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A300519
Convolution of n! and n^n.
0
1, 2, 7, 39, 321, 3603, 51391, 884873, 17770445, 406673247, 10431884283, 296262164637, 9224841015745, 312441152401067, 11434829066996087, 449675059390576257, 18908960744072894325, 846638474386244188311, 40213487658138717885907, 2019543479160709325145893
OFFSET
0,2
FORMULA
a(n) = Sum_{k=0..n} k^k * (n-k)!.
a(n) ~ n^n * (1 + exp(-1)/n).
MATHEMATICA
Table[Sum[If[k == 0, 1, k^k] * (n-k)!, {k, 0, n}], {n, 0, 20}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Mar 08 2018
STATUS
approved