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christopher
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oeis

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666,262,453B
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1999-12-11 03:00:00
2025-07-19 00:40:46
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32
32
A013301
E.g.f.: arctanh(arctanh(x)-log(x+1)).
[ "0", "1", "6", "150", "7560", "650160", "84823200", "15617281680", "3855823171200", "1229340262550400", "491641405006752000", "241000527467642342400", "142107676844443620710400", "99236357585615999548800000" ]
[ "nonn" ]
11
0
3
[ "A013301", "A219863" ]
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2016-11-29T10:48:06
oeisdata/seq/A013/A013301.seq
d0b1a4a155fd02c46835353f686222e1
A013302
E.g.f.: cosh(log(x+1)-arctanh(x)) (even powers only).
[ "1", "0", "3", "90", "4725", "396900", "49116375", "8428369950", "1917454163625", "558800927685000", "203054287097536875", "90020733946574681250", "47828015945815128148125", "30001210002374944020187500" ]
[ "nonn" ]
18
0
3
[ "A013299", "A013302" ]
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2023-03-05T10:31:46
oeisdata/seq/A013/A013302.seq
3e2b6a46437ccb17effbb46ea5d2a4ab
A013303
sec(log(x+1)-arctanh(x))=1+3/4!*x^4+90/6!*x^6+5145/8!*x^8...
[ "1", "0", "3", "90", "5145", "472500", "63877275", "11947285350", "2955047720625", "934039255149000", "367306824871861875", "175873128591661751250", "100738594342264429175625", "68014527663768884135437500" ]
[ "nonn" ]
6
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2018-05-15T17:53:27
oeisdata/seq/A013/A013303.seq
06d5affc078d5abf318818f9383ab5ad
A013304
sech(log(x+1)-arctanh(x))=1-3/4!*x^4-90/6!*x^6-4095/8!*x^8...
[ "1", "0", "-3", "-90", "-4095", "-283500", "-28534275", "-4001347350", "-754083705375", "-185224922883000", "-57754322803051875", "-22343321962162451250", "-10514758311176393649375", "-5917397284663573271062500" ]
[ "sign" ]
7
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2020-06-06T13:31:28
oeisdata/seq/A013/A013304.seq
bcd4af88f9266e15f4199ca5d25ee78f
A013305
Numerators of coefficients in Taylor series expansion of arccosh(exp(x)-sin(x)).
[ "0", "1", "1", "-1", "-1", "-5", "503", "521", "-13", "-827", "-1812469", "44303839", "9150959", "17949817", "-17645163013", "-256103154817", "128934425819", "869866425977", "7718787745279031", "-657691477236554437", "-23770118746323659", "9983376979312685189", "15480320293784856319969", "240884767523727873137", "-3694316464734123751573", "-12325434071961822974423" ]
[ "sign", "frac" ]
16
0
6
[ "A013305", "A202359" ]
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-05-01T21:16:00
oeisdata/seq/A013/A013305.seq
7a8d82f171e0d8e79dedd4273bb6f222
A013306
Numerator of [x^n] of the Taylor series arccosh(exp(x) - arcsin(x)).
[ "1", "0", "0", "-1", "0", "-1", "-1", "-344", "-2", "-7733", "-4873", "-10514857", "-3449", "-738707", "-71666467", "-129310473049", "-35839", "-19576627", "-45715711199", "-866367643482931", "-572765895007711", "-274989109970083277", "-266112669025361017" ]
[ "sign" ]
17
1
8
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2018-09-20T08:15:26
oeisdata/seq/A013/A013306.seq
50f9b4a8e3942a4dd97ef99ed4f21f08
A013307
Numerator of [x^n] in the Taylor series arccosh(exp(x) - tan(x)) = x - x^2/6 - x^3/72 - 43*x^4/432 - 221*x^5/10368 - 89513*x^6/2177280 - ...
[ "1", "-1", "-1", "-43", "-221", "-89513", "-149749", "-1084711", "-209435", "-27633784271", "-1480512386621", "-7957100794591", "-26770890495311", "-8901132809862257", "-397417885842749047", "-4636876735719615641" ]
[ "sign", "frac" ]
9
1
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2022-08-19T14:01:22
oeisdata/seq/A013/A013307.seq
3bf9c44d8e6ef85f9e603c2b8f8a3a15
A013308
Numerator of [x^n] of the Taylor series arccosh(exp(x)-arctan(x))= x+x^2/2 -x^3/8 -17*x^4/80 +109*x^5/1920 +299*x^6/2304 -813*x^7/25600 -...
[ "1", "1", "-1", "-17", "109", "299", "-813", "-373177", "9417917", "133861013", "-796664399", "-229876317317", "593496669853", "693397771163639", "-8404224858061139", "-282791345633671703", "1818027079738117517", "978930433926331599667" ]
[ "sign", "frac" ]
5
1
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2011-12-22T15:16:18
oeisdata/seq/A013/A013308.seq
adf4298a634af75e05951b37484b37ae
A013309
Expansion of e.g.f.: exp(exp(x)-cos(x))=1+x+3/2!*x^2+8/3!*x^3+29/4!*x^4+112/5!*x^5...
[ "1", "1", "3", "8", "29", "112", "489", "2326", "11937", "65856", "386561", "2406230", "15805473", "109131128", "789751577", "5972149246", "47079466913", "386051624736", "3286313327105", "28991306290278", "264621015301489", "2495440610319944" ]
[ "nonn" ]
7
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2016-10-24T14:02:42
oeisdata/seq/A013/A013309.seq
2f71e5c8b8363e951d4a318b33664f1a
A013310
sin(exp(x)-cos(x))=x+2/2!*x^2-12/4!*x^4-68/5!*x^5-208/6!*x^6...
[ "1", "2", "0", "-12", "-68", "-208", "-56", "3472", "26272", "119072", "234432", "-1600896", "-22177088", "-159056896", "-769693952", "-1571891456", "16806915328", "276758503424", "2610810796032", "18627861722112", "94941413343232", "121510785658880" ]
[ "sign" ]
7
1
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2024-02-11T14:39:13
oeisdata/seq/A013/A013310.seq
11835bb60865910c9159218a519b4a96
A013311
arcsin(exp(x)-cos(x))=x+2/2!*x^2+2/3!*x^3+12/4!*x^4+80/5!*x^5...
[ "1", "2", "2", "12", "80", "512", "4832", "53872", "654320", "9264032", "147228512", "2559080832", "48910122560", "1017566317952", "22822627908992", "550081215323392", "14178080204748800", "388900281882678272", "11314716065658294272" ]
[ "nonn" ]
7
1
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2014-12-21T16:36:38
oeisdata/seq/A013/A013311.seq
1c90abbfc23e3fbb6326f785eec8ae81
A013312
tan(exp(x)-cos(x)) = x + 2/2!*x^2 + 3/3!*x^3 + 24/4!*x^4 + 157/5!*x^5...
