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Convolution of n! and n^n.
0

%I #11 Mar 08 2018 04:02:07

%S 1,2,7,39,321,3603,51391,884873,17770445,406673247,10431884283,

%T 296262164637,9224841015745,312441152401067,11434829066996087,

%U 449675059390576257,18908960744072894325,846638474386244188311,40213487658138717885907,2019543479160709325145893

%N Convolution of n! and n^n.

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

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

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

%Y Cf. A000142, A000312, A061711, A277506.

%Y Cf. A107713, A108953, A110467.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Mar 08 2018