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 A365759 #11 Sep 18 2023 09:00:54
%S A365759 1,1,1,1,2,8,29,85,217,541,1471,4447,13975,43103,129083,382535,
%T A365759 1147956,3519462,10947483,34162483,106341406,330590764,1030528133,
%U A365759 3229411337,10170424724,32127163822,101633409379,321862281571,1020889305476,3244779281894,10335256815761
%N A365759 G.f. satisfies A(x) = 1 + x*A(x)*(1 + x^3*A(x)^5).
%F A365759 a(n) = Sum_{k=0..floor(n/4)} binomial(n-3*k,k) * binomial(n+2*k+1,n-3*k) / (n+2*k+1) = Sum_{k=0..floor(n/4)} binomial(n+2*k,6*k) * binomial(6*k,k) / (5*k+1).
%o A365759 (PARI) a(n) = sum(k=0, n\4, binomial(n-3*k, k)*binomial(n+2*k+1, n-3*k)/(n+2*k+1));
%Y A365759 Cf. A364472, A364523, A365760, A365761.
%Y A365759 Cf. A365757.
%K A365759 nonn
%O A365759 0,5
%A A365759 _Seiichi Manyama_, Sep 18 2023