A276399 - OEIS

%I #14 Sep 08 2022 08:46:17

%S 1,1,2,1,24,5,720,126,4480,6048,3628800,95040,479001600,55598400,

%T 5806080,1816214400,20922789888000,40327372800,6402373705728000,

%U 2501955993600,8911728967680000,193526296104960000,1124000727777607680000,696294353018880000,2256176006302688870400

%N Numerator of n!/(n^n-n).

%H Chai Wah Wu, <a href="/A276399/b276399.txt">Table of n, a(n) for n = 2..453</a>

%H Natasha Morrison and Alex Scott, <a href="https://people.maths.ox.ac.uk/scott/Papers/maxinduced.pdf">Maximizing the number of induced cycles in a graph</a>, Preprint, 2016. See Conj. 1.1.

%e 1, 1/4, 2/21, 1/26, 24/1555, 5/817, 720/299593, 126/134521, 4480/12345679, 6048/43229041, 3628800/67546215517, 95040/4622635937, 479001600/61054982558011, ...

%t Table[Numerator[n! / (n^n - n)], {n, 2, 30}] (* _Vincenzo Librandi_, Sep 12 2016 *)

%o (Python)

%o from __future__ import division

%o from math import factorial

%o from fractions import gcd

%o def A276399(n):

%o     a = factorial(n-1)

%o     return a//gcd(n**(n-1)-1,a) # _Chai Wah Wu_, Sep 11 2016

%o (Magma) [Numerator(Factorial(n)/(n^n-n)): n in [2..25]]; // _Vincenzo Librandi_, Sep 12 2016

%Y Cf. A276400.

%K nonn,frac

%O 2,3

%A _N. J. A. Sloane_, Sep 11 2016