A366647 - OEIS

%I #7 Oct 15 2023 09:26:10

%S 1,1,10,100,1120,13600,174352,2322880,31846720,446387200,6367988480,

%T 92154502912,1349572428800,19963252142080,297843703347200,

%U 4476750466785280,67724540010278912,1030392038941573120,15756269876770734080,242027462112980172800

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

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

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

%Y Partial sums give A349311.

%Y Cf. A006319, A213282, A213336.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Oct 15 2023