A331338 E.g.f.: Sum_{k>=1} (1 - sech(x^k)) (even powers only).

1, 7, 421, 10375, 1864921, 177588115, 43788506581, 5364386887855, 3746015060385841, 743097477083711275, 562069712763196977901, 208700966175150043937095, 201649817635812110915892361, 89621739407126401163202051715, 158792595367325562826629059282821

Offset: 1

Author

Ilya Gutkovskiy, Jan 14 2020

Keywords

• nonn

Crossrefs

Cf. A000364, A028296, A176474, A330255, A330528.

Programs

Mathematica

nmax = 15; Table[(CoefficientList[Series[Sum[1 - Sech[x^k], {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, EulerE[2 #]/(2 #)! &], {n, 1, 15}]

Formula

a(n) = -(2*n)! * Sum_{d|n} A028296(d) / (2*d)!.