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 A365757 #8 Sep 18 2023 08:59:18
%S A365757 1,1,1,1,2,8,29,86,229,619,1836,5846,18802,59356,185187,581476,
%T A365757 1855412,5997965,19491730,63395718,206433172,674452128,2213463944,
%U A365757 7293253791,24098638133,79791002807,264698873350,879945619711,2931486913728,9785457123420,32721317536787
%N A365757 G.f. satisfies A(x) = 1 + x*A(x) / (1 - x^3*A(x)^5).
%F A365757 a(n) = Sum_{k=0..floor(n/3)} binomial(n-2*k-1,k) * binomial(n+2*k+1,n-3*k) / (n+2*k+1).
%o A365757 (PARI) a(n) = sum(k=0, n\3, binomial(n-2*k-1, k)*binomial(n+2*k+1, n-3*k)/(n+2*k+1));
%Y A365757 Cf. A023432, A212383, A365243, A365756.
%Y A365757 Cf. A365695, A365759.
%K A365757 nonn
%O A365757 0,5
%A A365757 _Seiichi Manyama_, Sep 18 2023