login
A367011
a(n) = Sum_{k=0..n} k! * k^(n-k).
3
1, 1, 3, 11, 51, 287, 1899, 14447, 124251, 1192127, 12623979, 146250287, 1840024251, 24983863967, 364140992139, 5670546353807, 93960923507931, 1650688221777407, 30646388716777899, 599565840087487727, 12328458398407260411
OFFSET
0,3
LINKS
FORMULA
a(n) ~ Pi * n^(n+1) / exp(n).
a(n) ~ sqrt(Pi*n/2) * n!.
MATHEMATICA
Table[Sum[k! * k^(n-k), {k, 0, n}], {n, 1, 20}]
PROG
(PARI) a(n) = sum(k=0, n, k!*k^(n-k)); \\ Seiichi Manyama, Dec 31 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Nov 01 2023
EXTENSIONS
a(0)=1 prepended by Seiichi Manyama, Dec 31 2023
STATUS
approved