Datasets:
christopher
/
oeis

Dataset card Data Studio Files
xet
Community
2
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
A013401
arctan(arcsin(x)-tan(x)) = -1/3!*x^3 - 7/5!*x^5 - 47/7!*x^7 + 3649/9!*x^9...
[ "-1", "-7", "-47", "3649", "603913", "90832337", "16338507729", "3707053126657", "1069079235975961", "387242954208151825", "172585239298528416545", "92608073317490225768001", "58719694732194364215549993" ]
[ "sign" ]
10
4
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-11-21T12:46:02
oeisdata/seq/A013/A013401.seq
41c41cf29c0439f57501f21b58e46496
A013402
E.g.f.: cos(arcsin(x)-tan(x))=1-10/6!*x^6-392/8!*x^8-11814/10!*x^10...
[ "1", "0", "0", "-10", "-392", "-11814", "434412", "239703334", "66778596688", "19103113532274", "6219304575954900", "2372061571443015646", "1067602664492677013176", "566076503411492186181610", "351525681041566766571083772" ]
[ "sign" ]
6
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-05-30T15:22:27
oeisdata/seq/A013/A013402.seq
5fa3c101a8bfa2e53030ed7c5de599ee
A013403
arcsinh(arcsin(x)-tan(x))=-1/3!*x^3-7/5!*x^5-47/7!*x^7+3369/9!*x^9...
[ "-1", "-7", "-47", "3369", "571573", "88260053", "16352313521", "3805010266353", "1114309660688557", "405568733333445837", "180263147441643275337", "96121395297143070311401", "60524878000846286453504453" ]
[ "sign" ]
6
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2019-07-22T18:11:10
oeisdata/seq/A013/A013403.seq
fa8458099b450663f9630571295a2a89
A013404
cosh(arcsin(x)-tan(x))=1+10/6!*x^6+392/8!*x^8+11814/10!*x^10...
[ "1", "0", "0", "10", "392", "11814", "-403612", "-231855494", "-65488668048", "-19019872358258", "-6285428416936228", "-2426795058770532798", "-1100901702843643862296", "-585586283280926607971690", "-363295626691930416421332972" ]
[ "sign" ]
4
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:28
oeisdata/seq/A013/A013404.seq
8a35f4ffc57d772bf25403c3127a0eb1
A013405
sec(arcsin(x)-tan(x))=1+10/6!*x^6+392/8!*x^8+11814/10!*x^10...
[ "1", "0", "0", "10", "392", "11814", "-342012", "-216159814", "-62908810768", "-18841954586226", "-6408550630546884", "-2531899081824559102", "-1166225397113477182936", "-624827241398074401423850", "-387664428610356715107061452" ]
[ "sign" ]
6
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2017-09-26T16:23:35
oeisdata/seq/A013/A013405.seq
76c268ab57c355b715bdc77220c097ca
A013406
sech(arcsin(x)-tan(x))=1-10/6!*x^6-392/8!*x^8-11814/10!*x^10...
[ "1", "0", "0", "-10", "-392", "-11814", "496012", "255399014", "69358453968", "19258160456306", "6077931425640244", "2258231645186973342", "999755491596900217336", "527324363004530542073450", "328862882324660659119175452" ]
[ "sign" ]
6
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2021-08-30T18:23:53
oeisdata/seq/A013/A013406.seq
74e278cf58de082bac0e7303ca4d4be1
A013407
E.g.f.: exp(arcsin(x)-arctan(x))=1+3/3!*x^3-15/5!*x^5+90/6!*x^6+945/7!*x^7...
[ "1", "0", "0", "3", "0", "-15", "90", "945", "-2520", "-21735", "368550", "3898125", "-29313900", "-200675475", "7122965850", "76834382625", "-1133998866000", "-6451321251375", "432213196164750", "4637298724183125", "-115564330313932500" ]
[ "sign" ]
6
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2014-05-28T09:44:10
oeisdata/seq/A013/A013407.seq
4747b24b0c89f3e00bcc5d474ed1fb0d
A013408
arcsin(arcsin(x)-arctan(x))=3/3!*x^3-15/5!*x^5+945/7!*x^7-21735/9!*x^9...
[ "3", "-15", "945", "-21735", "3898125", "-200675475", "79558704225", "-7377590595375", "5270866955479125", "-797301690038728875", "870299379257314631625", "-199012078053904775034375", "299398813508124256529728125" ]
[ "sign" ]
4
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:28
oeisdata/seq/A013/A013408.seq
9dbf67518f0e6b842f2f65408fa02f13
A013409
tan(arcsin(x)-arctan(x))=3/3!*x^3-15/5!*x^5+945/7!*x^7-14175/9!*x^9...
[ "3", "-15", "945", "-14175", "3274425", "-30405375", "52996568625", "2290345682625", "2793516176075625", "471064785877310625", "385249723016564030625", "141236453715527936390625", "117605025896710529818265625" ]
[ "sign" ]
6
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2019-07-25T17:32:10
oeisdata/seq/A013/A013409.seq
575726ff12f31e759e36ba22c0e1fc01
A013410
Coefficient of x^(2n+1)/(2n+1)! in arctan(arcsin(x)-arctan(x))=3/3!*x^3-15/5!*x^5+945/7!*x^7-44415/9!*x^9...
[ "0", "3", "-15", "945", "-44415", "5769225", "-711485775", "171504558225", "-40549611477375", "15553976334521625", "-6025672551378855375", "3368007502842396038625", "-1937899053877871819109375", "1488068350680083972290115625" ]
[ "sign" ]
14
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-03-25T21:37:41
oeisdata/seq/A013/A013410.seq
292adb94ed15c4207fa404a71e769edd
A013411
cos(arcsin(x)-arctan(x))=1-90/6!*x^6+2520/8!*x^8-368550/10!*x^10...
[ "1", "0", "0", "-90", "2520", "-368550", "31808700", "-7577019450", "1338322986000", "-493346972868750", "147490229469082500", "-78563939419056341250", "35612399584500073335000", "-25974260672177759785593750" ]
[ "sign" ]
4
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:28
oeisdata/seq/A013/A013411.seq
5735929df5a1fafc12e391587ccf1624
A013412
arcsinh(arcsin(x)-arctan(x))=3/3!*x^3-15/5!*x^5+945/7!*x^7-36855/9!*x^9...
[ "3", "-15", "945", "-36855", "5145525", "-541215675", "137450538225", "-28334434503375", "11334312919054125", "-3890960916187219875", "2248877246697095639625", "-1162888838017333636584375", "916442062457996554007653125" ]
[ "sign" ]
6
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2016-04-27T16:19:30
oeisdata/seq/A013/A013412.seq
afb8cebf0be33c79fb0885e5d99963a2
A013413
cosh(arcsin(x)-arctan(x))=1+90/6!*x^6-2520/8!*x^8+368550/10!*x^10...
