A364738 G.f. satisfies A(x) = 1 + x*A(x) / (1 + x*A(x)^5).

1, 1, 0, -5, -10, 40, 245, -26, -4375, -11410, 53040, 377850, -12320, -7988194, -23011625, 106662595, 824671575, 64095550, -18490968680, -57052839001, 254513058375, 2098532784575, 419490572800, -48205987947600, -157458581103395, 666628546612606, 5824573247731250

Offset: 0

Author

Seiichi Manyama, Aug 05 2023

Keywords

• sign

Crossrefs

Cf. A364735, A364736, A364737.

Cf. A364734.

Programs

PARI

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

Formula

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