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 A360219 #42 Jul 13 2024 13:47:05
%S A360219 1,2,6,20,68,240,864,3152,11616,43136,161152,604992,2280416,8624832,
%T A360219 32714688,124399488,474066560,1810053120,6922776576,26517173760,
%U A360219 101710338048,390603984896,1501732753408,5779500226560,22263437981184,85835254221824,331193445626880
%N A360219 a(n) = Sum_{k=0..floor(n/4)} (-1)^k * binomial(n-3*k,k) * binomial(2*(n-3*k),n-3*k).
%C A360219 Diagonal of rational function 1/(1 - x - y + x^4*y^3). - _Seiichi Manyama_, Mar 23 2023
%H A360219 Seiichi Manyama, <a href="/A360219/b360219.txt">Table of n, a(n) for n = 0..1000</a>
%F A360219 G.f.: 1/sqrt(1 - 4*x*(1 - x^3)).
%F A360219 n*a(n) = 2*(2*n-1)*a(n-1) - 2*(2*n-4)*a(n-4).
%p A360219 A360219 := proc(n)
%p A360219 add((-1)^k*binomial(n-3*k,k)*binomial(2*(n-3*k),n-3*k),k=0..n/3) ;
%p A360219 end proc:
%p A360219 seq(A360219(n),n=0..70) ; # _R. J. Mathar_, Mar 12 2023
%o A360219 (PARI) a(n) = sum(k=0, n\4, (-1)^k*binomial(n-3*k, k)*binomial(2*(n-3*k), n-3*k));
%o A360219 (PARI) my(N=30, x='x+O('x^N)); Vec(1/sqrt(1-4*x*(1-x^3)))
%Y A360219 Cf. A157004, A360267, A374599.
%K A360219 nonn
%O A360219 0,2
%A A360219 _Seiichi Manyama_, Jan 31 2023