[ "1", "0", "0", "90", "-2520", "368550", "-29313900", "7122965850", "-1133998866000", "432213196164750", "-115564330313932500", "64225795369647161250", "-25965004352151980115000", "19884500689553832175593750" ]
[ "sign" ]
6
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-12-20T17:45:32
oeisdata/seq/A013/A013413.seq
ad1587ac1a22203623053dde6d3804cd
A013414
sec(arcsin(x)-arctan(x))=1+90/6!*x^6-2520/8!*x^8+368550/10!*x^10...
[ "1", "0", "0", "90", "-2520", "368550", "-24324300", "6214858650", "-725350626000", "318282066852750", "-56464293738352500", "40214549353890161250", "-9894502805503110795000", "10823754426851479957593750" ]
[ "sign" ]
4
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:28
oeisdata/seq/A013/A013414.seq
047a479fb4acbfc038f03bbcf7e18345
A013415
sech(arcsin(x)-arctan(x))=1-90/6!*x^6+2520/8!*x^8-368550/10!*x^10...
[ "1", "0", "0", "-90", "2520", "-368550", "36798300", "-8485126650", "1746971226000", "-623950950372750", "216093789514102500", "-111905269600936061250", "58297381976449590975000", "-41488228251938936311593750" ]
[ "sign" ]
6
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2023-03-22T17:52:04
oeisdata/seq/A013/A013415.seq
2f87976568c16d6eccb5de38583e8af1
A013416
Expansion of e.g.f.: exp(arcsin(x)-arcsinh(x))=1+2/3!*x^3+40/6!*x^6+450/7!*x^7+2240/9!*x^9...
[ "1", "0", "0", "2", "0", "0", "40", "450", "0", "2240", "108000", "1786050", "246400", "30888000", "1647734400", "36567781250", "11531520000", "1356752592000", "85195294912000", "2380490964101250", "1210714801920000", "153377369153840000" ]
[ "nonn" ]
6
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2017-12-11T12:05:09
oeisdata/seq/A013/A013416.seq
baca022762939c724fcbf81fdca4c97e
A013417
arcsin(arcsin(x)-arcsinh(x))=2/3!*x^3+450/7!*x^7+2240/9!*x^9...
[ "2", "0", "450", "2240", "1786050", "30888000", "36926539650", "1356752592000", "2425187135621250", "154415644664112000", "389167059569139101250", "38253175174710405000000", "129492439672113021377981250" ]
[ "nonn" ]
4
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:28
oeisdata/seq/A013/A013417.seq
f399e465a369acef616825b203a5e216
A013418
tan(arcsin(x)-arcsinh(x)) = 2/3!*x^3+450/7!*x^7+4480/9!*x^9...
[ "0", "2", "0", "450", "4480", "1786050", "61776000", "37240453250", "2713505184000", "2464296285701250", "308006231110240000", "397784819452992221250", "76036685958833418000000", "132964856302641623934781250" ]
[ "nonn" ]
13
1
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-02-06T13:07:34
oeisdata/seq/A013/A013418.seq
c3fa7b79204aae5aa02e5cd00249cb71
A013419
E.g.f.: cos(arcsin(x)-arcsinh(x))=1-40/6!*x^6-108000/10!*x^10+246400/12!*x^12...
[ "1", "0", "0", "-40", "0", "-108000", "246400", "-1647734400", "11531520000", "-85195294912000", "1210714801920000", "-11246246283767040000", "269211710490511360000", "-3174485131400558976000000", "114873496767979282944000000" ]
[ "sign" ]
6
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-05-27T11:26:13
oeisdata/seq/A013/A013419.seq
0c85da45ec48bffa7370abbe65e13a48
A013420
sec(arcsin(x)-arcsinh(x))=1+40/6!*x^6+108000/10!*x^10+1232000/12!*x^12...
[ "1", "0", "0", "40", "0", "108000", "1232000", "1647734400", "57657600000", "85927162048000", "6053574009600000", "11452742596189440000", "1349295190949488640000", "3261229190521061760000000", "577775664177165642240000000" ]
[ "nonn" ]
6
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2021-05-05T11:53:46
oeisdata/seq/A013/A013420.seq
ba5cad91a2879f450dcdae33931088fb
A013421
exp(arcsin(x)-tanh(x))=1+3/3!*x^3-7/5!*x^5+90/6!*x^6+497/7!*x^7...
[ "1", "0", "0", "3", "0", "-7", "90", "497", "-1176", "10649", "185094", "955757", "530772", "167741741", "1636156522", "18092867249", "170829306928", "6069742560593", "60742435952974", "1368824205107477", "18173279227072940", "584561380993184597" ]
[ "sign" ]
4
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:28
oeisdata/seq/A013/A013421.seq
607f075e36fed1dace2eaa912b3edf4e
A013422
E.g.f.: arcsin(arcsin(x)-tanh(x)) (odd coefficients only).
[ "0", "3", "-7", "497", "10649", "955757", "167741741", "20817188849", "5637483533393", "1653225944489237", "560689820639903957", "269465649695982142009", "138258119776900090716601", "87774869737967098700912797", "65239835100565334768577561149", "54460490625029012562328972397057" ]
[ "sign" ]
14
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-03-06T12:20:12
oeisdata/seq/A013/A013422.seq
b50f3befd721d643ebc0ba4f45230d28
A013423
tan(arcsin(x)-tanh(x))=3/3!*x^3-7/5!*x^5+497/7!*x^7+18209/9!*x^9...
[ "3", "-7", "497", "18209", "664697", "249795713", "20788071761", "7484066815937", "2018810597689577", "693966952243632545", "344692722450514980225", "170245123653326940700257", "112403414827841060460901977" ]
[ "sign" ]
4
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:28
oeisdata/seq/A013/A013423.seq
a3b0e2d4887608979c08cbe4f993521f
A013424
arctan(arcsin(x)-tanh(x))=3/3!*x^3-7/5!*x^5+497/7!*x^7-12031/9!*x^9...
[ "3", "-7", "497", "-12031", "1828937", "-78420175", "33163987313", "-1847431936639", "1836279812106137", "-90066800149588687", "250185010809212552449", "-1037398294518312251519", "71571989564012181483901417" ]
[ "sign" ]
6
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2022-10-14T16:27:37
oeisdata/seq/A013/A013424.seq
3c010e19b46e2b9228a2b27c441421fa
A013425
cos(arcsin(x)-tanh(x))=1-90/6!*x^6+1176/8!*x^8-185094/10!*x^10...
[ "1", "0", "0", "-90", "1176", "-185094", "1964028", "-1848048202", "-75962374768", "-67890529994062", "-11941170933349628", "-7295480526681684722", "-2786657669471759954024", "-1863106309893276602345910" ]
[ "sign" ]
4
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:28
oeisdata/seq/A013/A013425.seq
376bb18f02d4fd7b391eaf980c049561
A013426
arcsinh(arcsin(x)-tanh(x))=3/3!*x^3-7/5!*x^5+497/7!*x^7-4471/9!*x^9...
