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A347611
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a(n) is the n-th n-factorial number: a(n) = n!_n.
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2
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1, 1, 3, 52, 8925, 22661496, 1131162092095, 1375009641495014400, 48378633136349277767794425, 57001313848230245122464621625840000, 2552524038347870310755413660544832496799359491, 4859161865915056755501262525796512204608930674134393036800
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listen;
history;
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OFFSET
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0,3
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..36
Index entries for sequences related to factorial numbers
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FORMULA
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a(n) = Product_{j=1..n} (n^j-1)/(n-1) for n > 1, a(0) = a(1) = 1.
a(n) = A069777(n,n).
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MAPLE
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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);
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MATHEMATICA
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Array[QFactorial[#, #] &, 12, 0] (* Michael De Vlieger, Sep 09 2021 *)
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PROG
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(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
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CROSSREFS
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Main diagonal of A069777.
Sequence in context: A263530 A136723 A202649 * A302932 A143387 A228452
Adjacent sequences: A347608 A347609 A347610 * A347612 A347613 A347614
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KEYWORD
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nonn
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AUTHOR
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Alois P. Heinz, Sep 08 2021
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STATUS
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approved
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