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 A361727 #15 Mar 22 2023 12:48:29
%S A361727 1,0,0,2,4,2,6,24,36,44,126,300,470,860,2080,4192,7420,15260,33124,
%T A361727 64568,124558,259632,535668,1055460,2118414,4373412,8872644,17765396,
%U A361727 36138168,73972404,149793424,303140552,618565948,1261454064,2561056212,5211145368
%N A361727 Diagonal of rational function 1/(1 - (1 + x*y) * (x^3 + y^3)).
%H A361727 Winston de Greef, <a href="/A361727/b361727.txt">Table of n, a(n) for n = 0..3162</a>
%F A361727 G.f.: 1/sqrt(1 - 4 * x^3 * (1+x)^2).
%F A361727 a(n) = Sum_{k=0..floor(n/3)} binomial(2*k,k) * binomial(2*k,n-3*k).
%F A361727 From _Vaclav Kotesovec_, Mar 22 2023: (Start)
%F A361727 Recurrence: n*a(n) = 2*(2*n-3)*a(n-3) + 8*(n-2)*a(n-4) + 2*(2*n-5)*a(n-5).
%F A361727 a(n) ~ 1 / (sqrt((5 - 8*r^3 - 8*r^4)*Pi*n) * r^n), where r = 0.484163615233802299545617907511361266999078019358842974840776720... is the real root of the equation -1 + 4*r^3 + 8*r^4 + 4*r^5 = 0. (End)
%o A361727 (PARI) a(n) = sum(k=0, n\3, binomial(2*k, k)*binomial(2*k, n-3*k));
%Y A361727 Cf. A137635, A361726.
%K A361727 nonn
%O A361727 0,4
%A A361727 _Seiichi Manyama_, Mar 22 2023