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 A360293 #8 Feb 02 2023 10:44:42
%S A360293 1,2,6,18,58,194,662,2290,8002,28178,99830,355426,1270586,4557682,
%T A360293 16396454,59135458,213745922,774077986,2808105318,10202439858,
%U A360293 37118386490,135210620194,493082387766,1799998114770,6577045868866,24052649767730,88031695861590
%N A360293 a(n) = Sum_{k=0..floor(n/2)} (-1)^k * binomial(n-1-k,k) * binomial(2*n-4*k,n-2*k).
%F A360293 G.f.: 1 / sqrt(1-4*x/(1+x^2)).
%F A360293 n*a(n) = 2*(2*n-1)*a(n-1) - 2*(n-2)*a(n-2) + 2*(2*n-7)*a(n-3) - (n-4)*a(n-4).
%F A360293 a(n) ~ (1 + sqrt(3))^(2*n) / (3^(1/4) * sqrt(Pi*n) * 2^(n - 1/2)). - _Vaclav Kotesovec_, Feb 02 2023
%o A360293 (PARI) a(n) = sum(k=0, n\2, (-1)^k*binomial(n-1-k, k)*binomial(2*n-4*k, n-2*k));
%o A360293 (PARI) my(N=30, x='x+O('x^N)); Vec(1/sqrt(1-4*x/(1+x^2)))
%Y A360293 Cf. A360294, A360295.
%K A360293 nonn
%O A360293 0,2
%A A360293 _Seiichi Manyama_, Feb 01 2023