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 A365761 #12 Sep 18 2023 09:00:48
%S A365761 1,1,1,2,8,29,91,289,1009,3706,13606,49822,184726,696052,2648746,
%T A365761 10132072,38952970,150635860,585724594,2287631614,8968247626,
%U A365761 35281363830,139256375922,551306272137,2188516471579,8709331962133,34739262293455,138863195368540
%N A365761 G.f. satisfies A(x) = 1 + x*A(x)*(1 + x^2*A(x)^5).
%F A365761 a(n) = Sum_{k=0..floor(n/3)} binomial(n-2*k,k) * binomial(n+3*k+1,n-2*k) / (n+3*k+1) = Sum_{k=0..floor(n/3)} binomial(n+3*k,6*k) * binomial(6*k,k) / (5*k+1).
%o A365761 (PARI) a(n) = sum(k=0, n\3, binomial(n-2*k, k)*binomial(n+3*k+1, n-2*k)/(n+3*k+1));
%Y A365761 Cf. A364472, A364523, A365759, A365760.
%Y A365761 Cf. A365693.
%K A365761 nonn
%O A365761 0,4
%A A365761 _Seiichi Manyama_, Sep 18 2023