A009565 Expansion of e.g.f. sinh(exp(x)*x).

0, 1, 2, 4, 16, 96, 576, 3368, 20672, 141760, 1091200, 9098112, 79676928, 726208640, 6919738112, 69344336896, 731241201664, 8076031881216, 92856867250176, 1106883171037184, 13655807547883520, 174298975125127168, 2300708116863287296, 31372716744306524160

Offset: 0

Author

R. H. Hardin

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..541

Crossrefs

Cf. A009121.

Programs

Maple

a:= n-> add(`if`(k::odd, binomial(n, k)*k^(n-k), 0), k=0..n):
seq(a(n), n=0..25);  # Alois P. Heinz, Jan 15 2018

Mathematica

With[{nmax = 50}, CoefficientList[Series[Sinh[x*Exp[x]], {x, 0, nmax}], x]*Range[0, nmax]!] (* G. C. Greubel, Jan 21 2018 *)

PARI

x='x+O('x^30); concat([0], Vec(serlaplace(sinh(x*exp(x))))) \\ G. C. Greubel, Jan 21 2018

Extensions

Extended and signs tested by Olivier Gérard, Mar 15 1997