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A280735
Numerator of Product_{k=1..n-1} k^(2k-n-1).
2
1, 3, 4, 125, 225, 84035, 2458624, 162030456, 8930250000, 92844190333125, 9001015156742400, 942951673566712781829, 68987440762943255933340961, 14018304328535759323100326171875, 377177413291384771899817984000000
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
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
Sequence in context: A004124 A175504 A308944 * A356073 A290282 A331815
KEYWORD
nonn,frac
AUTHOR
N. J. A. Sloane, Jan 10 2017
STATUS
approved