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 A360294 #12 Feb 06 2023 18:56:28
%S A360294 1,2,6,20,68,240,864,3154,11628,43196,161430,606228,2285780,8647738,
%T A360294 32811378,124804104,475748330,1817005536,6951390372,26634502642,
%U A360294 102189927918,392559063268,1509684132394,5811772604124,22394185567728,86364110132930,333329513935842
%N A360294 a(n) = Sum_{k=0..floor(n/3)} (-1)^k * binomial(n-1-2*k,k) * binomial(2*n-6*k,n-3*k).
%H A360294 Seiichi Manyama, <a href="/A360294/b360294.txt">Table of n, a(n) for n = 0..1000</a>
%F A360294 G.f.: 1 / sqrt(1-4*x/(1+x^3)).
%F A360294 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).
%t A360294 CoefficientList[Series[1/Sqrt[1-4 x/(1+x^3)],{x,0,40}],x] (* _Harvey P. Dale_, Feb 06 2023 *)
%o A360294 (PARI) a(n) = sum(k=0, n\3, (-1)^k*binomial(n-1-2*k, k)*binomial(2*n-6*k, n-3*k));
%o A360294 (PARI) my(N=30, x='x+O('x^N)); Vec(1/sqrt(1-4*x/(1+x^3)))
%Y A360294 Cf. A360293, A360295.
%K A360294 nonn
%O A360294 0,2
%A A360294 _Seiichi Manyama_, Feb 01 2023