A374614 a(n) = Sum_{k=0..n} (k/n)^2 * binomial(n,k)^5.

1, 9, 136, 2585, 54126, 1227492, 29226688, 723533337, 18438032890, 480994824134, 12787403151744, 345355150592036, 9451729196625184, 261628075707534720, 7313361005558843136, 206190939973811373593, 5857313490484652859282

Offset: 1

Author

Seiichi Manyama, Jul 14 2024

Keywords

• nonn

Crossrefs

Cf. A005261, A374615, A374616.

Cf. A181067, A198256.

Programs

Mathematica

Table[Sum[(k/n)^2 Binomial[n,k]^5,{k,0,n}],{n,20}] (* Harvey P. Dale, Jun 16 2025 *)

PARI

a(n) = sum(k=0, n-1, binomial(n-1, k)^2*binomial(n, k)^3);

Formula

a(n) = Sum_{k=0..n-1} binomial(n-1,k)^2 * binomial(n,k)^3.