A351765 a(n) = n! * Sum_{k=0..n} n^(n-k) * (n-k)^k/k!.

1, 1, 12, 279, 11536, 746525, 69768036, 8902181575, 1487939919936, 315597946293657, 82839437215344100, 26366747854082944451, 10006618140321691249296, 4464690010732922712332149, 2313871692128866349730705924, 1378552938661073773617331110975

Offset: 0

Author

Seiichi Manyama, Feb 18 2022

Keywords

• nonn

Crossrefs

Main diagonal of A351761.

Cf. A332408, A351768, A351779.

Programs

Mathematica

Join[{1}, Table[n!*Sum[n^(n - k)*(n - k)^k/k!, {k, 0, n}], {n, 1, 20}]] (* Vaclav Kotesovec, Feb 19 2022 *)

PARI

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

Formula

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

From Vaclav Kotesovec, Feb 19 2022: (Start)

a(n) ~ exp(1) * n! * n^n.

a(n) ~ sqrt(2*Pi) * n^(2*n + 1/2) / exp(n-1). (End)