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A175567
(n!)^2 modulo n(n+1)/2.
3
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
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
KEYWORD
nonn
AUTHOR
John W. Layman, Jul 12 2010
STATUS
approved