A360310 a(n) = Sum_{k=0..floor(n/4)} binomial(n-1-3*k,n-4*k) * binomial(2*k,k).

1, 0, 0, 0, 2, 2, 2, 2, 8, 14, 20, 26, 52, 98, 164, 250, 426, 762, 1328, 2194, 3682, 6366, 11072, 18878, 32038, 54906, 94860, 163226, 279634, 479806, 826776, 1425542, 2454020, 4223170, 7279164, 12560466, 21671314, 37381714, 64512676, 111414042

Offset: 0

Author

Seiichi Manyama, Feb 03 2023

Keywords

• nonn

Crossrefs

Cf. A026585, A360309.

Cf. A360292, A360315.

Programs

PARI

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

PARI

my(N=40, x='x+O('x^N)); Vec(1/sqrt(1-4*x^4/(1-x)))

Formula

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

n*a(n) = 2*(n-1)*a(n-1) - (n-2)*a(n-2) + 2*(2*n-4)*a(n-4) - 2*(2*n-7)*a(n-5).