A360291 - OEIS

%I #13 Feb 03 2023 01:37:31

%S 1,2,6,20,72,264,984,3714,14148,54284,209482,812196,3161340,12345658,

%T 48348522,189807336,746740510,2943359208,11620961412,45950375602,

%U 181936110006,721233025332,2862271873966,11370584735100,45212101270728,179926167512914

%N a(n) = Sum_{k=0..floor(n/3)} binomial(n-1-2*k,k) * binomial(2*n-6*k,n-3*k).

%H Seiichi Manyama, <a href="/A360291/b360291.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: 1 / sqrt(1-4*x/(1-x^3)).

%F 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).

%o (PARI) a(n) = sum(k=0, n\3, binomial(n-1-2*k, k)*binomial(2*n-6*k, n-3*k));

%o (PARI) my(N=30, x='x+O('x^N)); Vec(1/sqrt(1-4*x/(1-x^3)))

%Y Cf. A085362, A360290, A360292.

%Y Cf. A360186, A360294.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Feb 01 2023