A377190 Expansion of 1/(1 - 4*x^2 - 4*x^3)^(7/2).

1, 0, 14, 14, 126, 252, 1050, 2772, 8778, 24948, 72072, 204204, 570570, 1585584, 4351776, 11879868, 32162130, 86582496, 231703472, 616900284, 1634721088, 4312944064, 11333823228, 29673291648, 77423101938, 201367680696, 522180220044, 1350350044316, 3482928560880

Offset: 0

Author

Seiichi Manyama, Oct 19 2024

Keywords

• nonn

Crossrefs

Cf. A115962, A377186, A377189.

Cf. A374513.

Programs

PARI

a(n) = sum(k=0, n\2, (-4)^k*binomial(-7/2, k)*binomial(k, n-2*k));

Formula

a(0) = 1, a(1) = 0, a(2) = 14; a(n) = (4*(n+5)*a(n-2) + 2*(2*n+15)*a(n-3))/n.

a(n) = Sum_{k=0..floor(n/2)} (-4)^k * binomial(-7/2,k) * binomial(k,n-2*k).