A356806 a(n) = Sum_{k=0..n} (k*n-1)^(n-k) * binomial(n,k).

1, 0, 4, 27, 448, 10625, 344736, 14437213, 753991680, 47974773393, 3650824000000, 326917384798301, 33956137832546304, 4041303651931462969, 545552768347831566336, 82828479894303251953125, 14040577418634835164921856, 2640293357854435329683551265

Offset: 0

Author

Seiichi Manyama, Aug 29 2022

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..274

Crossrefs

Cf. A052506, A351736, A351737.

Cf. A356811, A356814, A356817.

Programs

PARI

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

PARI

a(n) = n!*sum(k=0, n\2, n^(n-k)*stirling(n-k, k, 2)/(n-k)!);

Formula

a(n) = n! * [x^n] exp( x * (exp(n * x) - 1) ).

a(n) = n! * Sum_{k=0..floor(n/2)} n^(n-k) * Stirling2(n-k,k)/(n-k)!.

a(n) = [x^n] Sum_{k>=0} x^k / (1 - (n*k-1)*x)^(k+1).