A366437 G.f. A(x) satisfies A(x) = 1 + x * ((1 - x) / A(x))^(7/2).

1, 1, -7, 49, -427, 4165, -43435, 473977, -5344333, 61772179, -727993301, 8714701219, -105672771225, 1295237037815, -16021641194545, 199747074505773, -2507395464414008, 31664298046926328, -401994771266030880, 5127701624204157600, -65684716411944207144

Offset: 0

Author

Seiichi Manyama, Oct 09 2023

Keywords

• sign

Crossrefs

Partial sums give A366406.

Cf. A366431, A366432, A366433, A366434, A366435, A366436.

Programs

PARI

a(n) = (-1)^(n-1)*sum(k=0, n, binomial(9*k/2-1, k)*binomial(7*k/2, n-k)/(9*k/2-1));

Formula

a(n) = (-1)^(n-1) * Sum_{k=0..n} binomial(9*k/2-1,k) * binomial(7*k/2,n-k) / (9*k/2-1).