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%I #12 Nov 21 2013 12:50:19
%S 1,1,5,25,207,1901,22323,295597,4554763,78201805,1499474883,
%T 31541086853,724817679171,18030594344725,483229053783115,
%U 13872831410796973,424869901099340235,13824490678644370109,476299421571109945971,17321461645693901532181,663085324931813890398355
%N E.g.f.: A(x) = 1/(3-exp(x)-exp(x^2)).
%F a(n) = n!*sum(k=1..n, sum(j=0..k, k!*sum(m=floor((k-j)/2)..(n-j)/2, (stirling2(n-2*m,j)*stirling2(m,k-j))/((n-2*m)!*(m!))))), n>0, a(0)=1.
%F a(n) ~ n!/((exp(r)+2*exp(r^2)*r)*r^(n+1)), where r = 0.522452131... is the root of the equation exp(r)+exp(r^2) = 3. - _Vaclav Kotesovec_, Jun 27 2013
%t CoefficientList[Series[1/(3-Exp[x]-Exp[x^2]),{x,0,30}],x] Range[0,30]! (* _Harvey P. Dale_, Aug 15 2011 *)
%o (Maxima)
%o a(n):=n!*if n=0 then 0 else sum(sum(k!*sum((stirling2(n-2*m,j)*stirling2(m,k-j))/((n-2*m)!*(m!)),m,floor((k-j)/2),(n-j)/2),j,0,k),k,1,n);
%K nonn
%O 0,3
%A _Vladimir Kruchinin_, Aug 10 2011
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