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A175624
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a(n) = n! modulo n*(n+1)*(n+2)/3.
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1
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1, 2, 6, 24, 50, 48, 0, 0, 210, 120, 352, 168, 0, 0, 800, 288, 1122, 360, 0, 0, 2002, 528, 0, 0, 0, 0, 4032, 840, 4930, 960, 0, 0, 0, 0, 8400, 1368, 0, 0, 11440, 1680, 13202, 1848, 0, 0, 17250, 2208, 0, 0, 0, 0, 24752, 2808, 0, 0, 0, 0, 34162, 3480, 37760, 3720, 0, 0, 0, 0
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OFFSET
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1,2
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COMMENTS
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It appears that a(1)=1, a(2)=2, a(3)=6, and, for n>3, a(n) = n*(n+2) if n+1 is prime, else a(n) = n*(n+1)*(n+5)/6 if n+2 is prime, else a(n)=0. This has been verified for n up to 1000.
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LINKS
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MATHEMATICA
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Table[Mod[(n!), (n^3 + 3 n^2 + 2 n)/3], {n, 100}] (* Vincenzo Librandi, Jul 10 2014 *)
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PROG
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(PARI) a(n) = n! % (n*(n+1)*(n+2)/3); \\ Michel Marcus, Jul 09 2014
(Magma)
[Factorial(n) mod (2*Binomial(n+2, 3)): n in [1..80]]; // G. C. Greubel, Apr 12 2024
(SageMath)
[factorial(n)%(2*binomial(n+2, 3)) for n in range(1, 81)] # G. C. Greubel, Apr 12 2024
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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