[ "0", "1", "2", "3", "24", "157", "962", "8575", "88816", "948025", "11551682", "158525499", "2329270152", "37012621141", "638280394754", "11767984017847", "230953513192672", "4823470878737521", "106685348433700994", "2489115873636707187" ]
[ "nonn" ]
12
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-02-06T09:03:25
oeisdata/seq/A013/A013312.seq
c7a2c9851e6a9b309118a16d463741da
A013313
arctan(exp(x)-cos(x))=x+2/2!*x^2-1/3!*x^3-24/4!*x^4-115/5!*x^5...
[ "1", "2", "-1", "-24", "-115", "242", "9179", "65296", "-366535", "-14288158", "-124059241", "1440362616", "57563571845", "541440703442", "-11649746422861", "-473630058916064", "-4395343414984975", "168230486159471042" ]
[ "sign" ]
7
1
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-01-01T14:03:13
oeisdata/seq/A013/A013313.seq
e6a6edd48b2b8f0f2192cde8b89298ae
A013314
cos(exp(x)-cos(x))=1-1/2!*x^2-6/3!*x^3-15/4!*x^4+183/6!*x^6...
[ "1", "0", "-1", "-6", "-15", "0", "183", "1162", "4305", "4032", "-75169", "-720390", "-4057119", "-13316160", "17994039", "691795018", "6706003809", "45159313536", "210202685567", "247239745914", "-8759676926319", "-137896385117568", "-1415069646671241" ]
[ "sign" ]
7
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-11-21T12:46:02
oeisdata/seq/A013/A013314.seq
7e96cde9055dd3f3c9b6ffdb1dfa16b6
A013315
Expansion of e.g.f.: sinh(exp(x)-cos(x))=x+2/2!*x^2+2/3!*x^3+12/4!*x^4+72/5!*x^5...
[ "0", "1", "2", "2", "12", "72", "272", "968", "5488", "36144", "204512", "1135840", "7577856", "56287168", "406104064", "2933384704", "23084016896", "194919700480", "1664627753984", "14417113925632", "131148402111488", "1251412558922752", "12211894620549120" ]
[ "nonn" ]
7
1
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2019-07-30T14:00:19
oeisdata/seq/A013/A013315.seq
c38eb712df06696bea4c4c41825cf438
A013316
arcsinh(exp(x)-cos(x))=x+2/2!*x^2-12/4!*x^4-60/5!*x^5+32/6!*x^6...
[ "1", "2", "0", "-12", "-60", "32", "3360", "26768", "-70560", "-4368928", "-44014080", "286606848", "15535016640", "175871587712", "-2270496184320", "-116296341590272", "-1366735787784960", "31677729930493952", "1572363556732784640" ]
[ "sign" ]
5
1
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2011-12-22T15:07:10
oeisdata/seq/A013/A013316.seq
c19ae0173dddc76cc03285c99e573e5b
A013317
Expansion of e.g.f.: tanh(exp(x) - cos(x)) = x + (2/2!)*x^2 - (1/3!)*x^3 - (24/4!)*x^4 - (123/5!)*x^5 + ...
[ "0", "1", "2", "-1", "-24", "-123", "2", "5987", "54544", "66441", "-4948798", "-71261177", "-226393992", "9534896269", "201964922434", "1166083278955", "-34861258001632", "-1052810665903343", "-9456771887276926", "211545075206125327" ]
[ "sign" ]
12
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2023-03-19T17:47:07
oeisdata/seq/A013/A013317.seq
306982f4a5832b748047286ccde5bb85
A013318
arctanh(exp(x)-cos(x))=x+2/2!*x^2+3/3!*x^3+24/4!*x^4+165/5!*x^5...
[ "0", "1", "2", "3", "24", "165", "1202", "12663", "149744", "1945065", "29307362", "489387723", "8915702664", "178036818765", "3852374482322", "89628609049983", "2235770536642784", "59498096957789265", "1681835781220294082" ]
[ "nonn" ]
9
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-02-05T08:21:55
oeisdata/seq/A013/A013318.seq
84f66be4967317a80e0e58584e39db33
A013319
E.g.f.: cosh(exp(x)-cos(x))=1+1/2!*x^2+6/3!*x^3+17/4!*x^4+40/5!*x^5...
[ "1", "0", "1", "6", "17", "40", "217", "1358", "6449", "29712", "182049", "1270390", "8227617", "52843960", "383647513", "3038764542", "23995450017", "191131924256", "1621685573121", "14574192364646", "133472613190001", "1244028051397192", "12068806481240601" ]
[ "nonn" ]
6
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-01-29T13:34:44
oeisdata/seq/A013/A013319.seq
505cca53d07dc503150a71fa48e7f6b0
A013320
sec(exp(x)-cos(x))=1+1/2!*x^2+6/3!*x^3+21/4!*x^4+120/5!*x^5...
[ "1", "0", "1", "6", "21", "120", "1077", "8918", "83097", "952560", "11790649", "156839430", "2318954253", "37207496040", "637980683277", "11745733936022", "231142374081009", "4825295491430880", "106636356923768497", "2489165244414184326" ]
[ "nonn" ]
5
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2011-12-22T15:04:16
oeisdata/seq/A013/A013320.seq
0cac6ea7fae9c1cda34f2e27bbb5cc98
A013321
E.g.f.: sech(exp(x)-cos(x)).
[ "1", "0", "-1", "-6", "-11", "80", "923", "3682", "-26567", "-585120", "-3969849", "24427370", "948294477", "9793100720", "-42570639997", "-3129194240622", "-45887540775759", "90022891149760", "18204741288946383", "363299569735984474" ]
[ "sign" ]
16
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-06-06T15:06:25
oeisdata/seq/A013/A013321.seq
99d4ac6631737b363539d2b712c8771b
A013322
Golomb-type sequence over triangular numbers.
[ "1", "3", "3", "3", "6", "6", "6", "10", "10", "10", "15", "15", "15", "15", "15", "15", "21", "21", "21", "21", "21", "21", "28", "28", "28", "28", "28", "28", "36", "36", "36", "36", "36", "36", "36", "36", "36", "36", "45", "45", "45", "45", "45", "45", "45", "45", "45", "45", "55", "55", "55", "55", "55", "55", "55", "55", "55", "55", "66", "66", "66", "66", "66", "66", "66", "66", "66", "66", "66", "66" ]
[ "nonn", "easy" ]
16
1
2
[ "A001462", "A013322" ]
null
N. J. A. Sloane
2015-04-05T11:02:35
oeisdata/seq/A013/A013322.seq
84326f4c3ce2e2b86edad648c3a95688
A013323
Numerator of [x^n] in the Taylor series arccosh(exp(x)-arcsinh(x))= x+x^2/3 -x^3/18 -14*x^4/135 +47*x^5/3240 +3527*x^6/68040 -4787*x^7/680400-...
[ "1", "1", "-1", "-14", "47", "3527", "-4787", "-6421", "11467", "523798423", "-3983516101", "-1424955853", "1543134469573", "2574843844561", "-116899300585349", "-130778050341326449", "86229762965796109", "597078237074537664671" ]
[ "sign", "frac" ]
5
1
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2011-12-22T14:56:33
oeisdata/seq/A013/A013323.seq
508239a9887746e647db2ebc79e86f10
A013324
Numerator of [x^n] of the Taylor series arccosh(exp(x)-tanh(x))= x+x^2/2 -x^3/8 -7*x^4/48 +3*x^5/128 +631*x^6/11520 +37*x^7/15360 -12731*x^8/645120 -...