[ "3", "-7", "497", "-4471", "1537877", "3633797", "25642985825", "1187863670705", "1419759682006637", "193121697188029661", "200696541857404028889", "55695588453425762984841", "60791734371206895835586277" ]
[ "sign" ]
6
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2024-08-10T15:21:36
oeisdata/seq/A013/A013426.seq
0d20219fa1c53adf09d532150e33048a
A013427
cosh(arcsin(x)-tanh(x))=1+90/6!*x^6-1176/8!*x^8+185094/10!*x^10...
[ "1", "0", "0", "90", "-1176", "185094", "530772", "1636156522", "170829306928", "60742435952974", "18173279227072940", "7353969776707569554", "3655980234829231451912", "2065776616635942000462390", "1427955074795894359873706436", "1109745897830641117410245879226" ]
[ "sign" ]
9
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2014-07-24T03:27:48
oeisdata/seq/A013/A013427.seq
0795ef61428f04a354db98036ecf917f
A013428
sec(arcsin(x)-tanh(x))=1+90/6!*x^6-1176/8!*x^8+185094/10!*x^10...
[ "1", "0", "0", "90", "-1176", "185094", "5520372", "1212373162", "360563171248", "54782671966798", "28420007004983564", "9501613654091931218", "4976784878396711868488", "2978748297366502676647350" ]
[ "sign" ]
6
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-05-17T04:27:12
oeisdata/seq/A013/A013428.seq
2b9694451de422e989669d4ccfcd7220
A013429
sech(arcsin(x)-tanh(x))=1-90/6!*x^6+1176/8!*x^8-185094/10!*x^10...
[ "1", "0", "0", "-90", "1176", "-185094", "6953628", "-2271831562", "113771489552", "-90523142172238", "2740534463632996", "-9209167403962507058", "-464269042403340299048", "-2066044589238157561264950" ]
[ "sign" ]
4
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:28
oeisdata/seq/A013/A013429.seq
d988c6e06a52d5604fc9332abdfab01e
A013430
Expansion of e.g.f. exp(arcsin(x)-arctanh(x)).
[ "1", "0", "0", "-1", "0", "-15", "10", "-495", "840", "-29575", "87750", "-2805075", "12340900", "-387547875", "2304422250", "-73485787375", "556725078000", "-18311017515375", "169707184396750", "-5801182757296875", "63859173696337500" ]
[ "sign" ]
10
0
6
[ "A006228", "A013170", "A013430" ]
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2025-01-23T19:25:40
oeisdata/seq/A013/A013430.seq
e43f207fb04273f9a12d56895ea219c4
A013431
E.g.f.: -arcsin(arcsin(x) - arctanh(x)) (odd powers only).
[ "0", "1", "15", "495", "29575", "2805075", "387547875", "73496998575", "18322452939375", "5810121991600875", "2283796491396190875", "1089828106992320070375", "620645663306405750934375", "415796249727049685923771875", "323721378608985101109612121875", "289840773808099328924207553609375" ]
[ "nonn" ]
16
1
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-03-29T12:30:37
oeisdata/seq/A013/A013431.seq
939d915de748440c792869d3d343a110
A013432
tan(arctanh(x)-arcsin(x)) = 1/3!*x^3 + 15/5!*x^5 + 495/7!*x^7 + 29855/9!*x^9...
[ "0", "1", "15", "495", "29855", "2874375", "404150175", "78074371375", "19828087485375", "6403087440228375", "2561659553274989375", "1243334307147747189375", "719656795107349242609375", "489659786386680109910734375" ]
[ "nonn" ]
9
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-02-06T14:35:07
oeisdata/seq/A013/A013432.seq
57c91a1cddc9e1807bef2e4b1722b4b2
A013433
-arctan(arcsin(x)-arctanh(x))=1/3!*x^3+15/5!*x^5+495/7!*x^7+28735/9!*x^9...
[ "0", "1", "15", "495", "28735", "2597175", "337740975", "59815330575", "13857008709375", "4071452200086375", "1480690661198331375", "653488912610356197375", "344332933648569891309375", "213657034023415650312084375" ]
[ "nonn" ]
6
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2016-11-29T10:59:33
oeisdata/seq/A013/A013433.seq
1425c4c1cb85613cb758df28c959b048
A013434
cos(arcsin(x)-arctanh(x))=1-10/6!*x^6-840/8!*x^8-87750/10!*x^10...
[ "1", "0", "0", "-10", "-840", "-87750", "-12310100", "-2287605450", "-549013374000", "-166031512396750", "-61922192590147500", "-27960041702488691250", "-15045975711682274645000", "-9519627048988069071093750" ]
[ "sign" ]
6
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2014-11-12T12:53:06
oeisdata/seq/A013/A013434.seq
1afc073fbb43ffe1831f93d8c866887b
A013435
E.g.f.: arcsinh(arctanh(x) - arcsin(x)) (odd powers only).
[ "0", "1", "15", "495", "29015", "2666475", "354343275", "64361872575", "15331195839375", "4639834754377875", "1739923436670397875", "792214640482949058375", "430673843640390204684375", "275621285783640234105646875", "205164378528197702536594546875", "175791115887829825909515376359375" ]
[ "nonn" ]
32
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2018-08-07T03:35:34
oeisdata/seq/A013/A013435.seq
42f4ce9dacec55e256380bb1bc83b1f0
A013436
cosh(arcsin(x)-arctanh(x))=1+10/6!*x^6+840/8!*x^8+87750/10!*x^10...
[ "1", "0", "0", "10", "840", "87750", "12340900", "2304422250", "556725078000", "169707184396750", "63859173696337500", "29112458631692231250", "15824678904821697625000", "10117021949736621549093750", "7518098018091686976236812500" ]
[ "nonn" ]
10
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-11-21T12:46:02
oeisdata/seq/A013/A013436.seq
97dd8d180c0cf3469178ca8dca0a692f
A013437
sec(arcsin(x)-arctanh(x))=1+10/6!*x^6+840/8!*x^8+87750/10!*x^10...
[ "1", "0", "0", "10", "840", "87750", "12402500", "2338055850", "572148486000", "177069963820750", "67752690483757500", "31441329951467231250", "17409362545770168545000", "11342985795968641587093750", "8592815549188913685325312500" ]
[ "nonn" ]
6
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2016-08-16T10:32:01
oeisdata/seq/A013/A013437.seq
8369474f1e756306844950a5fdebc106
A013438
sech(arcsin(x)-arctanh(x))=1-10/6!*x^6-840/8!*x^8-87750/10!*x^10...
[ "1", "0", "0", "-10", "-840", "-87750", "-12248500", "-2253971850", "-533589966000", "-158691603820750", "-58067784952807500", "-25679245305449531250", "-13515821293834796365000", "-8355912675896675805093750" ]
[ "sign" ]
4
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:29
oeisdata/seq/A013/A013438.seq
266205e7b5ef1d5722a9fbf1a723caac
A013439
Expansion of e.g.f.: exp(tan(x)-log(x+1))=1+1/2!*x^2+9/4!*x^4-8/5!*x^5+225/6!*x^6...
