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 A361726 #23 Mar 23 2023 16:45:34
%S A361726 1,0,2,4,8,24,56,144,376,960,2512,6560,17184,45248,119296,315392,
%T A361726 835552,2217216,5893568,15687552,41810944,111567104,298016512,
%U A361726 796832256,2132456704,5711486976,15309014528,41062927360,110213725184,295995574272,795391639552
%N A361726 Diagonal of rational function 1/(1 - (1 + x*y) * (x^2 + y^2)).
%H A361726 Seiichi Manyama, <a href="/A361726/b361726.txt">Table of n, a(n) for n = 0..1000</a>
%F A361726 G.f.: 1/sqrt(1 - 4 * x^2 * (1+x)^2).
%F A361726 a(n) = Sum_{k=0..floor(n/2)} binomial(2*k,k) * binomial(2*k,n-2*k).
%F A361726 a(n) ~ (1 + sqrt(3))^(n + 1/2) / (2*3^(1/4)*sqrt(Pi*n)). - _Vaclav Kotesovec_, Mar 22 2023
%F A361726 n*a(n) = 2*(2*n-2)*a(n-2) + 4*(2*n-3)*a(n-3) + 2*(2*n-4)*a(n-4) for n > 3. - _Seiichi Manyama_, Mar 23 2023
%o A361726 (PARI) a(n) = sum(k=0, n\2, binomial(2*k, k)*binomial(2*k, n-2*k));
%Y A361726 Cf. A137635, A361727.
%Y A361726 Cf. A115962, A360266.
%K A361726 nonn
%O A361726 0,3
%A A361726 _Seiichi Manyama_, Mar 22 2023