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 A218295 #6 Apr 15 2025 14:17:40
%S A218295 1,2,14,158,2274,37410,670670,12786622,255519106,5302716866,
%T A218295 113586849614,2501007496542,56446396937186,1303401799574242,
%U A218295 30756416720161422,741216834445478270,18240706372460480002,458484823574294544770,11776969626284389958030
%N A218295 G.f. satisfies: A(x) = 1 + Sum_{n>=1} 2*x^n * A(x)^(3*n^2).
%C A218295 Given g.f. A(x), then Q = A(-x^2) satisfies:
%C A218295 Q = (1-x)*Sum_{n>=0} x^n*Product_{k=1..n} (1 - x*Q^(3*k))/(1 + x*Q^(3*k))
%C A218295 due to a q-series expansion for the Jacobi theta_4 function.
%e A218295 G.f.: A(x) = 1 + 2*x + 14*x^2 + 158*x^3 + 2274*x^4 + 37410*x^5 +...
%e A218295 where
%e A218295 A(x) = 1 + 2*x*A(x)^3 + 2*x^2*A(x)^12 + 2*x^3*A(x)^27 + 2*x^4*A(x)^48 + ...
%o A218295 (PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+sum(m=1, n, 2*x^m*(A+x*O(x^n))^(3*m^2))); polcoeff(A, n)}
%o A218295 for(n=0,30,print1(a(n),", "))
%Y A218295 Cf. A176719, A218294.
%K A218295 nonn
%O A218295 0,2
%A A218295 _Paul D. Hanna_, Oct 26 2012