A360291 a(n) = Sum_{k=0..floor(n/3)} binomial(n-1-2*k,k) * binomial(2*n-6*k,n-3*k).

1, 2, 6, 20, 72, 264, 984, 3714, 14148, 54284, 209482, 812196, 3161340, 12345658, 48348522, 189807336, 746740510, 2943359208, 11620961412, 45950375602, 181936110006, 721233025332, 2862271873966, 11370584735100, 45212101270728, 179926167512914

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

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

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).

Prog

(PARI) a(n) = sum(k=0, n\3, binomial(n-1-2*k, k)*binomial(2*n-6*k, n-3*k));
(PARI) my(N=30, x='x+O('x^N)); Vec(1/sqrt(1-4*x/(1-x^3)))

Crossrefs

Cf. A085362, A360290, A360292.

Cf. A360186, A360294.

Sequence in context: A194950 A150129 A360267 * A150130 A150131 A150132

Adjacent sequences: A360288 A360289 A360290 * A360292 A360293 A360294

Keyword

nonn

Author

Seiichi Manyama, Feb 01 2023

Status

approved