A175567 (n!)^2 modulo n(n+1)/2.

0, 1, 0, 6, 0, 15, 0, 0, 0, 45, 0, 66, 0, 0, 0, 120, 0, 153, 0, 0, 0, 231, 0, 0, 0, 0, 0, 378, 0, 435, 0, 0, 0, 0, 0, 630, 0, 0, 0, 780, 0, 861, 0, 0, 0, 1035, 0, 0, 0, 0, 0, 1326, 0, 0, 0, 0, 0, 1653, 0, 1770, 0, 0, 0, 0, 0, 2145, 0, 0, 0, 2415, 0, 2556, 0, 0, 0, 0, 0, 3003, 0, 0, 0, 3321

Offset: 1

Author

John W. Layman, Jul 12 2010

Keywords

• nonn

Comments

It appears that if n is one less than an odd prime then (n!)^2 modulo n(n+1)/2 is n(n-1)/2 else 0. This result appears to hold for any even power of n!. See A119690 for similar results related to odd powers of n!.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A119690, A169690, A175553.

Programs

Mathematica

Table[Mod[(n!)^2, (n^2 + n)/2], {n, 100}] (* Vincenzo Librandi, Jul 10 2014 *)
Table[PowerMod[n!,2,(n(n+1))/2],{n,100}] (* Harvey P. Dale, Aug 27 2016 *)

PARI

a(n) = (n!)^2 % (n*(n+1)/2); \\ Michel Marcus, Jul 09 2014