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A330255
Expansion of e.g.f. Sum_{k>=1} (cosh(x^k) - 1) (even powers only).
4
1, 13, 361, 21841, 1814401, 260124481, 43589145601, 11333696774401, 3210079038566401, 1317822591538252801, 562000363888803840001, 336953340897297630105601, 201645730563302817792000001, 165147853334842304408401920001, 132994909752412012763531673600001
OFFSET
1,2
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 07 2019
STATUS
approved