A009017 Expansion of e.g.f. cos(x*exp(x)).

1, 0, -1, -6, -23, -60, -1, 1526, 15121, 106344, 579359, 1870418, -8716487, -251210388, -3217413473, -31518844530, -245728084447, -1260370850736, 3075924210623, 208464730479658, 3846319817704841, 52691292058337940

Offset: 0

Author

R. H. Hardin

Keywords

• sign
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..250

Programs

Magma

m:=30; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Cos(x*Exp(x)))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Jul 21 2018

Mathematica

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

Maxima

a(n):=if n=0 then 1 else sum(binomial(n,2*k)*(2*k)^(n-2*k)*(-1)^k,k,0,n/2); /* Vladimir Kruchinin, Jun 29 2011 */

PARI

x='x+O('x^30); Vec(serlaplace(cos(x*exp(x)))) \\ G. C. Greubel, Jul 21 2018

Formula

a(n) = Sum_{k=0..n/2} binomial(n,2*k)*(2*k)^(n-2*k)*(-1)^k, n>0, a(0)=1. - Vladimir Kruchinin, Jun 29 2011

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997