A300519 Convolution of n! and n^n.

1, 2, 7, 39, 321, 3603, 51391, 884873, 17770445, 406673247, 10431884283, 296262164637, 9224841015745, 312441152401067, 11434829066996087, 449675059390576257, 18908960744072894325, 846638474386244188311, 40213487658138717885907, 2019543479160709325145893

Offset: 0

Author

Vaclav Kotesovec, Mar 08 2018

Keywords

• nonn

Crossrefs

Cf. A000142, A000312, A061711, A277506.

Cf. A107713, A108953, A110467.

Programs

Mathematica

Table[Sum[If[k == 0, 1, k^k] * (n-k)!, {k, 0, n}], {n, 0, 20}]

Formula

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

a(n) ~ n^n * (1 + exp(-1)/n).