[ "1", "1", "-1", "-7", "3", "631", "37", "-12731", "-37481", "771163", "590381", "-195597517", "-8025539", "-205204695149", "5456117628779", "3973785585851", "-3056850228539", "-168086791499223239" ]
[ "sign", "frac" ]
5
1
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2011-12-22T14:49:59
oeisdata/seq/A013/A013324.seq
5b3f5c941a49e05f6c34a5f672d1a166
A013325
Numerator of [x^n] in the Taylor series arccosh(exp(x)-arctanh(x))= x-x^2/6-x^3/72 -359*x^4/2160 -1681*x^5/51840 -52981*x^6/435456 -...
[ "1", "-1", "-1", "-359", "-1681", "-52981", "-1887113", "-27492467", "-3259141", "-1194145112779", "-55919619312049", "-7462251938940527", "-113201511292945547", "-1055956853774285077", "-44032898634010565651", "-75833822693358307239889" ]
[ "sign", "frac" ]
7
1
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2021-03-27T18:30:16
oeisdata/seq/A013/A013325.seq
9b0182904a23b8fd21d60643a4dfae42
A013326
Expansion of -(2*x^3-x^2+x-1)/(x^4-3*x^3+3*x^2-3*x+1).
[ "1", "2", "4", "7", "14", "31", "68", "146", "313", "674", "1453", "3130", "6740", "14515", "31262", "67331", "145012", "312314", "672637", "1448674", "3120041", "6719698", "14472356", "31169423", "67130254", "144579863", "311384740", "670635970", "1444363025" ]
[ "nonn", "changed" ]
9
0
2
null
null
N. J. A. Sloane
2025-07-08T02:47:35
oeisdata/seq/A013/A013326.seq
075b7af96ec5b601b327eb3aebc9dd0b
A013327
Expansion of e.g.f.: exp(exp(x)-sec(x))=1+x+1/2!*x^2+2/3!*x^3+1/4!*x^4-8/5!*x^5...
[ "1", "1", "1", "2", "1", "-8", "-83", "-572", "-3447", "-21672", "-123111", "-737240", "-3483619", "-13031484", "70815357", "2064032844", "35771746481", "493920403632", "6641490804273", "85856649793936", "1103675761610485", "14215393325698588" ]
[ "sign" ]
7
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-12-20T13:31:56
oeisdata/seq/A013/A013327.seq
233dec3c1d09502fc989d5142d0567e3
A013328
Expansion of e.g.f. sin(exp(x)-sec(x)).
[ "0", "1", "0", "0", "-4", "-8", "0", "-56", "1136", "-4976", "47040", "-541728", "2460416", "-51170624", "202185984", "-5359238912", "20705351936", "-673408564736", "2215089472512", "-100278515381760", "202372883465216", "-17008883052323840" ]
[ "sign" ]
13
0
5
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2018-08-06T02:41:34
oeisdata/seq/A013/A013328.seq
9d5fdf8a907fc94f5eb26755fc42a2d9
A013329
Expansion of e.g.f. arcsin(exp(x) - sec(x)).
[ "0", "1", "0", "2", "-4", "20", "-120", "632", "-6704", "44480", "-630240", "5566112", "-91544704", "1063375040", "-19258162560", "283305867392", "-5578129589504", "99671066259200", "-2135174387566080", "44678363702761472", "-1044242762736047104" ]
[ "sign" ]
9
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2018-08-06T02:41:41
oeisdata/seq/A013/A013329.seq
69776591f8d43d0730a5490ec1891349
A013330
E.g.f.: tan(exp(x)-sec(x))=x+3/3!*x^3-4/4!*x^4+37/5!*x^5-180/6!*x^6...
[ "0", "1", "0", "3", "-4", "37", "-180", "1015", "-11464", "57961", "-1001640", "6231819", "-117917644", "1041455053", "-18546221148", "232421139007", "-3887058864784", "64390950162769", "-1075269065795664", "21514220038798995", "-383113444907091604" ]
[ "sign" ]
6
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2014-08-21T14:07:52
oeisdata/seq/A013/A013330.seq
ad0907a72234d06328a5267d5cb68f80
A013331
Expansion of e.g.f. arctan(exp(x) - sec(x)).
[ "0", "1", "0", "-1", "-4", "5", "60", "-61", "-2504", "-8695", "100920", "873479", "-6889804", "-142058995", "-4843020", "19728547019", "98903242096", "-3531831462895", "-49401992303760", "493517141932559", "17048746833049196", "-29344831492412395", "-6329111550017193300", "-46994369824929657901", "2170046335781374467496" ]
[ "sign" ]
12
0
5
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2022-09-08T08:44:38
oeisdata/seq/A013/A013331.seq
1534bca7404bab7eaefee3cb6dedddc1
A013332
Expansion of e.g.f.: cos(exp(x)-sec(x))=1-1/2!*x^2-3/4!*x^4+20/5!*x^5+3/6!*x^6...
[ "1", "0", "-1", "0", "-3", "20", "3", "420", "-343", "8424", "-22249", "260040", "-239547", "10498748", "94138107", "-147119700", "19810696721", "-201766341168", "3757708820591", "-61124264974704", "781479753273933", "-16996638107062684" ]
[ "sign" ]
6
0
5
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2022-03-27T18:51:02
oeisdata/seq/A013/A013332.seq
ceecbb0da548bcc944b6403c330cbbb5
A013333
sinh(exp(x)-sec(x)) = x + 2/3!*x^3 - 4/4!*x^4 + 12/5!*x^5 - 120/6!*x^6 + ...
[ "0", "1", "0", "2", "-4", "12", "-120", "128", "-4464", "6912", "-206880", "776800", "-12788224", "95713984", "-1101528064", "13091780224", "-133871961344", "2061579919104", "-22144979338752", "381671021731840", "-4690276122840064", "83860033272100864" ]
[ "sign" ]
9
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-10-12T19:05:27
oeisdata/seq/A013/A013333.seq
8b6181d3ecaa7169706b0b24ba70c475
A013334
Expansion of e.g.f. arcsinh(exp(x) - sec(x)).
[ "0", "1", "0", "0", "-4", "0", "0", "0", "-1104", "-5040", "0", "184800", "-1784704", "-39948480", "-201801600", "2969366400", "24788541696", "-621491320320", "-12903078988800", "20131497484800", "2944178363780096", "8434762785469440", "-1051002016730265600", "-14118259471683840000", "255660771276061802496" ]
[ "sign" ]
12
0
5
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2022-09-08T08:44:38
oeisdata/seq/A013/A013334.seq
6963aa7960044f15f266233568be9491
A013335
Expansion of e.g.f. tanh(exp(x) - sec(x)).
