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

1,4

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

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 *)

Prog

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

Crossrefs

Cf. A119690, A169690, A175553.

Sequence in context: A320146 A283999 A240813 * A069828 A340951 A270536

Adjacent sequences: A175564 A175565 A175566 * A175568 A175569 A175570

Keyword

nonn

Author

John W. Layman, Jul 12 2010

Status

approved