A360315 a(n) = Sum_{k=0..floor(n/4)} (-1)^k * binomial(n-1-3*k,n-4*k) * binomial(2*k,k).

1, 0, 0, 0, -2, -2, -2, -2, 4, 10, 16, 22, 8, -26, -80, -154, -178, -82, 204, 750, 1374, 1642, 868, -1886, -6886, -12802, -15784, -8538, 17166, 64554, 122476, 152602, 86056, -157642, -616456, -1183666, -1493402, -878250, 1468080

Offset: 0

Author

Seiichi Manyama, Feb 03 2023

Keywords

• sign

Crossrefs

Cf. A360313, A360314.

Cf. A360295, A360310.

Programs

PARI

a(n) = sum(k=0, n\4, (-1)^k*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).