A176474
From the coefficients (times n!) of the expansion of the Sum_{k>=1} cos(x^k).
Original entry on oeis.org
0, 1, 11, 361, 18479, 1814401, 220207679, 43589145601, 9589093113599, 3210079038566401, 1115080757523532799, 562000363888803840001, 285218528618534141030399, 201645730563302817792000001
Offset: 1
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Rest@ Union[ -Range[0, 26]! CoefficientList[ Series[ Sum[ Cos[x^n], {n, 35}], {x, 0, 27}], x]]
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{ my(N=33, x='x+O('x^N)); v = Vec(serlaplace(-sum(k=1,N,cos(x^k)))); vector(#v\2-1, k, v[2*k+1])} \\ \\ Joerg Arndt, Apr 21 2017
A176475
The coefficients (times n!) of the expansion of the sum {k=1 to Inf.} of Tan(x^n).
Original entry on oeis.org
0, 1, 2, 8, 24, 136, 960, 5312, 40320, 491776, 4112640, 40270592, 638668800, 6249389056, 91883151360, 1919826163712, 20922789888000, 355897293438976, 8676514912665600, 121674189293944832, 2757288942600192000
Offset: 1
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Range[0, 25]! CoefficientList[ Series[ Sum[ Tan[x^n], {n, 35}], {x, 0, 25}], x]
A330254
Expansion of e.g.f. Sum_{k>=1} sinh(x^k).
Original entry on oeis.org
1, 2, 7, 24, 121, 840, 5041, 40320, 423361, 3659040, 39916801, 558835200, 6227020801, 87195588480, 1536517382401, 20922789888000, 355687428096001, 7469453633241600, 121645100408832001, 2453176191578112000, 59616236292028416001
Offset: 1
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nmax = 21; CoefficientList[Series[Sum[Sinh[x^k], {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! // Rest
Table[n! DivisorSum[n, 1/#! &, OddQ[#] &], {n, 1, 21}]
A330506
Expansion of e.g.f. Sum_{k>=1} arcsin(x^k).
Original entry on oeis.org
1, 2, 7, 24, 129, 840, 5265, 40320, 434385, 3900960, 40809825, 558835200, 6335076825, 91070179200, 1641957141825, 20922789888000, 359796258446625, 7663952552256000, 122832552380162625, 2615369658789888000, 62315614994643635625
Offset: 1
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nmax = 21; CoefficientList[Series[Sum[ArcSin[x^k], {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! // Rest
Table[n! DivisorSum[n, ((# - 2)!!)^2/#! &, OddQ[#] &], {n, 1, 21}]
Showing 1-4 of 4 results.