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 A191803 #7 Apr 19 2025 19:34:59
%S A191803 1,1,6,61,791,11701,188462,3225915,57840755,1076423857,20666351126,
%T A191803 407645638428,8237858879315,170229866493435,3592746391559133,
%U A191803 77393340642273491,1701286171473636404,38169860244429063080
%N A191803 G.f. satisfies: A(x) = Sum_{n>=0} x^n*A(x)^(5*n^2).
%F A191803 Let A = g.f. A(x), then A satisfies:
%F A191803 (1) A = Sum_{n>=0} x^n*A^(5*n)*Product_{k=1..n} (1-x*A^(20*k-15))/(1-x*A^(20*k-5));
%F A191803 (2) A = 1/(1- A^5*x/(1- A^5*(A^10-1)*x/(1- A^25*x/(1- A^15*(A^20-1)*x/(1- A^45*x/(1- A^25*(A^30-1)*x/(1- A^65*x/(1- A^35*(A^40-1)*x/(1- ...))))))))) (continued fraction);
%F A191803 due to a q-series identity and an identity of a partial elliptic theta function, respectively.
%e A191803 G.f.: A(x) = 1 + x + 6*x^2 + 61*x^3 + 791*x^4 + 11701*x^5 + 188462*x^6 +...
%e A191803 where the g.f. satisfies:
%e A191803 A(x) = 1 + x*A(x)^5 + x^2*A(x)^20 + x^3*A(x)^45 + x^4*A(x)^80 +...+ x^n*A(x)^(5*n^2) +...
%o A191803 (PARI) {a(n)=local(A=1+x);for(i=1,n,A=1+sum(m=1,n,x^m*(A+x*O(x^n))^(5*m^2)));polcoeff(A,n)}
%Y A191803 Cf. A107595, A191800, A191801, A191802, A191804.
%K A191803 nonn
%O A191803 0,3
%A A191803 _Paul D. Hanna_, Jun 16 2011