This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A191804 #7 Apr 19 2025 19:36:30
%S A191804 1,1,7,82,1221,20718,382315,7489683,153551487,3264643144,71545452946,
%T A191804 1609541143713,37065029428453,872037022019930,20935244357544798,
%U A191804 512498682139660135,12790021472251565047,325439165493879484025
%N A191804 G.f. satisfies: A(x) = Sum_{n>=0} x^n*A(x)^(6*n^2).
%F A191804 Let A = g.f. A(x), then A satisfies:
%F A191804 (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 A191804 (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 A191804 due to a q-series identity and an identity of a partial elliptic theta function, respectively.
%e A191804 G.f.: A(x) = 1 + x + 7*x^2 + 82*x^3 + 1221*x^4 + 20718*x^5 + 382315*x^6 +...
%e A191804 where the g.f. satisfies:
%e A191804 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 A191804 (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 A191804 Cf. A107595, A191800, A191801, A191802, A191803.
%K A191804 nonn
%O A191804 0,3
%A A191804 _Paul D. Hanna_, Jun 16 2011