A330254 Expansion of e.g.f. Sum_{k>=1} sinh(x^k).

1, 2, 7, 24, 121, 840, 5041, 40320, 423361, 3659040, 39916801, 558835200, 6227020801, 87195588480, 1536517382401, 20922789888000, 355687428096001, 7469453633241600, 121645100408832001, 2453176191578112000, 59616236292028416001

Offset: 1

Author

Ilya Gutkovskiy, Dec 07 2019

Keywords

• nonn

Crossrefs

Cf. A057625, A132958, A176473, A330255.

Programs

Mathematica

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}]

Formula

E.g.f.: Sum_{k>=1} x^(2*k - 1) / ((2*k - 1)! * (1 - x^(2*k - 1))).

a(n) = n! * Sum_{d|n, d odd} 1 / d!.