A270294
E.g.f.: Product_{k>=1} (1 + sinh(x^k)).
Original entry on oeis.org
1, 1, 2, 13, 48, 381, 3120, 26923, 255696, 3158137, 40008240, 519979791, 7942304040, 122856625477, 2131578891624, 39647280625891, 750423985762080, 15134456564892273, 334165931467245216, 7422976578858122647, 177254117413133743800, 4454974632071621551741
Offset: 0
-
nmax = 25; Range[0, nmax]!*CoefficientList[Series[Product[1+Sinh[x^k], {k, 1, nmax}], {x, 0, nmax}], x]
A229263
E.g.f.: Product_{n>=1} cosh(x^n).
Original entry on oeis.org
1, 1, 13, 541, 32761, 3782521, 570649861, 126354119893, 34059666142321, 12697511966492401, 5418397453551516541, 2950382131846118771341, 1848796902719228099999593, 1394126061848631877574788201, 1187817128863650862040235107701, 1196980698779612997551160117313861
Offset: 0
E.g.f.: A(x) = 1 + x^2/2! + 13*x^4/4! + 541*x^6/6! + 32761*x^8/8! +...
where
A(x) = cosh(x)*cosh(x^2)*cosh(x^3)*cosh(x^4)*cosh(x^5)*cosh(x^6)*...
-
{a(n)=(2*n)!*polcoeff(prod(m=1,n,cosh(x^m +x*O(x^(2*n)))),2*n)}
for(n=0,20,print1(a(n),", "))
A270663
E.g.f.: Product_{k>=1} cos(x^k) [even terms only].
Original entry on oeis.org
1, -1, -11, -181, -9239, -148681, -49402979, 6471717251, 42662277841, 658656817939439, 133531458273294661, 168943525289665105979, 19015164932231993967289, 62294481438650615377602599, 18546969159687034895328945901, 27398539855607539080934584895859
Offset: 0
-
nmax = 20; Table[(Range[0, 2*nmax]! * CoefficientList[Series[Product[Cos[x^k], {k, 1, 2*nmax}], {x, 0, 2*nmax}], x])[[2*n + 1]], {n, 0, nmax}]
A270664
E.g.f.: Product_{k>=1} (1 + tanh(x^k)).
Original entry on oeis.org
1, 1, 2, 10, 48, 336, 2400, 22240, 220416, 2496256, 30286080, 411725568, 6004838400, 94609106944, 1588301524992, 28577718427648, 546685777182720, 11027370474504192, 234498341381603328, 5253826506085629952, 123695389756163358720, 3039894623920125116416
Offset: 0
-
nmax = 25; Range[0, nmax]! * CoefficientList[Series[Product[(1+Tanh[x^k]), {k, 1, nmax}], {x, 0, nmax}], x]
A270666
E.g.f.: Product_{k>=1} (1 + tan(x^k)).
Original entry on oeis.org
1, 1, 2, 14, 48, 416, 3360, 29504, 274176, 3503104, 45192960, 579956992, 8982251520, 138130720768, 2456648183808, 45868468109312, 871166211686400, 17536583860060160, 393972064172900352, 8704569607311982592, 210657904645299240960, 5322004254737369399296
Offset: 0
-
nmax = 25; Range[0, nmax]! * CoefficientList[Series[Product[(1+Tan[x^k]), {k, 1, nmax}], {x, 0, nmax}], x]
A330514
Expansion of e.g.f. Product_{k>=1} 1 / (1 - sin(x^k)).
Original entry on oeis.org
1, 1, 4, 17, 112, 761, 6992, 65267, 749264, 8952097, 123035312, 1765177435, 28465913320, 475981018033, 8737060100680, 167186734385795, 3446660462332576, 73894280818392641, 1691674707666258848, 40160865451008020651, 1009283508170762388536
Offset: 0
Cf.
A000111,
A203716,
A229263,
A270294,
A270662,
A270663,
A270664,
A270665,
A270666,
A330515,
A330516,
A330517.
-
nmax = 20; CoefficientList[Series[Product[1/(1 - Sin[x^k]), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
A330515
Expansion of e.g.f. Product_{k>=1} 1 / (1 - sinh(x^k)).
Original entry on oeis.org
1, 1, 4, 19, 128, 921, 8912, 87109, 1045200, 13195681, 188639312, 2837096637, 47976425576, 837845855185, 16039578298200, 321739841159317, 6911395312352672, 154749452408120385, 3696709758990757856, 91546190261460505453, 2397650607409036823352
Offset: 0
Cf.
A006154,
A203716,
A229263,
A270294,
A270662,
A270663,
A270664,
A270665,
A270666,
A330514,
A330516,
A330517.
-
nmax = 20; CoefficientList[Series[Product[1/(1 - Sinh[x^k]), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
A330516
Expansion of e.g.f. Product_{k>=1} sec(x^k) (even powers only).
Original entry on oeis.org
1, 1, 17, 601, 44225, 4589041, 781157585, 162882093193, 48519650017025, 17223202538504161, 7898449818361655825, 4193448664548573675961, 2779065418077990268214465, 2061320859693223620523895761, 1836094285018667246330440863185
Offset: 0
Cf.
A000364,
A203716,
A229263,
A270294,
A270662,
A270663,
A270664,
A270665,
A270666,
A330514,
A330515,
A330517.
-
nmax = 14; Table[(CoefficientList[Series[Product[Sec[x^k], {k, 1, nmax}], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}]
A330517
Expansion of e.g.f. Product_{k>=1} sech(x^k) (even powers only).
Original entry on oeis.org
1, -1, -7, -241, -4495, -652801, -15004375, -7047990769, 1597056262625, -360304327144321, 286464442762907225, 560117092794518159, 78257061390674957994065, 5684812583023438995911039, 45666128878264725133259682185
Offset: 0
Cf.
A000364,
A203716,
A229263,
A270294,
A270662,
A270663,
A270664,
A270665,
A270666,
A330514,
A330515,
A330516.
-
nmax = 14; Table[(CoefficientList[Series[Product[Sech[x^k], {k, 1, nmax}], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}]
A330539
Expansion of e.g.f. Product_{k>=1} (1 + arcsin(x^k)).
Original entry on oeis.org
1, 1, 2, 13, 48, 389, 3120, 27483, 258384, 3209481, 40895280, 532286415, 8095233960, 125622532125, 2196944928360, 40755258858195, 773235510112800, 15597078326535825, 345588497493916320, 7674105262451228055, 183908428603335286200
Offset: 0
-
nmax = 20; CoefficientList[Series[Product[(1 + ArcSin[x^k]), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 20; CoefficientList[Series[Exp[Sum[Sum[(-1)^(d + 1) ArcSin[x^(k/d)]^d/d, {d, Divisors[k]}], {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
Showing 1-10 of 11 results.