

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
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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(n1)/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 A270536 A278712
Adjacent sequences: A175564 A175565 A175566 * A175568 A175569 A175570


KEYWORD

nonn


AUTHOR

John W. Layman, Jul 12 2010


STATUS

approved



