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%I #15 Feb 25 2014 03:56:50
%S 1,1,3,19,225,4801,185523,13298659,1815718305,481790947681,
%T 251592291767043,260427247041910099,536497603929547755585,
%U 2204489516030261302702561,18090090482887693483393912563,296659627048147988400872084439139
%N a(n) = Sum_{k=0..n-1} C(n-1,k)*a(k)*a(n-1-k)*2^k for n>0, with a(0)=1.
%C Generated by a generalization of a recurrence for the factorials.
%H Vincenzo Librandi, <a href="/A126444/b126444.txt">Table of n, a(n) for n = 0..80</a>
%F a(n) = Sum_{k=0..n*(n-1)/2} A126470(n,k)*2^k.
%F E.g.f. satisfies: A'(x) = A(x)*A(2x) with A(0)=1; the logarithmic derivative of e.g.f. A(x) equals A(2x). - _Paul D. Hanna_, Nov 22 2008
%F a(n) ~ c * 2^(n*(n-1)/2), where c = 7.32081762965209017732559... - _Vaclav Kotesovec_, Feb 23 2014
%t b = ConstantArray[0,21]; b[[1]]=1; b[[2]]=1; Do[b[[n+1]] = Sum[Binomial[n-1,k]*b[[k+1]]*b[[n-k]]*2^k,{k,0,n-1}],{n,2,20}]; b (* _Vaclav Kotesovec_, Feb 23 2014 *)
%o (PARI) a(n)=if(n==0,1,sum(k=0,n-1,binomial(n-1,k)*a(k)*a(n-1-k)*2^k))
%o (PARI) {a(n)=local(A=1+x);for(i=0,n,A=1+intformal(A*subst(A,x,2*x+x*O(x^n))));n!*polcoeff(A,n,x)} \\ _Paul D. Hanna_, Nov 22 2008
%Y Cf. A126470.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jan 01 2007
%E More terms from _Vincenzo Librandi_, Feb 25 2014
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