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 A363982 #49 Aug 06 2023 11:04:52
%S A363982 1,1,1,-1,-8,-16,16,195,491,-317,-6293,-18608,4610,230385,780625,
%T A363982 107615,-9028280,-34695607,-17401607,367885509,1598468196,1350497961,
%U A363982 -15317000747,-75391402496,-88375867528,643505487144,3611942077216,5376931884971
%N A363982 G.f. satisfies A(x) = 1 + x*A(x)^2 / (1 + x*A(x)^3).
%F A363982 a(n) = (1/n) * Sum_{k=0..n-1} (-1)^k * binomial(n,k) * binomial(2*n+k,n-1-k) for n > 0.
%o A363982 (PARI) a(n) = if(n==0, 1, sum(k=0, n-1, (-1)^k*binomial(n, k)*binomial(2*n+k, n-1-k))/n);
%Y A363982 Cf. A291534, A364051, A364764.
%Y A363982 Cf. A219537.
%K A363982 sign
%O A363982 0,5
%A A363982 _Seiichi Manyama_, Aug 05 2023