[ "0", "1", "0", "-1", "-4", "-3", "60", "107", "-264", "-11175", "-40200", "142903", "2392436", "8175637", "-327277132", "-3256146845", "-19824913424", "184016913969", "1628105059824", "-33266797736465", "-1067099983418644", "-14633634217342547", "-39212918007355092", "458935991667836379" ]
[ "sign" ]
15
0
5
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2022-09-08T08:44:38
oeisdata/seq/A013/A013335.seq
a22d899ede0aba0ae54f0e5ef071113e
A013336
Expansion of e.g.f.: arctanh(exp(x)-sec(x)).
[ "0", "1", "0", "3", "-4", "45", "-180", "1743", "-13704", "135705", "-1613160", "18065883", "-276222604", "3655783365", "-65652672540", "1034667581223", "-20865280018704", "387014665823025", "-8593188683674320", "184059142857923763", "-4464138375366282004", "108277288526211374685", "-2858191345505462554500" ]
[ "sign" ]
21
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2019-09-02T02:04:47
oeisdata/seq/A013/A013336.seq
7663f766b385b89b8394f1c5cf9abcaf
A013337
E.g.f.: cosh(exp(x)-sec(x))=1+1/2!*x^2+5/4!*x^4-20/5!*x^5+37/6!*x^6...
[ "1", "0", "1", "0", "5", "-20", "37", "-700", "1017", "-28584", "83769", "-1514040", "9304605", "-108745468", "1172343421", "-11027747380", "169643707825", "-1567659515472", "28786470143025", "-295814371937904", "5793951884450549", "-69644639946402276" ]
[ "sign" ]
6
0
5
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-01-16T14:47:47
oeisdata/seq/A013/A013337.seq
d4be4ed877ba70978d9a29bbe41502c8
A013338
Expansion of e.g.f.: sec(exp(x)-sec(x))=1+1/2!*x^2+9/4!*x^4-20/5!*x^5+177/6!*x^6...
[ "1", "0", "1", "0", "9", "-20", "177", "-1260", "7105", "-99144", "564049", "-10278840", "77134761", "-1412196188", "15082747617", "-257693157540", "3771722331457", "-62330454304272", "1150241027577697", "-19671866661968880", "420212562193269513" ]
[ "sign" ]
6
0
5
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2020-02-19T14:43:46
oeisdata/seq/A013/A013338.seq
f3155c1c0fc84ac00536c5dfb4d469cd
A013339
sech(exp(x)-sec(x))=1-1/2!*x^2+1/4!*x^4+20/5!*x^5+23/6!*x^6...
[ "1", "0", "-1", "0", "1", "20", "23", "-140", "-975", "-1656", "74751", "365640", "1284369", "-26269412", "-120532297", "1518753340", "37230940193", "312855107472", "-1646816770497", "-37424409392880", "-167334452580383", "9798194248744356" ]
[ "sign" ]
4
0
6
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:26
oeisdata/seq/A013/A013339.seq
51b3dba2e59a202d9494a850891cc733
A013340
arctanh(exp(x)-sech(x))=x+2/2!*x^2+3/3!*x^3+20/4!*x^4+165/5!*x^5...
[ "0", "1", "2", "3", "20", "165", "1142", "10983", "136040", "1753545", "25376042", "422373963", "7641560060", "149590274925", "3195495898142", "73536613981743", "1808159717424080", "47465557573756305", "1324783497842287442" ]
[ "nonn" ]
8
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-02-05T08:32:09
oeisdata/seq/A013/A013340.seq
15bc1711b1a1918758262402771960cd
A013341
E.g.f.: exp(sin(x)-log(x+1)).
[ "1", "0", "1", "-3", "9", "-53", "315", "-2149", "17409", "-156617", "1563219", "-17208081", "206502945", "-2684228909", "37580441899", "-563709546373", "9019300106369", "-153328265590929", "2759909907247651", "-52438275521652889", "1048765530491448353", "-22024076635965333173", "484529682070755145979" ]
[ "sign" ]
10
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-03-01T02:44:00
oeisdata/seq/A013/A013341.seq
cdb17844ee71eeefd8f47e974d8e5db4
A013342
Expansion of e.g.f.: exp(sin(x)-arcsin(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", "-13264", "62304", "-1040866", "6528896", "-128181272", "950205568", "-21880956098", "189104984064", "-4957876255136", "48968006626816", "-1441276692392770", "16013733248841728", "-522786344819213608" ]
[ "sign" ]
6
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2023-07-28T19:23:52
oeisdata/seq/A013/A013342.seq
4ff4d74032a0fc719e2da68859c10a30
A013343
-sin(sin(x)-arcsin(x))=2/3!*x^3+8/5!*x^5+226/7!*x^7+8784/9!*x^9...
[ "2", "8", "226", "8784", "745186", "87930776", "14731669954", "3284180017312", "942576417055042", "338316707471357480", "148485160867969449250", "78231095025601137037552", "48725086678004751268115746" ]
[ "nonn" ]
6
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2024-11-04T16:32:09
oeisdata/seq/A013/A013343.seq
ce311bc17e776e8afecb2275cc7be54d
A013344
tan(arcsin(x)-sin(x)) = 2/3!*x^3+8/5!*x^5+226/7!*x^7+15504/9!*x^9...
[ "0", "2", "8", "226", "15504", "1188706", "148306520", "26128271170", "5977691158048", "1757745580960834", "644493123719650472", "287811224662750272034", "153933334239209991266992", "97140471618560380314609826" ]
[ "nonn" ]
11
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2016-02-29T12:43:39
oeisdata/seq/A013/A013344.seq
75c07b145ba27e5f502daf75bd4dcbb6
A013345
-arctan(sin(x)-arcsin(x))=2/3!*x^3+8/5!*x^5+226/7!*x^7+6544/9!*x^9...
[ "2", "8", "226", "6544", "597346", "67805528", "12188457282", "2727880967200", "796141697431618", "286025228357713576", "126058973689765963298", "66521439788693954540976", "41531178576953648181886626" ]
[ "nonn" ]
4
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:27
oeisdata/seq/A013/A013345.seq
6dc2e6f7148b60b8784449a441ddf26e
A013346
cos(sin(x)-arcsin(x))=1-40/6!*x^6-896/8!*x^8-62304/10!*x^10...
[ "1", "0", "0", "-40", "-896", "-62304", "-6036096", "-878453888", "-172356091904", "-44229410876928", "-14356887611836416", "-5752160769829099520", "-2787961066322579554304", "-1607823657408554342604800" ]
[ "sign" ]
6
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2019-07-10T16:33:22
oeisdata/seq/A013/A013346.seq
5c6772b183d0f827dc80e80f30214a9d
A013347
-sinh(sin(x)-arcsin(x))=2/3!*x^3+8/5!*x^5+226/7!*x^7+13264/9!*x^9...
[ "2", "8", "226", "13264", "1040866", "128181272", "21880956098", "4957876255136", "1441276692392770", "522786344819213608", "231464628933637009186", "122855468800105032574832", "77004928448834740386437666" ]
[ "nonn" ]
6
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-03-14T10:58:36
oeisdata/seq/A013/A013347.seq
fcdf5b77c473897be360f8079febd9be
A013348
cosh(sin(x)-arcsin(x))=1+40/6!*x^6+896/8!*x^8+62304/10!*x^10...
