A365088 G.f. satisfies A(x) = 1 + x*A(x) / (1 + x*A(x))^5.

1, 1, -4, 1, 46, -129, -405, 3319, -1617, -59258, 199541, 642170, -6038395, 3886091, 119884973, -440626784, -1367688245, 14055527190, -11043763380, -290488387366, 1137260033731, 3336325340735, -36966844508130, 34098313310315, 776097820004580

Offset: 0

Author

Seiichi Manyama, Aug 21 2023

Keywords

• sign

Crossrefs

Cf. A090192, A365085, A365086, A365087.

Cf. A321799, A364738, A365084.

Programs

PARI

a(n) = sum(k=0, n, (-1)^(n-k)*binomial(n, k)*binomial(n+4*k-1, n-k)/(n-k+1));

Formula

a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * binomial(n+4*k-1,n-k) / (n-k+1).