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A009121
Expansion of e.g.f. cosh(exp(x)*x).
7
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
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
KEYWORD
nonn,easy
AUTHOR
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