A360092 - OEIS

A360092

Denominator of (n-2)!*Sum_{k=1..n} (-1)^(k+1)/((n-k)!*k^k).

%I #18 Jan 26 2023 03:39:36

%S 4,108,3456,3600000,48600000,8004837960000,43717088378880000,

%T 3319007595022909440000,2592974683611648000000000,

%U 82200659870363161557652992000000000,98640791844435793869183590400000000,2715985485838884679142342027478742851379200000000

%N Denominator of (n-2)!*Sum_{k=1..n} (-1)^(k+1)/((n-k)!*k^k).

%H Amiram Eldar, <a href="/A360092/b360092.txt">Table of n, a(n) for n = 2..57</a>

%H David Peter Hadrian Ulgenes, <a href="https://arxiv.org/abs/2301.09699">Series and Product Representations of Gamma and Pseudogamma Functions</a>, arXiv:2301.09699 [math.NT], 2023.

%t Array[Denominator[(# - 2)!* Sum[(-1)^(k + 1)/((# - k)!*k^k), {k, #}]] &, 13, 2] (* _Michael De Vlieger_, Jan 25 2023 *)

%o (PARI) a(n) = denominator((n-2)!*sum(k=1, n, (-1)^(k+1)/((n-k)!*k^k)));

%Y Cf. A360091 (numerators).

%K nonn,frac

%O 2,1

%A _Michel Marcus_, Jan 25 2023