A009252 E.g.f. exp(x*tan(x)) (even powers only).

1, 2, 20, 456, 18192, 1111840, 96035136, 11101474944, 1651123634432, 306656507699712, 69472549405824000, 18838618322988648448, 6019938761233443262464, 2237523930630521828745216, 956638251655236579066724352, 465986443313532664723710443520, 256462409164406988067105270726656

Offset: 0

Author

R. H. Hardin

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..238

Crossrefs

Cf. A024263.

Programs

Mathematica

Exp[ Tan[ x ]*x ] (* Even Part *)
With[{nn=40},Take[CoefficientList[Series[Exp[Tan[x]*x],{x,0,nn}],x]*Range[0,nn]!,{1,-1,2}]] (* Vaclav Kotesovec, Jan 20 2015 *)

Maxima

a(n):=sum((binomial(2*n,k)*sum(binomial(j-1,k-1)*j!*(-1)^(n+j)*2^(2*n-k-j)*stirling2(2*n-k,j),j,k,2*n-k)),k,1,n); /* Vladimir Kruchinin, Jun 06 2011 */

Formula

a(n)=sum(k=1..n, (binomial(2*n,k)*sum(j=k..2*n-k, binomial(j-1,k-1)*j!*(-1)^(n+j)*2^(2*n-k-j)*stirling2(2*n-k,j)))), n>0, a(0)=1. - Vladimir Kruchinin, Jun 06 2011

a(n) ~ n^(2*n-1/4) * 2^(4*n+1/4) * exp(2*sqrt(2*n)-2*n-1/2) / Pi^(2*n) * (1 - (Pi^2-1)/(12*sqrt(2*n))). - Vaclav Kotesovec, Jan 20 2015

Extensions

Extended and signs tested Mar 15 1997 by Olivier Gérard.