[ "1", "0", "1", "0", "9", "-8", "225", "-616", "11025", "-57584", "901089", "-7218288", "111426777", "-1206961208", "19455493057", "-263225301400", "4553837345057", "-73099331076960", "1373357039852353", "-25286525625615712", "517610171023053737" ]
[ "sign" ]
6
0
5
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2020-06-01T19:27:31
oeisdata/seq/A013/A013439.seq
1ac64adfec2ed91a47b9c48d742408f0
A013440
Expansion of e.g.f.: exp(tan(x)-arctan(x))=1+4/3!*x^3-8/5!*x^5+160/6!*x^6+992/7!*x^7...
[ "1", "0", "0", "4", "0", "-8", "160", "992", "-1792", "-14464", "484224", "3391232", "-30840832", "-175044608", "7718963200", "53080130560", "-1315838558208", "-6862446264320", "426971596029952", "2514483259473920", "-136067874243248128" ]
[ "sign" ]
10
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-08-12T16:22:41
oeisdata/seq/A013/A013440.seq
fccfee3b331cd3ee16b8e573974ece03
A013441
sin(tan(x)-arctan(x))=4/3!*x^3-8/5!*x^5+992/7!*x^7-50304/9!*x^9...
[ "4", "-8", "992", "-50304", "4573952", "-738222080", "127954033664", "-34953731964928", "10769261343309824", "-4380269574963986432", "2085941501322197073920", "-1202553346613607891730432", "808239805736578791916961792" ]
[ "sign" ]
6
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2024-12-30T12:34:13
oeisdata/seq/A013/A013441.seq
d538e1e1a2ccdead9d0a25a3eff8037c
A013442
arcsin(tan(x)-arctan(x))=4/3!*x^3-8/5!*x^5+992/7!*x^7-14464/9!*x^9...
[ "4", "-8", "992", "-14464", "3391232", "-175044608", "64560399360", "-8423762821120", "4197760943882240", "-1054662864854450176", "677817013904397697024", "-277456857021505605206016", "226696976060712490528407552" ]
[ "sign" ]
6
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2019-12-23T19:45:02
oeisdata/seq/A013/A013442.seq
ac5d9de3ee11df4cf459fe1ee6b1ef3b
A013443
tan(tan(x)-arctan(x))=4/3!*x^3-8/5!*x^5+992/7!*x^7+3456/9!*x^9...
[ "4", "-8", "992", "3456", "2799872", "106544128", "37168683008", "4255728041984", "1543239875821568", "355403465489907712", "155864209273777553408", "58585654628727325196288", "32351390426329866422976512" ]
[ "sign" ]
4
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:29
oeisdata/seq/A013/A013443.seq
925e781fda2247a9b7144f50192f47ce
A013444
cos(tan(x)-arctan(x))=1-160/6!*x^6+1792/8!*x^8-484224/10!*x^10...
[ "1", "0", "0", "-160", "1792", "-484224", "38725632", "-8292976640", "1743232565248", "-521161362997248", "188842450602393600", "-83511992640895975424", "44545415648776825077760", "-27875257165637958804439040" ]
[ "sign" ]
4
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:29
oeisdata/seq/A013/A013444.seq
dd641ad387383fb6810c7aad8a4194c6
A013445
tanh(tan(x)-arctan(x)) = 4/3!*x^3 - 8/5!*x^5 + 992/7!*x^7 - 68224/9!*x^9 + ...
[ "4", "-8", "992", "-68224", "5165312", "-1019810816", "186916489216", "-51926843359232", "18052796043493376", "-7489482677372846080", "3888725315407646818304", "-2359682003031000489132032", "1689998575261701932163530752" ]
[ "sign" ]
12
3
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-11-21T12:46:02
oeisdata/seq/A013/A013445.seq
ee8b1a2a011f7fc95b1b3b602644f359
A013446
cosh(tan(x)-arctan(x))=1+160/6!*x^6-1792/8!*x^8+484224/10!*x^10...
[ "1", "0", "0", "160", "-1792", "484224", "-30840832", "7718963200", "-1315838558208", "426971596029952", "-136067874243248128", "61019499461102272512", "-30246038986591439945728", "18590454932996390870056960" ]
[ "sign" ]
4
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:29
oeisdata/seq/A013/A013446.seq
9197de420d78c357bf59061be2b29a41
A013447
sec(tan(x)-arctan(x))=1+160/6!*x^6-1792/8!*x^8+484224/10!*x^10...
[ "1", "0", "0", "160", "-1792", "484224", "-15071232", "6570936320", "-461050544128", "285431558799360", "-41198126773469184", "31834693166688370688", "-8575650915562515595264", "7808988993818084822220800" ]
[ "sign" ]
6
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2016-03-19T11:03:13
oeisdata/seq/A013/A013447.seq
e3901e97e74b4234f51f5df1755b4585
A013448
sech(tan(x)-arctan(x))=1-160/6!*x^6+1792/8!*x^8-484224/10!*x^10...
[ "1", "0", "0", "-160", "1792", "-484224", "54495232", "-9441003520", "2598020579328", "-756380393635840", "305071008569196544", "-144297159065656885248", "81729693136918543335424", "-55094722790449057575731200" ]
[ "sign" ]
6
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2016-02-04T14:52:55
oeisdata/seq/A013/A013448.seq
5a9e3decdeefc439d7065cac5f2b90a2
A013449
exp(tan(x)-sinh(x))=1+1/3!*x^3+15/5!*x^5+10/6!*x^6+271/7!*x^7...
[ "1", "0", "0", "1", "0", "15", "10", "271", "840", "8215", "60870", "423091", "4980580", "35126715", "501501130", "4192844111", "63445348720", "652228720015", "10063325322190", "125163350892331", "1976669210391260", "28804173376146115" ]
[ "nonn" ]
4
0
6
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:29
oeisdata/seq/A013/A013449.seq
bea6a118f24feccf6e11f80e19c54d0d
A013450
exp(tan(x)-arcsinh(x)) = 1+3/3!*x^3+7/5!*x^5+90/6!*x^6+497/7!*x^7...
[ "1", "0", "0", "3", "0", "7", "90", "497", "1176", "4471", "185094", "1537877", "1964028", "-3633797", "1848048202", "22918664225", "-75962374768", "-1620122697905", "67890529994062", "1135357942624877", "-11941170933349628", "-252473078493886301" ]
[ "sign" ]
10
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-11-01T16:23:02
oeisdata/seq/A013/A013450.seq
91b5fbbf475c6bba0cabbb16ba2716dd
A013451
E.g.f.: exp(tan(x)-tanh(x))=1+4/3!*x^3+160/6!*x^6+544/7!*x^7+17920/9!*x^9...
