A347611 a(n) is the n-th n-factorial number: a(n) = n!_n.

1, 1, 3, 52, 8925, 22661496, 1131162092095, 1375009641495014400, 48378633136349277767794425, 57001313848230245122464621625840000, 2552524038347870310755413660544832496799359491, 4859161865915056755501262525796512204608930674134393036800

Offset: 0

Author

Alois P. Heinz, Sep 08 2021

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..36
• Index entries for sequences related to factorial numbers

Crossrefs

Main diagonal of A069777.

Cf. A366355.

Programs

Maple

b:= proc(n, k) option remember; `if`(n<2, 1,
      b(n-1, k)*(k^n-1)/(k-1))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..12);

Mathematica

Array[QFactorial[#, #] &, 12, 0] (* Michael De Vlieger, Sep 09 2021 *)

PARI

a(n) = if (n<=1, 1, prod(k=1, n, (n^k-1)/(n-1))); \\ Michel Marcus, Sep 09 2021

Python

from math import prod
def a(n):
    return 1 if n <= 1 else prod((n**k - 1)//(n - 1) for k in range(1, n+1))
print([a(n) for n in range(12)]) # Michael S. Branicky, Sep 09 2021

Formula

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

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

a(n) ~ exp(1) * n^(n*(n-1)/2). - Vaclav Kotesovec, Jun 09 2025