%I #6 Aug 24 2012 10:36:09
%S 1,1,0,6,12,100,780,-1092,43344,48816,1264320,24662880,-162851040,
%T 4327633440,-17686783296,275230488960,3743721112320,-70886371933440,
%U 2127136959383040,-25991855154846720,402985066993459200
%N E.g.f. (1+x)^(1+x^2+x^4)
%F a(n)=sum(k=1..n, sum(i=0..(n-k)/2, ((sum(j=0..k, binomial(j,i-j)*binomial(k,j)))*stirling1(n-2*i,k))/(n-2*i)!)), n>0, a(0)=1.
%t With[{nn=20},CoefficientList[Series[(1+x)^(1+x^2+x^4),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Aug 24 2012 *)
%o (Maxima)
%o a(n):=sum(sum(((sum(binomial(j,i-j)*binomial(k,j),j,0,k))*stirling1(n-2*i,k))/(n-2*i)!,i,0,(n-k)/2),k,1,n);
%K sign
%O 0,4
%A _Vladimir Kruchinin_, Jun 02 2011