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 A191802 #7 Apr 19 2025 19:36:25
%S A191802 1,1,5,43,473,5942,81393,1186342,18132473,287948903,4722077279,
%T A191802 79636530163,1377304530677,24382127678100,441294262119031,
%U A191802 8160739579770316,154169018332135841,2975846752734820345,58718914018159811186
%N A191802 G.f. satisfies: A(x) = Sum_{n>=0} x^n*A(x)^(4*n^2).
%F A191802 Let A = g.f. A(x), then A satisfies:
%F A191802 (1) A = Sum_{n>=0} x^n*A^(4*n)*Product_{k=1..n} (1-x*A^(16*k-12))/(1-x*A^(16*k-4));
%F A191802 (2) A = 1/(1- A^4*x/(1- A^4*(A^8-1)*x/(1- A^20*x/(1- A^12*(A^16-1)*x/(1- A^36*x/(1- A^20*(A^24-1)*x/(1- A^52*x/(1- A^28*(A^32-1)*x/(1- ...))))))))) (continued fraction);
%F A191802 due to a q-series identity and an identity of a partial elliptic theta function, respectively.
%e A191802 G.f.: A(x) = 1 + x + 5*x^2 + 43*x^3 + 473*x^4 + 5942*x^5 + 81393*x^6 +...
%e A191802 where the g.f. satisfies:
%e A191802 A(x) = 1 + x*A(x)^4 + x^2*A(x)^16 + x^3*A(x)^36 + x^4*A(x)^64 +...+ x^n*A(x)^(4*n^2) +...
%o A191802 (PARI) {a(n)=local(A=1+x);for(i=1,n,A=1+sum(m=1,n,x^m*(A+x*O(x^n))^(4*m^2)));polcoeff(A,n)}
%Y A191802 Cf. A107595, A191800, A191801, A191803, A191804.
%K A191802 nonn
%O A191802 0,3
%A A191802 _Paul D. Hanna_, Jun 16 2011