OFFSET
1,2
COMMENTS
Paul M. Jane observed in an email message to N. J. A. Sloane on Jan 10 2016 that the expression (n-1)!^(n-3) / Product_{k=1..n-2} k!^2 appears to be an integer if and only if n is a prime. That expression can be simplified to give Product_{k=1..n-1} k^(2k-n-1), and the result then follows from Vandendriessche and Lee, Problem A13 (compare A182484, which gives the values at the primes).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..70
Peter Vandendriessche and Hojoo Lee, Problems in elementary number theory, Problem A13
EXAMPLE
1, 3/2, 4, 125/6, 225, 84035/16, 2458624/9, 162030456/5, 8930250000, ...
MATHEMATICA
Numerator@Table[Product[k^(2 k - n - 1), {k, 1, n - 1}], {n, 3, 25}] (* Vincenzo Librandi, Jan 12 2017 *)
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
N. J. A. Sloane, Jan 10 2017
STATUS
approved