A367011 a(n) = Sum_{k=0..n} k! * k^(n-k).
1, 1, 3, 11, 51, 287, 1899, 14447, 124251, 1192127, 12623979, 146250287, 1840024251, 24983863967, 364140992139, 5670546353807, 93960923507931, 1650688221777407, 30646388716777899, 599565840087487727, 12328458398407260411
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..449
Programs
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Mathematica
Table[Sum[k! * k^(n-k), {k, 0, n}], {n, 1, 20}] -
PARI
a(n) = sum(k=0, n, k!*k^(n-k)); \\ Seiichi Manyama, Dec 31 2023
Formula
a(n) ~ Pi * n^(n+1) / exp(n).
a(n) ~ sqrt(Pi*n/2) * n!.
Extensions
a(0)=1 prepended by Seiichi Manyama, Dec 31 2023