[ "1", "0", "0", "40", "896", "62304", "6528896", "950205568", "189104984064", "48968006626816", "16013733248841728", "6455144284204947456", "3144635341624935219200", "1821357143607530260848640", "1237121524622739656337752064" ]
[ "nonn" ]
4
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:27
oeisdata/seq/A013/A013348.seq
fb468ac908eb7afb7b5b94dd49758c0f
A013349
sec(sin(x)-arcsin(x))=1+40/6!*x^6+896/8!*x^8+62304/10!*x^10...
[ "1", "0", "0", "40", "896", "62304", "7514496", "1093708928", "222602768384", "59177065262592", "19661155936868352", "8041910306499811328", "3968598123713485832192", "2324068812945480395448320", "1594018675642134181026299904" ]
[ "nonn" ]
7
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-11-21T12:46:02
oeisdata/seq/A013/A013349.seq
da5507f3b28d2e0f9ac67c06dbab230f
A013350
sech(sin(x)-arcsin(x))=1-40/6!*x^6-896/8!*x^8-62304/10!*x^10...
[ "1", "0", "0", "-40", "-896", "-62304", "-5050496", "-734950528", "-138858307584", "-35484086513152", "-11376927751841792", "-4526992734620571648", "-2178753470207843827712", "-1249669173876982577029120" ]
[ "sign" ]
4
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:27
oeisdata/seq/A013/A013350.seq
53518fd95df5c1bc9ac0455643dd5ca2
A013351
Expansion of e.g.f.: exp(sin(x)-tan(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", "-15495", "126630", "-977493", "9727740", "-88854675", "979548570", "-10671316113", "129584342160", "-1617243395055", "21655877754510", "-303182522321133", "4450716903531780", "-68820502388338635" ]
[ "sign" ]
6
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2023-08-08T17:20:21
oeisdata/seq/A013/A013351.seq
07be4f5ec9ba5628ba0a962671fa10a0
A013352
sin(sin(x)-tan(x))=-3/3!*x^3-15/5!*x^5-273/7!*x^7-375/9!*x^9...
[ "-3", "-15", "-273", "-375", "269907", "44118165", "6182721087", "965945373105", "171088458444267", "34527329266886445", "7854770103731451447", "1982591879388402922185", "541911653216772177150627", "153897247606992030028136325", "41291644532130509317439445807" ]
[ "sign" ]
6
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-11-26T08:59:19
oeisdata/seq/A013/A013352.seq
ca161313567eb5f3764809bdb71ea5e8
A013353
tan(tan(x)-sin(x)) = 3/3!*x^3 + 15/5!*x^5 + 273/7!*x^7 + 23055/9!*x^9...
[ "0", "3", "15", "273", "23055", "1601193", "155341095", "24206437713", "4645592799135", "1094690215087833", "324803673636221175", "116133164181717551553", "48989776965837082135215", "24245825813770391843700873" ]
[ "nonn" ]
11
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-02-06T12:29:15
oeisdata/seq/A013/A013353.seq
8cdd4f8fe21f32d9ced8ed5234fb914d
A013354
arctan(sin(x)-tan(x))=-3/3!*x^3-15/5!*x^5-273/7!*x^7+7185/9!*x^9...
[ "-3", "-15", "-273", "7185", "893607", "110604585", "6777315087", "-405484606815", "-441813428161833", "-137423041821531015", "-28797568231809153153", "2268330081740331047985", "6518378202627257740085127" ]
[ "sign" ]
6
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2019-07-05T15:54:21
oeisdata/seq/A013/A013354.seq
41d62879b7b3a450dd093aca92b2e019
A013355
cos(sin(x)-tan(x))=1-90/6!*x^6-2520/8!*x^8-126630/10!*x^10...
[ "1", "0", "0", "-90", "-2520", "-126630", "-7232940", "-525494970", "-41497943760", "-2901128941710", "81569169583020", "147991203194615550", "70007476191566027400", "29824424882002116303210" ]
[ "sign" ]
4
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:27
oeisdata/seq/A013/A013355.seq
4ab173f6185574c734bfbbd3d7e71b4f
A013356
sinh(sin(x)-tan(x))=-3/3!*x^3-15/5!*x^5-273/7!*x^7-15495/9!*x^9...
[ "3", "15", "273", "15495", "977493", "88854675", "10671316113", "1617243395055", "303182522321133", "68820502388338635", "18601481181446108553", "5903132077554100349415", "2173055397496643301830373" ]
[ "nonn" ]
4
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:27
oeisdata/seq/A013/A013356.seq
6b4f771191297d88a5ec1d2527db0032
A013357
cosh(sin(x)-tan(x))=1+90/6!*x^6+2520/8!*x^8+126630/10!*x^10...
[ "1", "0", "0", "90", "2520", "126630", "9727740", "979548570", "129584342160", "21655877754510", "4450716903531780", "1102163137590334050", "323261459451529176600", "110722946709029745152790", "43768619617333612645900620" ]
[ "nonn" ]
6
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2019-04-11T17:11:23
oeisdata/seq/A013/A013357.seq
19e04692652daeac4c8a5a6375e38a02
A013358
sec(sin(x)-tan(x))=1+90/6!*x^6+2520/8!*x^8+126630/10!*x^10...
[ "1", "0", "0", "90", "2520", "126630", "14717340", "1887655770", "305757138960", "67501799476110", "18267050784481380", "5925845719351577250", "2313597977247058464600", "1064286603125099115824790" ]
[ "nonn" ]
4
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:27
oeisdata/seq/A013/A013358.seq
8bc601de5bfaf010ecb33f62478f23be
A013359
sech(sin(x)-tan(x))=1-90/6!*x^6-2520/8!*x^8-126630/10!*x^10...
[ "1", "0", "0", "-90", "-2520", "-126630", "-2243340", "382612230", "134674853040", "26271944587890", "4394379581092620", "324925984573170750", "-181350289825568364600", "-145875833202121504544790" ]
[ "sign" ]
4
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:27
oeisdata/seq/A013/A013359.seq
61d0e411114df784a7b1c4f3b4c1ebc2
A013360
Expansion of e.g.f.: exp(sin(x)-arctan(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", "-40039", "152934", "3522539", "-21952084", "-447600515", "4051623706", "77667878287", "-956802094896", "-17678180216111", "283850233488142", "5114563630418963", "-103778358157367212" ]
[ "sign" ]
6
0
6
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-08-11T11:53:20
oeisdata/seq/A013/A013360.seq
8f2353d409c335048977331dad829723
A013361
sin(sin(x)-arctan(x))=1/3!*x^3-23/5!*x^5+719/7!*x^7-40599/9!*x^9...
