A360294 a(n) = Sum_{k=0..floor(n/3)} (-1)^k * binomial(n-1-2*k,k) * binomial(2*n-6*k,n-3*k).

1, 2, 6, 20, 68, 240, 864, 3154, 11628, 43196, 161430, 606228, 2285780, 8647738, 32811378, 124804104, 475748330, 1817005536, 6951390372, 26634502642, 102189927918, 392559063268, 1509684132394, 5811772604124, 22394185567728, 86364110132930, 333329513935842

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).

Mathematica

CoefficientList[Series[1/Sqrt[1-4 x/(1+x^3)], {x, 0, 40}], x] (* Harvey P. Dale, Feb 06 2023 *)

Prog

(PARI) a(n) = sum(k=0, n\3, (-1)^k*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. A360293, A360295.

Sequence in context: A363182 A150120 A360219 * A150121 A150122 A150123

Adjacent sequences: A360291 A360292 A360293 * A360295 A360296 A360297

Keyword

nonn

Author

Seiichi Manyama, Feb 01 2023

Status

approved