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

0,4

Links

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

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

Mathematica

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

Prog

(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
(Magma) m:=30; R<x>:=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

Crossrefs

Sequence in context: A273500 A189713 A162267 * A273540 A273214 A273276

Adjacent sequences: A009014 A009015 A009016 * A009018 A009019 A009020

Keyword

sign,easy

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Status

approved