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 A365250 #8 Aug 29 2023 08:57:47
%S A365250 1,1,3,13,67,379,2271,14158,90875,596506,3985661,27018149,185356123,
%T A365250 1284502886,8978432666,63225825415,448131632123,3194452061366,
%U A365250 22886882317758,164718040282975,1190311371951321,8633251770618136,62825467894307447
%N A365250 G.f. satisfies A(x) = 1 + x*A(x)^3/(1 - x^2*A(x)^6).
%F A365250 a(n) = (1/(3*n+1)) * Sum_{k=0..floor(n/2)} binomial(n-k-1,k) * binomial(3*n+1,n-2*k).
%t A365250 a[n_]:=Sum[Binomial[n-k-1,k]*Binomial[3*n+1,n-2*k],{k,0,Floor[n/2]}]/(3*n+1); Table[a[n],{n,0,22}] (* _Robert P. P. McKone_, Aug 29 2023 *)
%o A365250 (PARI) a(n) = sum(k=0, n\2, binomial(n-k-1, k)*binomial(3*n+1, n-2*k))/(3*n+1);
%Y A365250 Cf. A101785, A365246.
%Y A365250 Cf. A002293.
%K A365250 nonn
%O A365250 0,3
%A A365250 _Seiichi Manyama_, Aug 28 2023