[ "1", "0", "0", "4", "0", "0", "160", "544", "0", "17920", "261120", "707584", "3942400", "149360640", "1538068480", "5242548224", "111522611200", "2782416732160", "25458261360640", "166243180478464", "5279051703910400", "109528131284500480" ]
[ "nonn" ]
6
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-06-19T17:49:18
oeisdata/seq/A013/A013451.seq
dfb7a4b79dc1713d155c31e09ded65dc
A013452
sin(tan(x)-tanh(x))=4/3!*x^3+544/7!*x^7-17920/9!*x^9+707584/11!*x^11...
[ "4", "0", "544", "-17920", "707584", "-149360640", "5242548224", "-2782416732160", "166243180478464", "-109528131284500480", "13239205658628194304", "-8328889253838297497600", "1938205426199431158431744" ]
[ "sign" ]
6
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-07-21T15:33:04
oeisdata/seq/A013/A013452.seq
9f096811c50b3426e4abb6699486f323
A013453
tan(tan(x)-tanh(x))=4/3!*x^3+544/7!*x^7+35840/9!*x^9+707584/11!*x^11...
[ "0", "4", "0", "544", "35840", "707584", "298721280", "26768052224", "5564833464320", "1787224334270464", "379247341296680960", "181364573942845538304", "71776324876296729395200", "35085662010847230106271744" ]
[ "nonn" ]
8
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-02-06T15:40:06
oeisdata/seq/A013/A013453.seq
52f1bbccc7613c4e0a80dbac8c1dda0c
A013454
cos(tan(x)-tanh(x))=1-160/6!*x^6-261120/10!*x^10+3942400/12!*x^12...
[ "1", "0", "0", "-160", "0", "-261120", "3942400", "-1538068480", "111522611200", "-25458261360640", "5279051703910400", "-1021353507684352000", "440307608869404672000", "-89935097031558126632960" ]
[ "sign" ]
6
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2019-03-31T11:48:39
oeisdata/seq/A013/A013454.seq
6ba3d0ed0d2565ec3fd89e902417f58a
A013455
Expansion of e.g.f. sec(tan(x) - tanh(x)) (even-indexed coefficients only).
[ "1", "0", "0", "160", "0", "261120", "19712000", "1538068480", "557613056000", "72297758064640", "26395258519552000", "9009548633571328000", "3030117499561574400000", "1720760994441294994472960", "838542041341593366036480000", "545911029456375473017632849920", "403794537898256808435202916352000" ]
[ "nonn" ]
25
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2025-01-02T10:49:33
oeisdata/seq/A013/A013455.seq
e6165d3713331663640a6621ff9ef31b
A013456
Expansion of e.g.f.: exp(tan(x)-arctanh(x))=1-8/5!*x^5-448/7!*x^7-32384/9!*x^9+8064/10!*x^10...
[ "1", "0", "0", "0", "0", "-8", "0", "-448", "0", "-32384", "8064", "-3275008", "2838528", "-456633344", "863070208", "-85339110400", "280413765632", "-20783183790080", "103486230003712", "-6429447050002432", "44250652523855872" ]
[ "sign" ]
6
0
6
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-12-27T12:55:07
oeisdata/seq/A013/A013456.seq
0afd32d8e71663b1f379f91d044aeb12
A013457
sin(tan(x)-arctanh(x))=-8/5!*x^5-448/7!*x^7-32384/9!*x^9...
[ "8", "448", "32384", "3275008", "456633344", "85209957376", "20642665299968", "6317122591227904", "2385636036677599232", "1090226048919008706560", "593123978260373222981632", "378879965375277796067115008" ]
[ "nonn" ]
4
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:30
oeisdata/seq/A013/A013457.seq
ad30895cb1c2267b80ddc975c16d5571
A013458
cos(tan(x)-arctanh(x))=1-8064/10!*x^10-2838528/12!*x^12...
[ "1", "0", "0", "0", "0", "-8064", "-2838528", "-863070208", "-280413765632", "-103486230003712", "-44246647746887680", "-22012763373859241984", "-12714213783118211448832", "-8481868824110022304727040", "-6494340221977598984831631360" ]
[ "sign" ]
4
0
6
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:30
oeisdata/seq/A013/A013458.seq
86c0f678bb04caf1c721cb65a6e18d85
A013459
Expansion of e.g.f. exp(arctan(x) - log(x+1)).
[ "1", "0", "1", "-4", "9", "-40", "385", "-2700", "15505", "-145360", "1886625", "-19796500", "190881625", "-2654379000", "44269902625", "-625468889500", "8553276590625", "-156119043652000", "3194978818578625", "-57041478987070500" ]
[ "sign" ]
17
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2018-01-29T02:54:05
oeisdata/seq/A013/A013459.seq
0751108013188bc6f2d6c7563516e71b
A013460
exp(arctan(x)-sinh(x))=1-3/3!*x^3+23/5!*x^5+90/6!*x^6-721/7!*x^7...
[ "1", "0", "0", "-3", "0", "23", "90", "-721", "-3864", "32759", "326214", "-2672461", "-38496876", "310461227", "6363118762", "-49895013169", "-1391451773264", "10516703525327", "390207547318222", "-2811203923750741", "-136581823796686036" ]
[ "sign" ]
4
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:30
oeisdata/seq/A013/A013460.seq
f2bffa3030c58fbc702cffb11961ede9
A013461
Expansion of e.g.f. exp(arctan(x)-arcsinh(x)) = 1-1/3!*x^3+15/5!*x^5+10/6!*x^6-495/7!*x^7...
[ "1", "0", "0", "-1", "0", "15", "10", "-495", "-840", "29015", "87750", "-2666475", "-12310100", "354343275", "2287605450", "-64350661375", "-549013374000", "15319760415375", "166031512396750", "-4630895520073875", "-61922192590147500" ]
[ "sign" ]
9
0
6
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-11-22T16:37:05
oeisdata/seq/A013/A013461.seq
8e3c7004d3b36f95f3bee9fcae84dd80
A013462
Expansion of e.g.f.: exp(arctan(x)-arctanh(x))=1-4/3!*x^3+160/6!*x^6-1440/7!*x^7...
[ "1", "0", "0", "-4", "0", "0", "160", "-1440", "0", "-17920", "691200", "-7257600", "3942400", "-395366400", "14125363200", "-175791616000", "295206912000", "-24049778688000", "902471385088000", "-13090802909184000", "43911376404480000" ]
[ "sign" ]
7
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2016-05-25T15:51:09
oeisdata/seq/A013/A013462.seq
4d136bd04edade1815fd95dd01c4c145
A013463
E.g.f.: sin(arctan(x) - arctanh(x)) (odd powers only).
