A366647 G.f. A(x) satisfies A(x) = 1 + x * (A(x) / (1 - x))^5.

1, 1, 10, 100, 1120, 13600, 174352, 2322880, 31846720, 446387200, 6367988480, 92154502912, 1349572428800, 19963252142080, 297843703347200, 4476750466785280, 67724540010278912, 1030392038941573120, 15756269876770734080, 242027462112980172800

Offset: 0

Author

Seiichi Manyama, Oct 15 2023

Keywords

• nonn

Crossrefs

Partial sums give A349311.

Cf. A006319, A213282, A213336.

Programs

PARI

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

Formula

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