[ "1", "-23", "719", "-40599", "3735059", "-510402683", "96691506911", "-24171783139087", "7694747756773355", "-3036089243696854595", "1453467770211562096727", "-829717294037701503696727", "556699159289263988695878179" ]
[ "sign" ]
4
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:27
oeisdata/seq/A013/A013361.seq
da3de03b3e6a4add97ab418181426317
A013362
tan(sin(x)-arctan(x))=1/3!*x^3-23/5!*x^5+719/7!*x^7-39759/9!*x^9...
[ "1", "-23", "719", "-39759", "3416279", "-416199431", "68177084975", "-14464255598623", "3858701385264167", "-1264194279838439447", "498983377122586500671", "-233538587496361280678767", "127884277134966430982474999" ]
[ "sign" ]
7
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-11-21T12:46:02
oeisdata/seq/A013/A013362.seq
5d1261aa73e378588587f241446a6f04
A013363
arctan(sin(x)-arctan(x))=1/3!*x^3-23/5!*x^5+719/7!*x^7-40879/9!*x^9...
[ "0", "1", "-23", "719", "-40879", "3841319", "-541803767", "106235553423", "-27468995761375", "9037325540918231", "-3685351559546907751", "1824543182108925373567", "-1078031616167494916871951", "749297439398817941026337799" ]
[ "sign" ]
6
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2016-11-29T10:54:59
oeisdata/seq/A013/A013363.seq
9c30ed1ca34cd70b856de7b535f1c050
A013364
E.g.f.: cos(sin(x)-arctan(x))=1-10/6!*x^6+1288/8!*x^8-152934/10!*x^10...
[ "1", "0", "0", "-10", "1288", "-152934", "21982884", "-4077409466", "972083601136", "-292315200462606", "108645176948603484", "-48996211090048870850", "26383142439992849750056", "-16729383446320867555995350" ]
[ "sign" ]
6
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-08-20T17:29:49
oeisdata/seq/A013/A013364.seq
63fde278069589d4798679a112845a9d
A013365
sinh(sin(x)-arctan(x))=1/3!*x^3-23/5!*x^5+719/7!*x^7-40039/9!*x^9...
[ "1", "-23", "719", "-40039", "3522539", "-447600515", "77667878287", "-17678180216111", "5114563630418963", "-1833901052655286363", "798306636459002471063", "-414704864473303294302407", "253396539072278830083000859" ]
[ "sign" ]
7
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-11-21T12:46:02
oeisdata/seq/A013/A013365.seq
48cd088240cab39024d5908ba83eb356
A013366
cosh(sin(x)-arctan(x))=1+10/6!*x^6-1288/8!*x^8+152934/10!*x^10...
[ "1", "0", "0", "10", "-1288", "152934", "-21952084", "4051623706", "-956802094896", "283850233488142", "-103778358157367212", "45952155963779123106", "-24267844868956822679176", "15082728649311299637576790" ]
[ "sign" ]
6
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-11-14T15:42:43
oeisdata/seq/A013/A013366.seq
5ce6e7e244a260c2cd69e12d573047c8
A013367
sec(sin(x)-arctan(x))=1+10/6!*x^6-1288/8!*x^8+152934/10!*x^10...
[ "1", "0", "0", "10", "-1288", "152934", "-21890484", "4000052186", "-926239082416", "266931734963214", "-94074704256622668", "39914182012094267618", "-20108103789380727679816", "11884006709783387983027670" ]
[ "sign" ]
4
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:27
oeisdata/seq/A013/A013367.seq
ec44aa401270db506b7b751dc91c9df0
A013368
sech(sin(x)-arctan(x))=1-10/6!*x^6+1288/8!*x^8-152934/10!*x^10...
[ "1", "0", "0", "-10", "1288", "-152934", "22044484", "-4128980986", "1002646613616", "-309256569835534", "118408798212804028", "-55134457643443006338", "30684616930799120314216", "-20117431906536006109520470" ]
[ "sign" ]
6
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-01-31T11:36:17
oeisdata/seq/A013/A013368.seq
9fdb90b2888b59efb7675615271a4738
A013369
Expansion of e.g.f. exp(sin(x)-sinh(x)).
[ "1", "0", "0", "-2", "0", "0", "40", "-2", "0", "-2240", "480", "-2", "246400", "-137280", "8320", "-44844802", "51251200", "-10325120", "12197916160", "-24831206402", "11394406400", "-4636033573760", "15296025241600", "-13230894476802", "2348235343872000" ]
[ "sign" ]
16
0
4
[ "A013025", "A013369", "A307978" ]
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2022-03-17T11:42:14
oeisdata/seq/A013/A013369.seq
6646dc652d73ba46054a0fe88785a768
A013370
sin(sin(x)-sinh(x))=-2/3!*x^3-2/7!*x^7+2240/9!*x^9-2/11!*x^11...
[ "-2", "0", "-2", "2240", "-2", "137280", "-44844802", "10325120", "-24831206402", "4636033573760", "-13230894476802", "11727021909179200", "-1532148866787968002", "24717753365658325440" ]
[ "sign" ]
9
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2025-06-21T18:15:33
oeisdata/seq/A013/A013370.seq
29614e1913eeedb0d7abac1c20b9c273
A013371
Expansion of tan(sinh(x)-sin(x)) = 2/3!*x^3 + 2/7!*x^7 + 4480/9!*x^9 + 2/11!*x^11 + ...
[ "0", "2", "0", "2", "4480", "2", "274560", "717516802", "20650240", "397299302402", "1260764869707520", "211694311628802", "3189730834295158400", "12098583209553471488002", "6723227372694939050880" ]
[ "nonn" ]
8
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-02-06T12:33:11
oeisdata/seq/A013/A013371.seq
83c80b1b72ee5c20754b70b2437f6435
A013372
arctan(sin(x)-sinh(x)) = -2/3!*x^3 - 2/7!*x^7 + 4480/9!*x^9 - 2/11!*x^11 + ...
[ "-2", "0", "-2", "4480", "-2", "274560", "-1076275202", "20650240", "-595948953602", "3337315890251520", "-317541467443202", "8443404916271478400", "-61468170244569234432002", "17796778320664208810880", "-497337594356972616069888002", "4456181603844910120400213608960" ]
[ "sign" ]
11
3
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-10-11T14:34:27
oeisdata/seq/A013/A013372.seq
f1efc56201bddb419954df7bd7bab7e0
A013373
cos(sin(x)-sinh(x))=1-40/6!*x^6-480/10!*x^10+246400/12!*x^12...
[ "1", "0", "0", "-40", "0", "-480", "246400", "-8320", "51251200", "-12197916160", "11394406400", "-15296025241600", "2348235343872000", "-17026923803402240", "10977173716094976000", "-1257676453660275015680" ]
[ "sign" ]
4
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:27
oeisdata/seq/A013/A013373.seq
f69dc3cec0e338bdeca6242e9f0ea23b
A013374
arcsinh(sin(x)-sinh(x))=-2/3!*x^3-2/7!*x^7+2240/9!*x^9-2/11!*x^11...