[ "0", "-4", "0", "-1440", "17920", "-7257600", "395366400", "-175791616000", "24049778688000", "-13090802909184000", "3482386518507520000", "-2338795470534082560000", "1043344639170183168000000", "-855872901958901432320000000" ]
[ "sign" ]
30
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2018-12-18T11:11:10
oeisdata/seq/A013/A013463.seq
8f01cafadf401576ea8e0f1518cc8380
A013464
arctan(arctan(x)-arctanh(x))=-4/3!*x^3-1440/7!*x^7+35840/9!*x^9...
[ "0", "-4", "0", "-1440", "35840", "-7257600", "790732800", "-208797388800", "48099557376000", "-19670079356928000", "7390762646372352000", "-4427057815048028160000", "2474680614543006105600000", "-2020995311309719496294400000" ]
[ "sign" ]
6
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2016-11-29T11:01:41
oeisdata/seq/A013/A013464.seq
256ee7902d2fcd171b2bc03cb06f6769
A013465
cos(arctan(x)-arctanh(x))=1-160/6!*x^6-691200/10!*x^10+3942400/12!*x^12...
[ "1", "0", "0", "-160", "0", "-691200", "3942400", "-14125363200", "295206912000", "-902471385088000", "43911376404480000", "-140627264197754880000", "12856220870209699840000", "-45500991975079280640000000" ]
[ "sign" ]
6
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2016-11-29T11:03:30
oeisdata/seq/A013/A013465.seq
9a11f0a7dbbec2680edc75ed7420f5b8
A013466
sec(arctan(x)-arctanh(x))=1+160/6!*x^6+691200/10!*x^10+19712000/12!*x^12...
[ "1", "0", "0", "160", "0", "691200", "19712000", "14125363200", "1476034560000", "949310881792000", "219556882022400000", "161772486589808640000", "65109683806263050240000", "58457850571785240576000000" ]
[ "nonn" ]
6
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2016-11-29T11:04:41
oeisdata/seq/A013/A013466.seq
83dc2e53000ff3af3b6020330366bc78
A013467
Expansion of e.g.f. -log(cos(x) - log(x+1)).
[ "0", "1", "1", "4", "7", "53", "215", "1895", "12122", "132205", "1144627", "14912291", "164213696", "2477432371", "33228911417", "569758644845", "9014907260096", "173288317530505", "3159048447572983", "67337939660404735", "1389152842003647000", "32545156966898107751", "749093688443752763861", "19146060950641834007177" ]
[ "nonn" ]
15
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2022-09-08T08:44:38
oeisdata/seq/A013/A013467.seq
69d3e262be7886fd6f1561f4f7802237
A013468
Expansion of e.g.f.: exp(cos(x)-exp(x))=1-x-1/2!*x^2+4/3!*x^3+5/4!*x^4-32/5!*x^5...
[ "1", "-1", "-1", "4", "5", "-32", "-55", "390", "961", "-6432", "-22463", "134550", "649761", "-3443208", "-22456551", "105379838", "911433121", "-3787776224", "-42942180863", "157078439014", "2324211078513", "-7384507525560", "-143088139308519" ]
[ "sign" ]
9
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2019-03-11T11:57:57
oeisdata/seq/A013/A013468.seq
9fe12c8e8f6290d14b393457779a362c
A013469
exp(cos(x)-cosh(x))=1-2/2!*x^2+12/4!*x^4-122/6!*x^6+1792/8!*x^8...
[ "1", "-2", "12", "-122", "1792", "-35282", "889152", "-27747722", "1045556992", "-46640267042", "2424156352512", "-144890071612442", "9849171061952512", "-754330752297972722", "64566114865428283392" ]
[ "sign" ]
4
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:30
oeisdata/seq/A013/A013469.seq
6cfecc6f5d70ba11c956844c024bf04b
A013470
Coefficient of [x^(4*n+2)] in e.g.f. sin(cos(x) - cosh(x)).
[ "-2", "118", "-25202", "7567558", "2826256798", "-14573118501482", "-6535594068553682", "260913788268313031398", "425088959122294634122558", "-25651592227639570801390633802", "-191452930887085308581148320293682", "8951371730395255528928644148861984518" ]
[ "sign" ]
13
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2018-08-07T03:16:35
oeisdata/seq/A013/A013470.seq
26ed053a19351ff0575df99d274be3e2
A013471
Coefficient of [x^(4*n+2)] in e.g.f. arcsin(cosh(x) - cos(x)).
[ "2", "122", "277202", "3983059082", "200112585065762", "26008401336337737242", "7277388248057262118433522", "3872999317699675699454283234602", "3585401782089744868804837371127740482", "5396888276982771143162586362050799875871162" ]
[ "nonn" ]
10
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2018-08-07T03:30:40
oeisdata/seq/A013/A013471.seq
800cd273890c46b55d0b96d5b9fc9a23
A013472
Coefficient of [x^(4*n+2)] in e.g.f. tan(cosh(x) - cos(x)).
[ "2", "242", "493922", "4867022162", "146803464634562", "10586916198380287922", "1560405836504795306526242", "421594801591208996367201480722", "192759827198349576131799688610789762" ]
[ "nonn" ]
14
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2018-08-07T03:32:15
oeisdata/seq/A013/A013472.seq
eb82973879e05a70f3914889ba314512
A013473
arctan(cos(x)-cosh(x))=238/6!*x^6-715682/10!*x^10+12212600398/14!*x^14...
[ "-2", "238", "-715682", "12212600398", "-693692750003522", "99086243037690160558", "-29914788669101073817179362", "16957033980662331163451765544718", "-16560275867709925788740349268459459202", "26102948307736145181548875145546574191456878" ]
[ "sign" ]
7
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2016-04-08T12:23:02
oeisdata/seq/A013/A013473.seq
9f81ae5597217a701b4cf95754c0433d
A013474
Expansion of cos(cos(x)-cosh(x)).
[ "1", "-12", "1568", "-445632", "76844288", "278739068928", "-467851397312512", "-2679102291371999232", "13369295760767407751168", "198192229563606535497842688", "-1400852802790123139561996419072", "-65350779506647538962325382377766912" ]
[ "sign", "easy" ]
8
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2020-05-02T16:15:16
oeisdata/seq/A013/A013474.seq
bbf406711b7493ac4f26bed0ee687145
A013475
Coefficient of [x^(4*n+2)] in e.g.f. sinh(cosh(x) - cos(x)).
[ "2", "122", "35282", "27747722", "46640267042", "144890071612442", "754330752297972722", "6132809160585358346282", "73810833499088630365101122", "1261113117777698263842030054842", "29574312688030228358559752005274642" ]
[ "nonn" ]
14
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2018-08-07T03:36:14
oeisdata/seq/A013/A013475.seq
635c0c42d2899af6b2dbf0c9c6ed7bf3
A013476
Coefficient of x^(4*n+2) in e.g.f. arcsinh(cos(x) - cosh(x)).
