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%I #15 Jan 20 2015 12:53:30
%S 1,2,20,456,18192,1111840,96035136,11101474944,1651123634432,
%T 306656507699712,69472549405824000,18838618322988648448,
%U 6019938761233443262464,2237523930630521828745216
%N E.g.f. exp(x*tan(x)) (even powers only).
%H Vaclav Kotesovec, <a href="/A009252/b009252.txt">Table of n, a(n) for n = 0..238</a>
%F 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]
%F 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
%t Exp[ Tan[ x ]*x ] (* Even Part *)
%t 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 *)
%o (Maxima)
%o 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]
%Y Cf. A024263.
%K nonn
%O 0,2
%A _R. H. Hardin_
%E Extended and signs tested Mar 15 1997 by _Olivier Gérard_.
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