[ "0", "-2", "0", "-2", "2240", "-2", "137280", "-403603202", "10325120", "-223480857602", "1042911543845760", "-119078050291202", "2638564062897339200", "-16807721436490038912002", "5561493227350293205440" ]
[ "sign" ]
11
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-02-04T05:00:08
oeisdata/seq/A013/A013374.seq
531220e835f5186013456e1be006d4f9
A013375
sec(sin(x)-sinh(x))=1+40/6!*x^6+480/10!*x^10+1232000/12!*x^12...
[ "1", "0", "0", "40", "0", "480", "1232000", "8320", "256256000", "744065052160", "56972032000", "933057413785600", "3248379673651200000", "1038642349994762240", "15202354034221486080000", "62540998641516972945735680" ]
[ "nonn" ]
6
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2018-10-19T17:43:43
oeisdata/seq/A013/A013375.seq
63b086dca6287f03955beefa0361a0c9
A013376
exp(sin(x)-arcsinh(x)) = 1-8/5!*x^5+224/7!*x^7-11024/9!*x^9+8064/10!*x^10...
[ "1", "0", "0", "0", "0", "-8", "0", "224", "0", "-11024", "8064", "893024", "-1419264", "-108056024", "262662400", "18196891712", "-59455492096", "-4073700728096", "16726941245440", "1171230240813632", "-5792855942807552", "-420783754605743528" ]
[ "sign" ]
10
0
6
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-11-01T15:28:47
oeisdata/seq/A013/A013376.seq
3233b8fd85b86364a8406763b66a522b
A013377
sin(sin(x)-arcsinh(x)) = -8/5!*x^5+224/7!*x^7-11024/9!*x^9...
[ "0", "0", "-8", "224", "-11024", "893024", "-108056024", "18326044736", "-4143959973152", "1203673701847616", "-436556568694967720", "193325069835999174688", "-102646741662885247765552", "64363759451798102692787104" ]
[ "sign" ]
9
0
3
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-11-01T16:29:12
oeisdata/seq/A013/A013377.seq
afa3b1abf61b33d3a26e7359e04944e6
A013378
cos(sin(x)-arcsinh(x)) = 1-8064/10!*x^10 + 1419264/12!*x^12 ...
[ "1", "0", "0", "0", "0", "-8064", "1419264", "-262662400", "59455492096", "-16726941245440", "5796860719775744", "-2439524053684551680", "1228699611612771516416", "-730845840019971307929600", "507327256430827248463380480" ]
[ "sign" ]
10
0
6
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2022-06-20T20:09:46
oeisdata/seq/A013/A013378.seq
66d4f008894c7bc8d9d2af691994d48a
A013379
Expansion of e.g.f.: exp(sin(x)-tanh(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", "-7655", "60870", "284491", "-4949780", "-9609795", "484684330", "-382526689", "-57168678320", "229639178065", "7957246947790", "-65098408980269", "-1270811040444460", "17837435546853925" ]
[ "sign" ]
6
0
6
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2019-08-19T13:57:37
oeisdata/seq/A013/A013379.seq
b23150bc7fe04a968852369653132533
A013380
Expansion of e.g.f. sin(sin(x) - tanh(x)), odd powers only.
[ "1", "-15", "271", "-8215", "423091", "-35126715", "4192844111", "-652228720015", "125163350892331", "-28804173376146115", "7819440342923915751", "-2475114876516159269015", "904874211609774006906371", "-378873316356391869172808715", "180284311084647508248207800191", "-96800336889159425029828580541215" ]
[ "sign" ]
14
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2018-03-06T02:49:17
oeisdata/seq/A013/A013380.seq
f08df503e81fdbcf0e393241c0072e71
A013381
tan(sin(x)-tanh(x))=1/3!*x^3-15/5!*x^5+271/7!*x^7-7375/9!*x^9...
[ "1", "-15", "271", "-7375", "215191", "3148665", "-2649191089", "649131707105", "-146075501268569", "33189954373043945", "-7481610904728705249", "1478339075346879047185", "-99742476113106129277129" ]
[ "sign" ]
4
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:27
oeisdata/seq/A013/A013381.seq
35becfd990164fb97f21e5948c599374
A013382
arctan(sin(x)-tanh(x))=1/3!*x^3-15/5!*x^5+271/7!*x^7-8495/9!*x^9...
[ "1", "-15", "271", "-8495", "492391", "-47885175", "6512761711", "-1126039513055", "241996705222231", "-64384007995020135", "20971047413824897951", "-8203471786087609654415", "3781059328242133245372871" ]
[ "sign" ]
6
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2017-05-08T17:55:09
oeisdata/seq/A013/A013382.seq
6c8d454f6a239c5bfc713373e8fb5577
A013383
cos(sin(x)-tanh(x))=1-10/6!*x^6+840/8!*x^8-60870/10!*x^10...
[ "1", "0", "0", "-10", "840", "-60870", "4980580", "-501501130", "63445348720", "-10063325322190", "1976669210391260", "-472760236462102450", "135256173623772004200", "-45534410854433395672310", "17782334849654204122443540" ]
[ "sign" ]
7
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2013-11-21T12:46:02
oeisdata/seq/A013/A013383.seq
3bd86e66e3a9e2002ad11425295fb0d3
A013384
sinh(sin(x)-tanh(x))=1/3!*x^3-15/5!*x^5+271/7!*x^7-7655/9!*x^9...
[ "1", "-15", "271", "-7655", "284491", "-9609795", "-382526689", "229639178065", "-65098408980269", "17837435546853925", "-5217817960366272249", "1673172596073749841785", "-591805818675678286322629" ]
[ "sign" ]
6
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2016-09-17T11:28:13
oeisdata/seq/A013/A013384.seq
a3c1fce11808c48d77bb50bca9eecd9f
A013385
cosh(sin(x)-tanh(x))=1+10/6!*x^6-840/8!*x^8+60870/10!*x^10...
[ "1", "0", "0", "10", "-840", "60870", "-4949780", "484684330", "-57168678320", "7957246947790", "-1270811040444460", "224172849477365650", "-40867049294767840200", "6397467145495026664310", "40199264206917072158460" ]
[ "sign" ]
6
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-02-25T19:46:44
oeisdata/seq/A013/A013385.seq
613e076f834794f5cf0f521beee4c1b9
A013386
sec(sin(x)-tanh(x))=1+10/6!*x^6-840/8!*x^8+60870/10!*x^10...
[ "1", "0", "0", "10", "-840", "60870", "-4888180", "451050730", "-44615337520", "3756525622990", "121350724409140", "-252176627984091950", "129656734144811047800", "-57182907798391521511690", "24201188340561567892562460" ]
[ "sign" ]
6
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2024-12-15T16:23:36
oeisdata/seq/A013/A013386.seq
0637c98037a60948d01c583c8c0b765e
A013387
sech(sin(x)-tanh(x))=1-10/6!*x^6+840/8!*x^8-60870/10!*x^10...
