%I #5 Dec 07 2019 08:15:28

%S 1,13,361,21841,1814401,260124481,43589145601,11333696774401,

%T 3210079038566401,1317822591538252801,562000363888803840001,

%U 336953340897297630105601,201645730563302817792000001,165147853334842304408401920001,132994909752412012763531673600001

%N Expansion of e.g.f. Sum_{k>=1} (cosh(x^k) - 1) (even powers only).

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

%F a(n) = (2*n)! * Sum_{d|n} 1 / (2*d)!.

%t nmax = 15; Table[(CoefficientList[Series[Sum[Cosh[x^k] - 1, {k, 1, nmax}], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}] // Rest

%t Table[(2 n)! DivisorSum[n, 1/(2 #)! &], {n, 1, 15}]

%Y Cf. A057625, A132958, A176474, A330254.

%K nonn

%O 1,2

%A _Ilya Gutkovskiy_, Dec 07 2019