A351881 Expansion of e.g.f. 1 / (1 - x)^cosh(x).

1, 1, 2, 9, 42, 235, 1605, 12446, 108836, 1061565, 11402565, 133806134, 1703059974, 23366177055, 343788954691, 5399655967642, 90173526680152, 1595513146457993, 29817130502252169, 586883850601630054, 12135450890055396810, 263012688923611212107, 5962155058714267567319

Offset: 0

Author

Ilya Gutkovskiy, Feb 23 2022

Keywords

• nonn

Crossrefs

Cf. A009193, A009231, A009416, A191365, A351880.

Programs

Mathematica

nmax = 22; CoefficientList[Series[1/(1 - x)^Cosh[x], {x, 0, nmax}], x] Range[0, nmax]!

PARI

my(x='x+O('x^30)); Vec(serlaplace(1/(1-x)^cosh(x))) \\ Michel Marcus, Feb 23 2022

Formula

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1) * |A009416(k)| * a(n-k).

a(n) ~ n! * n^(cosh(1)-1) / Gamma(cosh(1)). - Vaclav Kotesovec, Feb 23 2022