A364759 G.f. satisfies A(x) = 1 + x*A(x)^5 / (1 + x*A(x)).

1, 1, 4, 25, 182, 1447, 12175, 106575, 960579, 8854622, 83089537, 791063172, 7622317663, 74191096721, 728389554533, 7204640725610, 71727367291455, 718195853746770, 7227785937663908, 73069500402699226, 741712341691454837, 7556704348506425398

Offset: 0

Author

Seiichi Manyama, Aug 05 2023

Keywords

• nonn

Crossrefs

Cf. A090192, A106228, A364758.

Cf. A364748.

Programs

PARI

a(n) = if(n==0, 1, sum(k=0, n-1, (-1)^k*binomial(n, k)*binomial(5*n-4*k, n-1-k))/n);

Formula

a(n) = (1/n) * Sum_{k=0..n-1} (-1)^k * binomial(n,k) * binomial(5*n-4*k,n-1-k) for n > 0.