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A191804 G.f. satisfies: A(x) = Sum_{n>=0} x^n*A(x)^(6*n^2). 4

%I

%S 1,1,7,82,1221,20718,382315,7489683,153551487,3264643144,71545452946,

%T 1609541143713,37065029428453,872037022019930,20935244357544798,

%U 512498682139660135,12790021472251565047,325439165493879484025

%N G.f. satisfies: A(x) = Sum_{n>=0} x^n*A(x)^(6*n^2).

%F Let A = g.f. A(x), then A satisfies:

%F (1) A = Sum_{n>=0} x^n*A^(6*n)*Product_{k=1..n} (1-x*A^(24*k-18))/(1-x*A^(24*k-6));

%F (2) A = 1/(1- A^6*x/(1- A^6*(A^12-1)*x/(1- A^30*x/(1- A^18*(A^24-1)*x/(1- A^54*x/(1- A^30*(A^36-1)*x/(1- A^78*x/(1- A^42*(A^48-1)*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 + 7*x^2 + 82*x^3 + 1221*x^4 + 20718*x^5 + 382315*x^6 +...

%e where the g.f. satisfies:

%e A(x) = 1 + x*A(x)^6 + x^2*A(x)^24 + x^3*A(x)^54 + x^4*A(x)^96 +...+ x^n*A(x)^(6*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))^(6*m^2)));polcoeff(A,n)}

%Y Cf. A107595, A191800, A191801, A191802, A191803.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Jun 16 2011

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Last modified September 19 17:40 EDT 2020. Contains 337179 sequences. (Running on oeis4.)