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 A363140 #11 May 17 2023 12:48:22
%S A363140 1,2,5,20,86,396,1887,9277,46748,240189,1253474,6625814,35401302,
%T A363140 190878795,1037296173,5675580349,31240459117,172871809365,
%U A363140 961124621229,5366264076784,30076030970681,169149177823245,954301797559301,5399467787889483,30631118027908197
%N A363140 Expansion of g.f. A(x) satisfying 2 = Sum_{n=-oo..+oo} (-1)^n * x^n * (A(x) + x^(2*n))^(2*n+1).
%H A363140 Paul D. Hanna, <a href="/A363140/b363140.txt">Table of n, a(n) for n = 0..300</a>
%F A363140 G.f. A(x) = Sum_{n>=0} a(n)*x^n satisfies the following.
%F A363140 (1) 2 = Sum_{n=-oo..+oo} (-1)^n * x^n * (A(x) + x^(2*n))^(2*n+1).
%F A363140 (2) 2 = Sum_{n=-oo..+oo} (-1)^n * x^(n*(4*n-3)) / (1 + A(x)*x^(2*n))^(2*n-1).
%e A363140 G.f.: A(x) = 1 + 2*x + 5*x^2 + 20*x^3 + 86*x^4 + 396*x^5 + 1887*x^6 + 9277*x^7 + 46748*x^8 + 240189*x^9 + 1253474*x^10 + ...
%o A363140 (PARI) {a(n) = my(A=[1]); for(i=1,n, A = concat(A,0);
%o A363140 A[#A] = polcoeff(2 - sum(m=-#A, #A, (-1)^m * x^m * (Ser(A) + x^(2*m))^(2*m+1) ),#A-1));A[n+1]}
%o A363140 for(n=0,30,print1(a(n),", "))
%Y A363140 Cf. A357232.
%K A363140 nonn
%O A363140 0,2
%A A363140 _Paul D. Hanna_, May 17 2023