%I #5 Dec 07 2019 08:15:22

%S 1,2,7,24,121,840,5041,40320,423361,3659040,39916801,558835200,

%T 6227020801,87195588480,1536517382401,20922789888000,355687428096001,

%U 7469453633241600,121645100408832001,2453176191578112000,59616236292028416001

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

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

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

%t nmax = 21; CoefficientList[Series[Sum[Sinh[x^k], {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! // Rest

%t Table[n! DivisorSum[n, 1/#! &, OddQ[#] &], {n, 1, 21}]

%Y Cf. A057625, A132958, A176473, A330255.

%K nonn

%O 1,2

%A _Ilya Gutkovskiy_, Dec 07 2019