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%I #4 Nov 23 2018 07:47:41
%S 1,1,3,7,25,80,342,1818,11502,86626,707359,6202212,57655266,563021626,
%T 5762459074,61582852498,685183190074,7919267757340,94878751361581,
%U 1176171409288897,15062758843882271,198997851380457874,2708587403764115335,37938389537270197751,546245195916221529029,8076733428378707580710,122523819509730133116908,1905311108531544568628670
%N G.f.: A(x) = Sum_{n>=0} x^n * (1+x)^(3*n^2) / A(x)^(n^2).
%C Note that if G(x) = Sum_{n>=0} x^n * (1+x)^(2*n^2) / G(x)^(n^2), then G(x) has negative coefficients.
%H Paul D. Hanna, <a href="/A321606/b321606.txt">Table of n, a(n) for n = 0..200</a>
%e G.f.: A(x) = 1 + x + 3*x^2 + 7*x^3 + 25*x^4 + 80*x^5 + 342*x^6 + 1818*x^7 + 11502*x^8 + 86626*x^9 + 707359*x^10 + 6202212*x^11 + 57655266*x^12 + ...
%e such that
%e A(x) = 1 + x*(1+x)^3/A(x) + x^2*(1+x)^12/A(x)^4 + x^3*(1+x)^27/A(x)^9 + x^4*(1+x)^48/A(x)^16 + x^5*(1+x)^75/A(x)^25 + x^6*(1+x)^108/A(x)^36 + ...
%o (PARI) {a(n) = my(A=[1]); for(i=1,n, A=concat(A,0); A[#A] = polcoeff( sum(n=0,#A,x^n*(1+x +x*O(x^#A))^(4*n^2)/Ser(A)^(n^2+1) ),#A-1) );A[n+1]}
%o for(n=0,30, print1(a(n),", "))
%K nonn
%O 0,3
%A _Paul D. Hanna_, Nov 23 2018
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