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 A360291 #18 May 01 2025 08:24:38
%S A360291 1,2,6,20,72,264,984,3714,14148,54284,209482,812196,3161340,12345658,
%T A360291 48348522,189807336,746740510,2943359208,11620961412,45950375602,
%U A360291 181936110006,721233025332,2862271873966,11370584735100,45212101270728,179926167512914
%N A360291 a(n) = Sum_{k=0..floor(n/3)} binomial(n-1-2*k,k) * binomial(2*n-6*k,n-3*k).
%H A360291 Seiichi Manyama, <a href="/A360291/b360291.txt">Table of n, a(n) for n = 0..1000</a>
%F A360291 G.f.: 1 / sqrt(1-4*x/(1-x^3)).
%F A360291 n*a(n) = 2*(2*n-1)*a(n-1) + 2*(n-3)*a(n-3) - 2*(2*n-10)*a(n-4) - (n-6)*a(n-6).
%F A360291 a(n) = A383581(n) - A383581(n-3). - _Seiichi Manyama_, May 01 2025
%o A360291 (PARI) a(n) = sum(k=0, n\3, binomial(n-1-2*k, k)*binomial(2*n-6*k, n-3*k));
%o A360291 (PARI) my(N=30, x='x+O('x^N)); Vec(1/sqrt(1-4*x/(1-x^3)))
%Y A360291 Cf. A085362, A360290, A360292.
%Y A360291 Cf. A360186, A360294, A383581.
%K A360291 nonn
%O A360291 0,2
%A A360291 _Seiichi Manyama_, Feb 01 2023