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 A361772 #11 Apr 22 2025 21:56:01
%S A361772 1,1,8,61,600,6072,65804,733435,8415694,98529785,1173278329,
%T A361772 14162417506,172914841649,2131621288494,26495818020038,
%U A361772 331706510158239,4178800564364333,52935845003315662,673878770026778330,8616336680850069832,110606714769468383785,1424933340070339610543
%N A361772 Expansion of g.f. A(x) satisfying 1 = Sum_{n=-oo..+oo} x^n * (2*A(x) - (-x)^n)^(2*n-1).
%H A361772 Paul D. Hanna, <a href="/A361772/b361772.txt">Table of n, a(n) for n = 0..300</a>
%F A361772 G.f. A(x) = Sum_{n>=0} a(n)*x^n may be defined by the following.
%F A361772 (1) 1 = Sum_{n=-oo..+oo} x^n * (2*A(x) - (-x)^n)^(2*n-1).
%F A361772 (2) 1 = Sum_{n=-oo..+oo} (-1)^(n+1) * x^(2*n^2) / (1 - 2*A(x)*(-x)^n)^(2*n+1).
%e A361772 G.f.: A(x) = 1 + x + 8*x^2 + 61*x^3 + 600*x^4 + 6072*x^5 + 65804*x^6 + 733435*x^7 + 8415694*x^8 + 98529785*x^9 + 1173278329*x^10 + ...
%o A361772 (PARI) {a(n) = my(A=[1]); for(i=1, n, A=concat(A, 0);
%o A361772 A[#A] = polcoeff( sum(m=-#A, #A, x^m * (2*Ser(A) - (-x)^m)^(2*m-1) ), #A-1)/2); A[n+1]}
%o A361772 for(n=0, 30, print1(a(n), ", "))
%Y A361772 Cf. A361771, A361773, A361774.
%Y A361772 Cf. A363112, A355865, A357227, A359712, A357232.
%K A361772 nonn
%O A361772 0,3
%A A361772 _Paul D. Hanna_, May 13 2023