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 A364397 #19 Oct 21 2023 11:07:13
%S A364397 1,2,-12,124,-1560,21776,-324256,5046096,-81086112,1335113408,
%T A364397 -22408067200,381942129792,-6593494698752,115044039049728,
%U A364397 -2025580621035520,35943759448886528,-642162301086308864,11541259115333684224,-208521418711421405184
%N A364397 G.f. satisfies A(x) = 1 + x/A(x)^2*(1 + 1/A(x)^2).
%F A364397 G.f.: A(x) = 1/B(-x) where B(x) is the g.f. of A363311.
%F A364397 a(n) = (-1)^(n-1) * (1/n) * Sum_{k=0..n} binomial(n,k) * binomial(3*n+2*k-2,n-1) for n > 0.
%F A364397 a(n) ~ c*(-1)^(n+1)*27^n*4^(-n)*3F2([-n, 3*n/2, (3n-1)/2], [n, n+1/2], -1)*n^(-3/2), with c = 1/(3*sqrt(3*Pi)). - _Stefano Spezia_, Oct 21 2023
%o A364397 (PARI) a(n) = if(n==0, 1, (-1)^(n-1)*sum(k=0, n, binomial(n, k)*binomial(3*n+2*k-2, n-1))/n);
%Y A364397 Cf. A364393, A364395, A364399.
%Y A364397 Cf. A363311.
%K A364397 sign
%O A364397 0,2
%A A364397 _Seiichi Manyama_, Jul 22 2023