%I
%S 1,1,3,9,33,137,619,3017,15617,84625,474771,2723721,15730209,89487257,
%T 482793211,2259370697,6292321025,41172399839,1066104760797,
%U 14517156416247,163539106749663,1652237279663959,15169567281615221
%N E.g.f. exp(sin(x)*exp(x)).
%F a(n)=2*sum(k=1..n, sum(j=0..(nk)/2, binomial(n,nk2*j)*(k^(nk2*j)*sum(i=0..k/2, (2*ik)^(k+2*j)*binomial(k,i)*(1)^(k+ji))))/(2^k*k!)), n>0, a(0)=1. [From Vladimir Kruchinin, Jun 13 2011]
%t Array[ SeriesCoefficient[ Series[ Exp[ Sin[ x ]*Exp[ x ] ], {x, 0, 30} ], # ]*#!&, 29, 0 ]
%o (Maxima)
%o a(n):=2*sum(sum(binomial(n,nk2*j)*(k^(nk2*j)*sum((2*ik)^(k+2*j)*binomial(k,i)*(1)^(k+ji),i,0,k/2)),j,0,(nk)/2)/(2^k*k!),k,1,n); [From Vladimir Kruchinin, Jun 13 2011]
%K sign,easy
%O 0,3
%A _R. H. Hardin_
%E Extended with signs Mar 15 1997 by _Olivier GĂ©rard_.
