A009121 Expansion of e.g.f. cosh(exp(x)*x).

1, 0, 1, 6, 25, 100, 481, 2954, 20721, 151848, 1146721, 9111982, 77652169, 710421452, 6891125697, 69961213170, 738718169569, 8108554524112, 92647353941569, 1101958783026134, 13616813607795321, 174287243264606388, 2304515271134124577, 31424734896799742170

Offset: 0

Author

R. H. Hardin

Keywords

• nonn
• easy

Links

• Iain Fox, Table of n, a(n) for n = 0..541

Crossrefs

Cf. A000248, A009017, A009448, A009565, A009635, A009768.

Programs

Magma

m:=30; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Cosh(x*Exp(x)))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Jul 26 2018

Maple

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

Mathematica

With[{nn=30},CoefficientList[Series[Cosh[Exp[x]*x],{x,0,nn}],x] Range[ 0,nn]!] (* Harvey P. Dale, Dec 28 2015 *)

PARI

first(n) = x='x+O('x^n); Vec(serlaplace(cosh(exp(x)*x))) \\ Iain Fox, Dec 23 2017

Extensions

Extended and signs tested by Olivier Gérard, Mar 15 1997

Definition clarified and prior Mathematica program replaced by Harvey P. Dale, Dec 28 2015