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

0,4

Links

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

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 *)

Prog

(PARI) first(n) = x='x+O('x^n); Vec(serlaplace(cosh(exp(x)*x))) \\ Iain Fox, Dec 23 2017
(Magma) m:=30; R<x>:=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

Crossrefs

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

Sequence in context: A286433 A034559 A034347 * A327504 A346390 A323824

Adjacent sequences: A009118 A009119 A009120 * A009122 A009123 A009124

Keyword

nonn,easy

Author

R. H. Hardin

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

Status

approved