A280735 Numerator of Product_{k=1..n-1} k^(2k-n-1).

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

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

Cf. A182484, A280736.

Sequence in context: A004124 A175504 A308944 * A356073 A290282 A331815

Adjacent sequences: A280732 A280733 A280734 * A280736 A280737 A280738

Keyword

nonn,frac

Author

N. J. A. Sloane, Jan 10 2017

Status

approved