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 A363114 #5 May 15 2023 08:46:57
%S A363114 1,4,138,6571,353935,20694945,1276853497,81834405039,5395444806588,
%T A363114 363600236084796,24933767742193052,1734273108108910743,
%U A363114 122058422998192278797,8676376795137864622232,622018188741046650309066,44922343315319150402783783,3265215115112327274815579250
%N A363114 Expansion of g.f. A(x) satisfying 1 = Sum_{n=-oo..+oo} x^n * (2*A(x) - x^n)^(4*n-1).
%F A363114 Generating function A(x) = Sum_{n>=0} a(n)*x^n satisfies the following formulas.
%F A363114 (1) 1 = Sum_{n=-oo..+oo} x^n * (2*A(x) - x^n)^(4*n-1).
%F A363114 (2) -1 = Sum_{n=-oo..+oo} x^(4*n^2) / (1 - 2*A(x)*x^n)^(4*n+1).
%e A363114 G.f.: A(x) = 1 + 4*x + 138*x^2 + 6571*x^3 + 353935*x^4 + 20694945*x^5 + 1276853497*x^6 + 81834405039*x^7 + 5395444806588*x^8 + ...
%o A363114 (PARI) {a(n) = my(A=[1]); for(i=1, n, A=concat(A, 0);
%o A363114 A[#A] = polcoeff(-1 + sum(m=-#A, #A, x^m * (2*Ser(A) - x^m)^(4*m-1) ), #A-1)/2); A[n+1]}
%o A363114 for(n=0, 30, print1(a(n), ", "))
%o A363114 (PARI) {a(n) = my(A=[1]); for(i=1, n, A=concat(A, 0);
%o A363114 A[#A] = polcoeff(1 - sum(m=-#A, #A, x^(4*m^2)/(1 - 2*Ser(A)*x^m)^(4*m+1) ), #A-1)/2); A[n+1]}
%o A363114 for(n=0, 30, print1(a(n), ", "))
%Y A363114 Cf. A357227, A363112, A363113.
%Y A363114 Cf. A361774.
%K A363114 nonn
%O A363114 0,2
%A A363114 _Paul D. Hanna_, May 14 2023