%I #16 Jun 05 2019 09:28:36
%S 1,0,1,1,6,20,95,525,2975,20300,143640,1131900,9548385,86096010,
%T 831475645,8488104625,91828436700,1045926081200,12517301471675,
%U 157022728337475,2058625791347125,28160968442356750,401055626173702500,5936491984459286250
%N E.g.f. exp(exp(1/2*x^2+1/6*x^3)-1).
%F a(n)=n!*sum(m=1..n, sum(k=m..n, (stirling2(k,m)*binomial(k,n-2*k)*3^(2*k-n)*2^(-k))/k!)), n>0, a(0)=1.
%o (Maxima)
%o a(n):=n!*sum(sum((stirling2(k,m)*binomial(k,n-2*k)*3^(2*k-n)*2^(-k))/k!,k,m,n),m,1,n);
%K nonn
%O 0,5
%A _Vladimir Kruchinin_, Jun 05 2011