A330255 Expansion of e.g.f. Sum_{k>=1} (cosh(x^k) - 1) (even powers only).

1, 13, 361, 21841, 1814401, 260124481, 43589145601, 11333696774401, 3210079038566401, 1317822591538252801, 562000363888803840001, 336953340897297630105601, 201645730563302817792000001, 165147853334842304408401920001, 132994909752412012763531673600001

Offset

1,2

Links

Table of n, a(n) for n=1..15.

Formula

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

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

Mathematica

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

Crossrefs

Cf. A057625, A132958, A176474, A330254.

Sequence in context: A218419 A165391 A061015 * A280796 A183472 A009040

Adjacent sequences: A330252 A330253 A330254 * A330256 A330257 A330258

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 07 2019

Status

approved