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 A355865 #11 Oct 30 2023 12:07:03
%S A355865 1,3,25,254,2844,34031,426498,5526399,73433377,995167783,13701794657,
%T A355865 191122323160,2695092314319,38357425655599,550268824751092,
%U A355865 7948720164361366,115517358604881329,1687796954715824015,24777722054035138573,365305177280838473896
%N A355865 Expansion of g.f. A(x) satisfying 0 = Sum_{n=-oo..+oo} x^n * (x^n - (-1)^n*2*A(x))^(2*n+1).
%C A355865 Compare to the identity: 0 = Sum_{n=-oo..+oo} x^n * (y - x^n)^n which holds for all y.
%H A355865 Paul D. Hanna, <a href="/A355865/b355865.txt">Table of n, a(n) for n = 0..200</a>
%F A355865 G.f. A(x) = Sum_{n>=0} a(n)*x^n satisfies the following formulas.
%F A355865 (1) 0 = Sum_{n=-oo..+oo} (-x)^n * ((-x)^n - 2*A(x))^(2*n+1).
%F A355865 (2) 0 = Sum_{n=-oo..+oo} x^(2*n*(n-1)) / (1 - 2*A(x)*(-x)^n)^(2*n-1).
%e A355865 G.f.: A(x) = 1 + 3*x + 25*x^2 + 254*x^3 + 2844*x^4 + 34031*x^5 + 426498*x^6 + 5526399*x^7 + 73433377*x^8 + 995167783*x^9 + 13701794657*x^10 + ...
%o A355865 (PARI) {a(n) = my(A=[1]); for(i=1,n, A=concat(A,0);
%o A355865 A[#A] = polcoeff( sum(m=-#A,#A, x^m * (x^m - (-1)^m*2*Ser(A))^(2*m+1) ), #A-1)/2);A[n+1]}
%o A355865 for(n=0,20,print1(a(n),", "))
%Y A355865 Cf. A355866.
%K A355865 nonn
%O A355865 0,2
%A A355865 _Paul D. Hanna_, Aug 04 2022