A360292 a(n) = Sum_{k=0..floor(n/4)} binomial(n-1-3*k,k) * binomial(2*n-8*k,n-4*k).

1, 2, 6, 20, 70, 254, 936, 3492, 13150, 49882, 190318, 729576, 2807816, 10841962, 41983588, 162973568, 633994982, 2471010742, 9646981054, 37718873700, 147676286078, 578883674722, 2271704404900, 8923807316892, 35087269756344, 138075819924306

Offset: 0

Author

Seiichi Manyama, Feb 01 2023

Keywords

• nonn

Links

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

Crossrefs

Cf. A085362, A360290, A360291.

Cf. A360295, A383582.

Programs

PARI

a(n) = sum(k=0, n\4, binomial(n-1-3*k, k)*binomial(2*n-8*k, n-4*k));

PARI

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

Formula

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

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).

a(n) = A383582(n) - A383582(n-4). - Seiichi Manyama, May 01 2025