[ "-2", "118", "-267122", "3801437638", "-188997287445602", "24300893634392843158", "-6725983870126469414416082", "3540538990952328979449335176678", "-3241779510843677923729210281115258562" ]
[ "sign" ]
14
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2018-08-16T13:25:16
oeisdata/seq/A013/A013476.seq
454cf5f18fb62fff6ce4abedb88824d5
A013477
Coefficient of [x^(4*n+2)] in expansion of e.g.f. tanh(cos(x) - cosh(x)).
[ "-2", "238", "-473762", "4544139598", "-133366253033282", "9357776691549409198", "-1341930712996828590536162", "352757692963898925496158362638", "-156922931120424993062032606256707202", "111108598565238227067101723645812683396718" ]
[ "sign" ]
10
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2024-07-20T15:15:09
oeisdata/seq/A013/A013477.seq
47be2c365ad644dbf93460617794a428
A013478
E.g.f. -arctanh(cos(x)-cosh(x)), coefficients of (4*i+2) only.
[ "2", "242", "735842", "12696924242", "729261623797442", "105330801708282667442", "32155390653420235027326242", "18430773614710132775756232045842", "18200656974294045189446138614387578242", "29009142008847262758691664682458471045155442" ]
[ "nonn" ]
21
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-07-29T10:21:35
oeisdata/seq/A013/A013478.seq
2bce3e1292c162db18c477301a1c4401
A013479
cosh(cos(x)-cosh(x))=1+12/4!*x^4+1792/8!*x^8+889152/12!*x^12...
[ "1", "12", "1792", "889152", "1045556992", "2424156352512", "9849171061952512", "64566114865428283392", "642433596401162586161152", "9255521545388420536885051392", "185972570219438391836588939149312", "5054977199391984218529977072942579712" ]
[ "nonn" ]
6
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-05-24T16:09:26
oeisdata/seq/A013/A013479.seq
465cd03e6f4424787dbeb08ea5c574d5
A013480
sec(cos(x)-cosh(x)) = 1+12/4!*x^4+8512/8!*x^8+41692992/12!*x^12...
[ "1", "12", "8512", "41692992", "748457181952", "35753146158600192", "3745546830245915840512", "756079630242293501892083712" ]
[ "nonn" ]
5
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:30
oeisdata/seq/A013/A013480.seq
8a203a68dc772b0873e38ae133eb0b39
A013481
sech(cos(x)-cosh(x)) = 1-12/4!*x^4+8288/8!*x^8-39475392/12!*x^12...
[ "1", "-12", "8288", "-39475392", "689369608448", "-32038788679636992", "3265606511334528831488", "-641363922266872095050022912" ]
[ "sign" ]
6
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:30
oeisdata/seq/A013/A013481.seq
3070c04ebbee75e3cfbc1cf1b209986b
A013482
exp(cos(x)-sech(x))=1-4/4!*x^4+60/6!*x^6-824/8!*x^8+120/10!*x^10...
[ "1", "0", "-4", "60", "-824", "120", "1331156", "-151389420", "15474229936", "-1609208740560", "165275248217516", "-13317787644945300", "-752763454703346104", "1012558531283275284360", "-490748297800639153012924" ]
[ "sign" ]
6
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2019-09-21T14:46:12
oeisdata/seq/A013/A013482.seq
5a630e93f3bdcf7157fa1ae579f933a4
A013483
E.g.f.: sin(cos(x)-sech(x)) (even powers only).
[ "0", "0", "-4", "60", "-1384", "50520", "-2333164", "98460180", "2691348656", "-2502877578960", "816953866876076", "-250462447769994900", "80927047278922241096", "-28429551522622456235640", "10951929595731882160395716" ]
[ "sign" ]
15
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2014-03-10T08:19:44
oeisdata/seq/A013/A013483.seq
328b45ae278779df6ef9573b83732371
A013484
arcsin(cos(x)-sech(x))=-4/4!*x^4+60/6!*x^6-1384/8!*x^8+50520/10!*x^10...
[ "-4", "60", "-1384", "50520", "-3072364", "300261780", "-41474372944", "7312636929840", "-1583769010071124", "419274242117870700", "-135426142315445694904", "52712459533258432020360", "-24241226489057470908932284" ]
[ "sign" ]
4
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:30
oeisdata/seq/A013/A013484.seq
e8835c985680e08946dcfac88eaf1704
A013485
tan(cos(x)-sech(x))=-4/4!*x^4+60/6!*x^6-1384/8!*x^8+50520/10!*x^10...
[ "-4", "60", "-1384", "50520", "-3441964", "401162580", "-63557233744", "12220394184240", "-2791952278560724", "763176800730283500", "-250643745125452446904", "98116093958813794548360", "-45044453508933100607756284" ]
[ "sign" ]
4
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:31
oeisdata/seq/A013/A013485.seq
45bd87fac307da14b17b5ff6e8745f6f
A013486
arctan(cos(x)-sech(x))=-4/4!*x^4+60/6!*x^6-1384/8!*x^8+50520/10!*x^10...
[ "-4", "60", "-1384", "50520", "-1963564", "-2440620", "24774209456", "-7410634833360", "1946918835205676", "-504022869697607700", "125734569960701153096", "-25506896972028634763640", "-308739978510619283180284" ]
[ "sign" ]
4
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:31
oeisdata/seq/A013/A013486.seq
93d97f2d19b185d35eaffdefe719e84b
A013487
cos(cos(x)-sech(x))=1-560/8!*x^8+50400/10!*x^10-4403520/12!*x^12...
[ "1", "0", "0", "0", "-560", "50400", "-4403520", "451651200", "-55603258880", "8098495142400", "-1364657183216640", "258905686980864000", "-53203592135631564800", "11000355030582368256000", "-1812425415209721012879360" ]
[ "sign" ]
6
0
5
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2014-11-30T11:33:35
oeisdata/seq/A013/A013487.seq
d8879f069c6ace7561bae5dab1545279
A013488
Expansion of e.g.f.: exp(sinh(x)-log(x+1))=1+1/2!*x^2-1/3!*x^3+9/4!*x^4-33/5!*x^5...
[ "1", "0", "1", "-1", "9", "-33", "235", "-1517", "12593", "-111465", "1122819", "-12313409", "147949593", "-1922353925", "26918452691", "-403744456541", "6460109224801", "-109820584161393", "1976779056442179", "-37558742545087481" ]
[ "sign" ]
6
0
5
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-12-21T20:22:09
oeisdata/seq/A013/A013488.seq
c9d24abe3e457dba4b4bc408154bf0c8
A013489
exp(sinh(x)-arcsinh(x))=1+2/3!*x^3-8/5!*x^5+40/6!*x^6+226/7!*x^7...
[ "1", "0", "0", "2", "0", "-8", "40", "226", "-896", "-8784", "62304", "745186", "-6036096", "-87930776", "878453888", "14731669954", "-172356091904", "-3284180017312", "44229410876928", "942576417055042", "-14356887611836416", "-338316707471357480" ]
[ "sign" ]
8
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-11-01T15:35:28
oeisdata/seq/A013/A013489.seq
d2812240d66fd5c66a5dbfb021ea9661
A013490
E.g.f.: exp(sinh(x)-tanh(x))=1+3/3!*x^3-15/5!*x^5+90/6!*x^6+273/7!*x^7...
