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 A361753 #17 Mar 23 2023 19:32:11
%S A361753 1,2,6,20,74,276,1044,3994,15426,60008,234764,922716,3640700,14411952,
%T A361753 57210750,227659704,907853778,3627085932,14515139376,58174092472,
%U A361753 233463067284,938061587212,3773298437204,15193083455580,61230698571372,246978403761112
%N A361753 a(n) = Sum_{k=0..floor(n/3)} binomial(2*(n-3*k),k) * binomial(2*(n-3*k),n-3*k).
%C A361753 Diagonal of rational function 1/(1 - (1 + (x*y)^3) * (x + y)).
%H A361753 Seiichi Manyama, <a href="/A361753/b361753.txt">Table of n, a(n) for n = 0..1000</a>
%F A361753 G.f.: 1/sqrt(1 - 4*x*(1 + x^3)^2).
%F A361753 Recurrence: n*a(n) = 2*(2*n-1)*a(n-1) + 8*(n-2)*a(n-4) + 2*(2*n-7)*a(n-7). - _Vaclav Kotesovec_, Mar 23 2023
%o A361753 (PARI) a(n) = sum(k=0, n\3, binomial(2*(n-3*k), k)*binomial(2*(n-3*k), n-3*k));
%o A361753 (Python)
%o A361753 from math import comb
%o A361753 def A361753(n): return sum(comb(m:=(r:=n-3*k)<<1,k)*comb(m,r) for k in range(n//3+1)) # _Chai Wah Wu_, Mar 23 2023
%Y A361753 Cf. A137635, A361752.
%Y A361753 Cf. A360267.
%K A361753 nonn
%O A361753 0,2
%A A361753 _Seiichi Manyama_, Mar 23 2023