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%I #4 Mar 30 2012 18:37:26
%S 1,1,4,28,251,2573,28813,343833,4308210,56154805,756731761,
%T 10499096630,149551069156,2182935186698,32613646656198,
%U 498420592612153,7790219357236805,124545937719356873,2037614647316548891,34134979366157116560
%N G.f. satisfies: A(x) = Sum_{n>=0} x^n*A(x)^(3*n^2).
%F Let A = g.f. A(x), then A satisfies:
%F (1) A = Sum_{n>=0} x^n*A^(3*n)*Product_{k=1..n} (1-x*A^(12*k-9))/(1-x*A^(12*k-3));
%F (2) A = 1/(1- A^3*x/(1- A^3*(A^6-1)*x/(1- A^15*x/(1- A^9*(A^12-1)*x/(1- A^27*x/(1- A^15*(A^18-1)*x/(1- A^39*x/(1- A^21*(A^24-1)*x/(1- ...))))))))) (continued fraction);
%F due to a q-series identity and an identity of a partial elliptic theta function, respectively.
%e G.f.: A(x) = 1 + x + 4*x^2 + 28*x^3 + 251*x^4 + 2573*x^5 + 28813*x^6 +...
%e where the g.f. satisfies:
%e A(x) = 1 + x*A(x)^3 + x^2*A(x)^12 + x^3*A(x)^27 + x^4*A(x)^48 +...+ x^n*A(x)^(3*n^2) +...
%o (PARI) {a(n)=local(A=1+x);for(i=1,n,A=1+sum(m=1,n,x^m*(A+x*O(x^n))^(3*m^2)));polcoeff(A,n)}
%Y Cf. A107595, A191800, A191802, A191803, A191804.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jun 16 2011
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