[ "1", "0", "0", "-10", "840", "-60870", "5042180", "-535134730", "75998689520", "-14286917494990", "3407940125324860", "-990760306939592050", "342314173738467052200", "-138600427075503715528310", "65139256364305112582847540" ]
[ "sign" ]
4
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:27
oeisdata/seq/A013/A013387.seq
ae0b98ee8da6bf9265cb1b6bdc2dba93
A013388
Expansion of e.g.f.: exp(sin(x)-arctanh(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", "-47879", "326214", "-4585141", "40991676", "-647541971", "7059334282", "-125142649633", "1612242903824", "-31683946165871", "471247352116174", "-10177278274781101", "171640057469660548" ]
[ "sign" ]
6
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2023-05-15T11:39:36
oeisdata/seq/A013/A013388.seq
a31e217516c5a202dc9255279d0eca29
A013389
sin(sin(x)-arctanh(x))=-3/3!*x^3-23/5!*x^5-721/7!*x^7-32759/9!*x^9...
[ "3", "23", "721", "32759", "2672461", "310461227", "49895013169", "10516703525327", "2811203923750741", "926105108276716115", "367211453075540071769", "171643737525955364628727", "92766252900694480314741821" ]
[ "nonn" ]
6
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2014-01-01T15:18:17
oeisdata/seq/A013/A013389.seq
6636a0da4dd458e0fed93dad3fe3a567
A013390
tan(arctanh(x)-sin(x)) = 3/3!*x^3 + 23/5!*x^5 + 721/7!*x^7 + 55439/9!*x^9...
[ "0", "3", "23", "721", "55439", "5541481", "816082343", "167874570865", "44930591850143", "15238326353365081", "6394194823965172727", "3248353545402758819489", "1964538978111655728427567", "1394689558266289975472153801" ]
[ "nonn" ]
9
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2015-02-06T12:57:29
oeisdata/seq/A013/A013390.seq
5d41077ab072425d8c17efa75c36a60d
A013391
-arctan(sin(x)-arctanh(x))=3/3!*x^3+23/5!*x^5+721/7!*x^7+25199/9!*x^9...
[ "0", "3", "23", "721", "25199", "1716121", "141920855", "20103619537", "4016386229855", "1241116799607721", "494609567396520071", "244232906612554953633", "140315440295583485315151", "92810530303082004433849401" ]
[ "nonn" ]
6
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2016-11-29T10:57:15
oeisdata/seq/A013/A013391.seq
93e19128668dfac704033997d6a1342d
A013392
cos(sin(x)-arctanh(x))=1-90/6!*x^6-3864/8!*x^8-326214/10!*x^10...
[ "1", "0", "0", "-90", "-3864", "-326214", "-38496876", "-6363118762", "-1391451773264", "-390207547318222", "-136581823796686036", "-58397588436566980370", "-29960029691855345080504", "-18169010205146250870789750" ]
[ "sign" ]
6
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2022-09-07T16:13:58
oeisdata/seq/A013/A013392.seq
7d0c5deb5acf1e029afa50f1156f0f84
A013393
sinh(sin(x)-arctanh(x))=-3/3!*x^3-23/5!*x^5-721/7!*x^7-47879/9!*x^9...
[ "3", "23", "721", "47879", "4585141", "647541971", "125142649633", "31683946165871", "10177278274781101", "4042622917874613323", "1945427918214115672569", "1115191589596355708429607", "750796364377542533286862341" ]
[ "nonn" ]
4
0
1
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:28
oeisdata/seq/A013/A013393.seq
f7b7aae758c5d69c8ca3a4ea05778baa
A013394
cosh(sin(x)-arctanh(x))=1+90/6!*x^6+3864/8!*x^8+326214/10!*x^10...
[ "1", "0", "0", "90", "3864", "326214", "40991676", "7059334282", "1612242903824", "471247352116174", "171640057469660548", "76238487501368295026", "40569187584659105627992", "25481546086075766773695990" ]
[ "nonn" ]
4
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:28
oeisdata/seq/A013/A013394.seq
205abbcb2870f6e9c730305965850462
A013395
sec(sin(x)-arctanh(x))=1+90/6!*x^6+3864/8!*x^8+326214/10!*x^10...
[ "1", "0", "0", "90", "3864", "326214", "45981276", "8451765322", "2053825164944", "641663385808078", "249042559475513572", "117658592297847708338", "66515862023755958383768", "44326271307924691256260470" ]
[ "nonn" ]
6
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2017-06-08T15:04:33
oeisdata/seq/A013/A013395.seq
5f61833447c7504f0e2044790bc1816f
A013396
E.g.f.: sech(sin(x)-arctanh(x))=1-90/6!*x^6-3864/8!*x^8-326214/10!*x^10...
[ "1", "0", "0", "-90", "-3864", "-326214", "-33507276", "-4970687722", "-949869512144", "-236464361818318", "-73751391110641012", "-28454096973841135058", "-13304169550531141566328", "-7432891904926457008929270" ]
[ "sign" ]
6
0
4
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-07-04T14:38:02
oeisdata/seq/A013/A013396.seq
83cbaefc59d9bc7dbc0b553e330ba7b9
A013397
exp(arcsin(x)-log(x+1))=1+1/2!*x^2-1/3!*x^3+9/4!*x^4-25/5!*x^5...
[ "1", "0", "1", "-1", "9", "-25", "235", "-1125", "12145", "-83305", "1037475", "-9280225", "132009625", "-1456021125", "23378099875", "-306453818125", "5493040502625", "-83388492864625", "1652566180607875", "-28500730684349625", "619275939126495625" ]
[ "sign" ]
6
0
5
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2021-05-06T17:27:52
oeisdata/seq/A013/A013397.seq
bfb571ffbf6de5d84aba0b640018ef61
A013398
exp(arcsin(x)-tan(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", "2809", "11814", "506893", "-403612", "83115485", "-231855494", "16349094305", "-65488668048", "3986249084945", "-19019872358258", "1200454846441429", "-6285428416936228", "441567328473394021" ]
[ "sign" ]
4
0
6
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:28
oeisdata/seq/A013/A013398.seq
4185e2c791255940cebd1d9f23eec7fd
A013399
arcsin(arcsin(x)-tan(x))=-1/3!*x^3-7/5!*x^5-47/7!*x^7+2809/9!*x^9...
[ "-1", "-7", "-47", "2809", "506893", "83115485", "16337883105", "3980912553745", "1198885514196949", "441311715413932261", "196017910100566581641", "103733615818680354449241", "64634094120174715384992573" ]
[ "sign" ]
4
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:28
oeisdata/seq/A013/A013399.seq
ec5341faf6dbc26f80785cc5a0c576fc
A013400
tan(arcsin(x)-tan(x))=-1/3!*x^3-7/5!*x^5-47/7!*x^7+2529/9!*x^9...
[ "-1", "-7", "-47", "2529", "474553", "80543201", "16320858097", "4064194232641", "1239800275237225", "458973088380970433", "203990713313188606561", "107678055191713549688737", "66805939165628021795993113" ]
[ "sign" ]
4
0
2
null
null
Patrick Demichel (patrick.demichel(AT)hp.com)
2012-02-24T12:51:28
oeisdata/seq/A013/A013400.seq
4cd1aeef4be4a059a118227b0f883319