A365224 G.f. satisfies A(x) = 1 + x*A(x)^4 / (1 + x*A(x)^5).

1, 1, 3, 10, 30, 56, -167, -2813, -21515, -126135, -601812, -2179039, -3455504, 32238155, 430944400, 3334419890, 20083350422, 97094186751, 338485665435, 274332822425, -8491831747320, -97735154210032, -732963337489636, -4341176221239330

Offset: 0

Author

Seiichi Manyama, Aug 27 2023

Keywords

• sign

Crossrefs

Cf. A001764, A219537, A317133, A364758, A364865.

Cf. A365223, A365226.

Programs

PARI

a(n) = sum(k=0, n, (-1)^(n-k)*binomial(5*n-k+1, k)*binomial(n-1, n-k)/(5*n-k+1));

Formula

a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(5*n-k+1,k) * binomial(n-1,n-k)/(5*n-k+1).