A009233 Expansion of e.g.f. exp(sinh(x)*x) (even powers only).

1, 2, 16, 246, 5944, 202330, 9099564, 517447126, 36048776656, 3003924569778, 293835907664980, 33232296062419630, 4291773869167401720, 626311538509296801226, 102365694283336181089084, 18595053487766135171539590, 3729223211361742071603266464

Offset: 0

Author

R. H. Hardin

Keywords

• nonn

Crossrefs

Cf. A009214, A352254.

Programs

Mathematica

With[{nn=30},Take[CoefficientList[Series[Exp[Sinh[x]*x],{x,0,nn}],x] Range[0,nn]!,{1,-1,2}]] (* Harvey P. Dale, Jul 31 2020 *)

PARI

my(x='x+O('x^40), v=Vec(serlaplace(exp(sinh(x)*x)))); vector(#v\2, k, v[2*k-1]) \\ Michel Marcus, Mar 10 2022

Formula

a(0) = 1; a(n) = 2 * Sum_{k=1..n} binomial(2*n-1,2*k-1) * k * a(n-k). - Ilya Gutkovskiy, Mar 10 2022

Extensions

Extended and signs tested by Olivier Gérard, Mar 15 1997

Previous Mathematica program replaced by Harvey P. Dale, Jul 31 2020