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 A360314 #10 Feb 03 2023 08:17:48
%S A360314 1,0,0,-2,-2,-2,4,10,16,2,-32,-86,-90,26,332,646,534,-690,-3040,-4934,
%T A360314 -2270,9066,27260,35198,532,-101946,-232752,-230730,158986,1039078,
%U A360314 1899364,1265370,-2714160,-9926158,-14625008,-4036358,34062386,89744810,104123084
%N A360314 a(n) = Sum_{k=0..floor(n/3)} (-1)^k * binomial(n-1-2*k,n-3*k) * binomial(2*k,k).
%F A360314 G.f.: 1 / sqrt(1+4*x^3/(1-x)).
%F A360314 n*a(n) = 2*(n-1)*a(n-1) - (n-2)*a(n-2) - 2*(2*n-3)*a(n-3) + 2*(2*n-6)*a(n-4).
%o A360314 (PARI) a(n) = sum(k=0, n\3, (-1)^k*binomial(n-1-2*k, n-3*k)*binomial(2*k, k));
%o A360314 (PARI) my(N=40, x='x+O('x^N)); Vec(1/sqrt(1+4*x^3/(1-x)))
%Y A360314 Cf. A360313, A360315.
%Y A360314 Cf. A360294, A360309.
%K A360314 sign
%O A360314 0,4
%A A360314 _Seiichi Manyama_, Feb 03 2023