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 A191800 #7 Apr 19 2025 19:36:14
%S A191800 1,1,3,16,109,851,7275,66393,637239,6371848,65961782,703953599,
%T A191800 7722738071,86924392498,1002603956938,11842465020207,143208130730229,
%U A191800 1773099186411938,22483740028949531,292129222113885503,3891268435685371911
%N A191800 G.f. satisfies: A(x) = Sum_{n>=0} x^n*A(x)^(2*n^2).
%F A191800 Let A = g.f. A(x), then A satisfies:
%F A191800 (1) A = Sum_{n>=0} x^n*A^(2*n)*Product_{k=1..n} (1-x*A^(8*k-6))/(1-x*A^(8*k-2));
%F A191800 (2) A = 1/(1- A^2*x/(1- A^2*(A^4-1)*x/(1- A^10*x/(1- A^6*(A^8-1)*x/(1- A^18*x/(1- A^10*(A^12-1)*x/(1- A^26*x/(1- A^14*(A^16-1)*x/(1- ...))))))))) (continued fraction);
%F A191800 due to a q-series identity and an identity of a partial elliptic theta function, respectively.
%e A191800 G.f.: A(x) = 1 + x + 3*x^2 + 16*x^3 + 109*x^4 + 851*x^5 + 7275*x^6 +...
%e A191800 where the g.f. satisfies:
%e A191800 A(x) = 1 + x*A(x)^2 + x^2*A(x)^8 + x^3*A(x)^18 + x^4*A(x)^32 +...+ x^n*A(x)^(2*n^2) +...
%o A191800 (PARI) {a(n)=local(A=1+x);for(i=1,n,A=1+sum(m=1,n,x^m*(A+x*O(x^n))^(2*m^2)));polcoeff(A,n)}
%Y A191800 Cf. A107595, A191801, A191802, A191803, A191804.
%K A191800 nonn
%O A191800 0,3
%A A191800 _Paul D. Hanna_, Jun 16 2011