A009214 E.g.f. exp(x*sin(x)) (even powers only).

1, 2, 8, 6, -792, -10790, 281940, 13531350, -260660176, -33714262350, 550333492140, 158933551076014, -2777269276818168, -1301993178430302774, 33725324008920743108, 17091479764089813623430

Offset: 0

Author

R. H. Hardin

Keywords

• sign

Crossrefs

Cf. A009233.

Programs

Mathematica

nmax = 30; Take[CoefficientList[Series[Exp[x Sin[x]], {x, 0, nmax}], x] Range[0, nmax]!, {1, -1, 2}]

Maxima

a(n):=sum(binomial(2*n,k)*(sum((2*i-k)^(2*n-k)*binomial(k,i)*(-1)^(n-i),i,0,k/2))/(2^(k-1)),k,1,n); /* Vladimir Kruchinin, Jun 06 2011 */

PARI

my(x='x+O('x^40), v=Vec(serlaplace(exp(x*sin(x))))); vector(#v\2, k, v[2*k-1]) \\ Michel Marcus, Mar 10 2022

Formula

a(n)=sum(k=1..n, binomial(2*n,k)*(i=0..k/2, sum((2*i-k)^(2*n-k)*binomial(k,i)*(-1)^(n-i)))/(2^(k-1))). - Vladimir Kruchinin, Jun 06 2011

a(0) = 1; a(n) = 2 * Sum_{k=1..n} (-1)^(k+1) * binomial(2*n-1,2*k-1) * k * a(n-k). - Ilya Gutkovskiy, Mar 10 2022

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997