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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 (list; graph; refs; listen; history; text; internal format)
 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 A270536 A278712 Adjacent sequences:  A175564 A175565 A175566 * A175568 A175569 A175570 KEYWORD nonn AUTHOR John W. Layman, Jul 12 2010 STATUS approved

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Last modified December 6 14:15 EST 2019. Contains 329806 sequences. (Running on oeis4.)