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 A360292 #17 May 01 2025 08:24:30
%S A360292 1,2,6,20,70,254,936,3492,13150,49882,190318,729576,2807816,10841962,
%T A360292 41983588,162973568,633994982,2471010742,9646981054,37718873700,
%U A360292 147676286078,578883674722,2271704404900,8923807316892,35087269756344,138075819924306
%N A360292 a(n) = Sum_{k=0..floor(n/4)} binomial(n-1-3*k,k) * binomial(2*n-8*k,n-4*k).
%H A360292 Seiichi Manyama, <a href="/A360292/b360292.txt">Table of n, a(n) for n = 0..1000</a>
%F A360292 G.f.: 1 / sqrt(1-4*x/(1-x^4)).
%F A360292 n*a(n) = 2*(2*n-1)*a(n-1) + 2*(n-4)*a(n-4) - 2*(2*n-13)*a(n-5) - (n-8)*a(n-8).
%F A360292 a(n) = A383582(n) - A383582(n-4). - _Seiichi Manyama_, May 01 2025
%o A360292 (PARI) a(n) = sum(k=0, n\4, binomial(n-1-3*k, k)*binomial(2*n-8*k, n-4*k));
%o A360292 (PARI) my(N=30, x='x+O('x^N)); Vec(1/sqrt(1-4*x/(1-x^4)))
%Y A360292 Cf. A085362, A360290, A360291.
%Y A360292 Cf. A360295, A383582.
%K A360292 nonn
%O A360292 0,2
%A A360292 _Seiichi Manyama_, Feb 01 2023