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 A218294 #8 Nov 07 2024 15:21:05
%S A218294 1,2,10,82,866,10482,138698,1957346,29024642,448005922,7153738058,
%T A218294 117681081522,1988787934818,34465473701522,611806834645642,
%U A218294 11118408274591938,206835953956603394,3939803761941599042,76880490874588995978,1538019374456939130386
%N A218294 G.f. satisfies: A(x) = 1 + Sum_{n>=1} 2*x^n * A(x)^(2*n^2).
%C A218294 Given g.f. A(x), then Q = A(-x^2) satisfies:
%C A218294 Q = (1-x)*Sum_{n>=0} x^n*Product_{k=1..n} (1 - x*Q^(2*k))/(1 + x*Q^(2*k))
%C A218294 due to a q-series expansion for the Jacobi theta_4 function.
%e A218294 G.f.: A(x) = 1 + 2*x + 10*x^2 + 82*x^3 + 866*x^4 + 10482*x^5 + 138698*x^6 +...
%e A218294 where
%e A218294 A(x) = 1 + 2*x*A(x)^2 + 2*x^2*A(x)^8 + 2*x^3*A(x)^18 + 2*x^4*A(x)^32 + ...
%o A218294 (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))^(2*m^2))); polcoeff(A, n)}
%o A218294 for(n=0,30,print1(a(n),", "))
%Y A218294 Cf. A176719, A218295.
%K A218294 nonn
%O A218294 0,2
%A A218294 _Paul D. Hanna_, Oct 26 2012