-12/5!*x^5-48/6!*x^6...
|
[
"0",
"1",
"0",
"-2",
"8",
"-12",
"-48",
"432",
"-2112",
"10000",
"14080",
"-1500512",
"17517568",
"-18269760",
"-1666201600",
"16350361856",
"-45064462336",
"922523568384",
"-4131436888064",
"-990634832194048",
"21402743134224384",
"92553699220882432"
] |
[
"sign"
] | 8 | 0 | 4 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2013-11-01T18:48:29 |
oeisdata/seq/A013/A013190.seq
|
a2bdb601b431e22f4793db23d97fecbb
|
A013191
|
Expansion of e.g.f. log(cosh(x) + tanh(x)).
|
[
"0",
"1",
"0",
"-3",
"12",
"-15",
"-120",
"1197",
"-6048",
"-255",
"428160",
"-5448003",
"29812992",
"241437105",
"-8332047360",
"104019879597",
"-293043130368",
"-17849464279935",
"456591699640320",
"-5108933510880003",
"-26996975653552128"
] |
[
"sign"
] | 9 | 0 | 4 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2021-06-20T12:46:22 |
oeisdata/seq/A013/A013191.seq
|
a1d072aa8e37f081354e07fc70053ba0
|
A013192
|
Expansion of e.g.f. log(cosh(x) + arctanh(x)).
|
[
"0",
"1",
"0",
"1",
"-4",
"33",
"-168",
"1377",
"-9504",
"99649",
"-930560",
"11796673",
"-137207552",
"2017677153",
"-28086102016",
"471591223841",
"-7659623550976",
"144742585812609",
"-2686461109796864",
"56447611418620289"
] |
[
"sign"
] | 9 | 0 | 5 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2019-02-06T12:26:08 |
oeisdata/seq/A013/A013192.seq
|
b520cb18b78c2b7bfaec7426ee4a0afe
|
A013193
|
Expansion of e.g.f. log(sec(x) + log(x+1)).
|
[
"0",
"1",
"-1",
"4",
"-15",
"93",
"-633",
"5381",
"-51506",
"565957",
"-6922205",
"93992413",
"-1398890284",
"22689478823",
"-398141898399",
"7519118564551",
"-152056970221072",
"3278894568674073",
"-75103176871966409",
"1821102601528126265"
] |
[
"sign"
] | 9 | 0 | 4 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2023-02-25T17:07:12 |
oeisdata/seq/A013/A013193.seq
|
d233d215ad95c5dc3e0c2a90edec2a5b
|
A013194
|
Expansion of e.g.f. log(sec(x) + sin(x)).
|
[
"0",
"1",
"0",
"-2",
"12",
"-40",
"120",
"208",
"-6048",
"64640",
"-428160",
"986368",
"29812992",
"-652487680",
"8332047360",
"-60911593472",
"-293043130368",
"20973645824000",
"-456591699640320",
"6185783347314688",
"-26996975653552128"
] |
[
"sign"
] | 9 | 0 | 4 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2023-03-15T15:22:50 |
oeisdata/seq/A013/A013194.seq
|
b35f58a83a04d0fa608508e2e2d50826
|
A013195
|
E.g.f.: log(sec(x) + arcsin(x)).
|
[
"0",
"1",
"0",
"0",
"4",
"-12",
"72",
"-168",
"544",
"8144",
"-91520",
"1384768",
"-11984128",
"149032128",
"-1158162432",
"16299168896",
"-125837340672",
"2859883876608",
"-32260942757888",
"1008997773326336",
"-15535095938220032",
"466978134769624064"
] |
[
"sign"
] | 14 | 0 | 5 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2021-06-05T11:37:01 |
oeisdata/seq/A013/A013195.seq
|
f4439bf98f0dfc2ecd7877b93c374a47
|
A013196
|
Expansion of e.g.f. log(sec(x) + arctan(x)).
|
[
"0",
"1",
"0",
"-3",
"16",
"-27",
"-48",
"777",
"-5504",
"48905",
"-149120",
"-4320107",
"76593152",
"-424303635",
"-2866784256",
"77237001761",
"-1179358298112",
"20512289602833",
"-131744654655488",
"-6321209675239123",
"194063863443816448"
] |
[
"sign"
] | 7 | 0 | 4 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2018-08-01T20:55:29 |
oeisdata/seq/A013/A013196.seq
|
2bca756d0ae557663e8de42aa43d3d34
|
A013197
|
Expansion of e.g.f. log(sec(x) + sinh(x)).
|
[
"0",
"1",
"0",
"0",
"4",
"-20",
"120",
"-560",
"2784",
"-7920",
"-24960",
"1034880",
"-14625536",
"172569280",
"-1661936640",
"12339608320",
"-13269651456",
"-1902800305920",
"53452617646080",
"-1037015219466240",
"16547577836929024",
"-208832669083243520"
] |
[
"sign"
] | 7 | 0 | 5 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2018-08-01T21:01:47 |
oeisdata/seq/A013/A013197.seq
|
cb479e9fa1b710f08942c1c86469a977
|
A013198
|
E.g.f.: log(sec(x)+arcsinh(x)) = x-2/3!*x^3+12/4!*x^4-32/5!*x^5+72/6!*x^6...
|
[
"0",
"1",
"0",
"-2",
"12",
"-32",
"72",
"152",
"-3808",
"48448",
"-333440",
"289408",
"26461952",
"-393649024",
"4126861312",
"-34249082624",
"-93963415552",
"12871254335488",
"-272828216803328",
"2591959365570560",
"6130847346393088"
] |
[
"sign"
] | 11 | 0 | 4 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2018-08-01T21:03:25 |
oeisdata/seq/A013/A013198.seq
|
e0c6867effa986bd91d187b4acb87f85
|
A013199
|
Expansion of e.g.f. log(sec(x) + tanh(x)).
|
[
"0",
"1",
"0",
"-3",
"16",
"-35",
"0",
"1057",
"-9984",
"59865",
"0",
"-5446683",
"85897216",
"-726781835",
"0",
"133713611977",
"-2848077840384",
"32440474082865",
"0",
"-10034804733270963",
"271157029126537216",
"-3854719922524818035",
"0",
"1800259494456990656497"
] |
[
"sign"
] | 14 | 0 | 4 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2022-11-27T13:59:32 |
oeisdata/seq/A013/A013199.seq
|
b304d393b3d2b8c338d55167b851bcb3
|
A013200
|
Expansion of e.g.f. log(sec(x)+arctanh(x)).
|
[
"0",
"1",
"0",
"1",
"0",
"13",
"-48",
"677",
"-4480",
"54937",
"-471680",
"6248713",
"-65916928",
"988579109",
"-12514310144",
"212756765101",
"-3159842455552",
"60179200959793",
"-1026648500830208",
"21632158018229009",
"-416691460525064192"
] |
[
"sign"
] | 14 | 0 | 6 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2023-03-09T04:20:02 |
oeisdata/seq/A013/A013200.seq
|
25046f2918415c44b6530e701184afa2
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.