A367011 - OEIS

%I #15 Dec 31 2023 10:22:36

%S 1,1,3,11,51,287,1899,14447,124251,1192127,12623979,146250287,

%T 1840024251,24983863967,364140992139,5670546353807,93960923507931,

%U 1650688221777407,30646388716777899,599565840087487727,12328458398407260411

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

%H Seiichi Manyama, <a href="/A367011/b367011.txt">Table of n, a(n) for n = 0..449</a>

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

%F a(n) ~ sqrt(Pi*n/2) * n!.

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

%o (PARI) a(n) = sum(k=0, n, k!*k^(n-k)); \\ _Seiichi Manyama_, Dec 31 2023

%Y Cf. A026898, A112541, A367012.

%Y Cf. A003422, A233449, A368555.

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Nov 01 2023

%E a(0)=1 prepended by _Seiichi Manyama_, Dec 31 2023