A347611 - OEIS

%I #24 Sep 09 2021 10:46:19

%S 1,1,3,52,8925,22661496,1131162092095,1375009641495014400,

%T 48378633136349277767794425,57001313848230245122464621625840000,

%U 2552524038347870310755413660544832496799359491,4859161865915056755501262525796512204608930674134393036800

%N a(n) is the n-th n-factorial number: a(n) = n!_n.

%H Alois P. Heinz, <a href="/A347611/b347611.txt">Table of n, a(n) for n = 0..36</a>

%H <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>

%F a(n) = Product_{j=1..n} (n^j-1)/(n-1) for n > 1, a(0) = a(1) = 1.

%F a(n) = A069777(n,n).

%p b:= proc(n, k) option remember; `if`(n<2, 1,

%p       b(n-1, k)*(k^n-1)/(k-1))

%p     end:

%p a:= n-> b(n$2):

%p seq(a(n), n=0..12);

%t Array[QFactorial[#, #] &, 12, 0] (* _Michael De Vlieger_, Sep 09 2021 *)

%o (PARI) a(n) = if (n<=1, 1, prod(k=1, n, (n^k-1)/(n-1))); \\ _Michel Marcus_, Sep 09 2021

%o (Python)

%o from math import prod

%o def a(n):

%o     return 1 if n <= 1 else prod((n**k - 1)//(n - 1) for k in range(1, n+1))

%o print([a(n) for n in range(12)]) # _Michael S. Branicky_, Sep 09 2021

%Y Main diagonal of A069777.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Sep 08 2021