%I #15 Apr 01 2017 11:38:17
%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..(n-k)/2, binomial(n,n-k-2*j)*(k^(n-k-2*j)*sum(i=0..k/2, (2*i-k)^(k+2*j)*binomial(k,i)*(-1)^(k+j-i))))/(2^k*k!)), n>0, a(0)=1. - _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,n-k-2*j)*(k^(n-k-2*j)*sum((2*i-k)^(k+2*j)*binomial(k,i)*(-1)^(k+j-i),i,0,k/2)),j,0,(n-k)/2)/(2^k*k!),k,1,n); /* _Vladimir Kruchinin_, Jun 13 2011 */
%K sign,easy
%O 0,3
%A _R. H. Hardin_
%E Extended with signs by _Olivier GĂ©rard_, Mar 15 1997