[ "1", "0", "0", "3", "0", "-15", "90", "273", "-2520", "-375", "126630", "-269907", "-7232940", "44118165", "525494970", "-6182721087", "-41497943760", "965945373105", "2901128941710", "-171088458444267", "81569169583020", "34527329266886445" ]
[ "sign" ]
6
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-12-08T11:25:24
oeisdata/seq/A013/A013490.seq
21b5d9e8cb7447b79ff711193e68f1ac
A013491
exp(sinh(x)-arctanh(x))=1-1/3!*x^3-23/5!*x^5+10/6!*x^6-719/7!*x^7...
[ "1", "0", "0", "-1", "0", "-23", "10", "-719", "1288", "-40599", "152934", "-3735059", "21982884", "-510402683", "4077409466", "-96691506911", "972083601136", "-24171783139087", "292315200462606", "-7694747756773355", "108645176948603484" ]
[ "sign" ]
4
0
6
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:31
oeisdata/seq/A013/A013491.seq
730e78cc05f1eb25f71553518ab40eaa
A013492
exp(arcsinh(x)-log(x+1)) = 1+1/2!*x^2-3/3!*x^3+9/4!*x^4-45/5!*x^5...
[ "1", "0", "1", "-3", "9", "-45", "315", "-2205", "16065", "-144585", "1545075", "-16995825", "194126625", "-2523646125", "36735774075", "-551036611125", "8542663754625", "-145225283828625", "2683905224875875", "-50994199272641625" ]
[ "sign" ]
11
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-11-01T16:25:46
oeisdata/seq/A013/A013492.seq
71490f4e0cf8504e28a46ee769bbf2be
A013493
exp(arcsinh(x)-tanh(x))=1+1/3!*x^3-7/5!*x^5+10/6!*x^6+47/7!*x^7...
[ "1", "0", "0", "1", "0", "-7", "10", "47", "-392", "3369", "11814", "-571573", "434412", "88260053", "-239703334", "-16363524721", "66778596688", "3810346797553", "-19103113532274", "-1115878992933037", "6219304575954900", "405808123338059597" ]
[ "sign" ]
7
0
6
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-02-04T05:11:02
oeisdata/seq/A013/A013493.seq
a37be7beed9bc3dacdbcc4850e499ca4
A013494
exp(arcsinh(x)-arctanh(x)) = 1-3/3!*x^3-15/5!*x^5+90/6!*x^6-945/7!*x^7...
[ "1", "0", "0", "-3", "0", "-15", "90", "-945", "2520", "-36855", "368550", "-5145525", "31808700", "-541215675", "7577019450", "-134726216625", "1338322986000", "-27408165159375", "493346972868750", "-10700744687758125", "147490229469082500" ]
[ "sign" ]
10
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-11-01T15:54:43
oeisdata/seq/A013/A013494.seq
36b6aab3ba65b3f54f624c2b6d87edf8
A013495
Expansion of e.g.f.: exp(tanh(x)-log(x+1))=1+1/2!*x^2-4/3!*x^3+9/4!*x^4-48/5!*x^5...
[ "1", "0", "1", "-4", "9", "-48", "385", "-2420", "17297", "-170688", "1760289", "-18395012", "219987801", "-2936841776", "40948952993", "-606801250484", "9752505856033", "-166636197964032", "2990053004436417", "-56703580249101188" ]
[ "sign" ]
7
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-01-15T18:27:34
oeisdata/seq/A013/A013495.seq
f50ef42518717993aeb8c32ba2ec4aa3
A013496
Expansion of e.g.f.: exp(tanh(x)-arctanh(x))=1-4/3!*x^3-8/5!*x^5+160/6!*x^6-992/7!*x^7...
[ "1", "0", "0", "-4", "0", "-8", "160", "-992", "1792", "-50304", "484224", "-4573952", "38725632", "-738222080", "8292976640", "-127954033664", "1743232565248", "-34953731964928", "521161362997248", "-10769261343309824", "188842450602393600" ]
[ "sign" ]
7
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2022-04-17T14:40:52
oeisdata/seq/A013/A013496.seq
6011ce6dbf8d07eb391d8f2d6fc831a0
A013497
E.g.f. log(cosh(x)-log(x+1))= -x+1/2!*x^2+2/3!*x^3+5/4!*x^4-13/5!*x^5...
[ "-1", "1", "2", "5", "-13", "-63", "-453", "1822", "9683", "174325", "-960133", "-2767796", "-180618579", "1333355779", "-2799332651", "400791892784", "-3944083024649", "32532084129049", "-1656524167774985", "21382796711385164", "-305269868753768647" ]
[ "sign" ]
8
1
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-11-21T12:46:02
oeisdata/seq/A013/A013497.seq
e0e136103af57c0393c841a678902e75
A013498
Number of permutations in S_n with a certain property.
[ "1", "0", "1", "3", "5", "12", "22", "50", "95", "210", "406", "882", "1722", "3696", "7260", "15444", "30459", "64350", "127270", "267410", "529958", "1108536", "2200276", "4585308", "9111830", "18929092", "37650172", "78004500", "155266100", "320932800", "639191160" ]
[ "nonn", "easy", "changed" ]
10
1
4
null
null
N. J. A. Sloane
2025-07-08T02:47:40
oeisdata/seq/A013/A013498.seq
41e806d635a6c400c9ed2dbac70b6ea3
A013499
a(n) = 2*n^n, n >= 2, otherwise a(n) = 1.
[ "1", "1", "8", "54", "512", "6250", "93312", "1647086", "33554432", "774840978", "20000000000", "570623341222", "17832200896512", "605750213184506", "22224013651116032", "875787780761718750", "36893488147419103232", "1654480523772673528354" ]
[ "nonn" ]
30
0
3
[ "A007889", "A013499" ]
null
N. J. A. Sloane
2017-07-26T07:52:55
oeisdata/seq/A013/A013499.seq
2281cf7c83d0cd7d069cc8216f9c1aca
A013500
Expansion of e.g.f.: log(sec(x)-log(x+1))=-1*x+1/2*x^2+1/3*x^3+3/8*x^4+7/120*x^5-1/240*x^6-593/5040*x^7-37/960*x^8+...
[ "0", "-1", "1", "2", "9", "7", "-3", "-593", "-1554", "-11125", "167725", "778307", "16757708", "-89177255", "-119165473", "-33154669351", "100077477488", "-2532930861593", "104388972197833", "-390031832553017", "23726173002432588", "-516211740521004739", "4636274532540279299", "-240069627985237851811", "4178391586103026282384", "-78940184342962927515381" ]
[ "sign" ]
9
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2014-10-16T17:41:10
oeisdata/seq/A013/A013500.seq
c881bfd967d3d88b3bd86b81a99a48a8