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Search: id:A134295
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| A134295 |
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Sum[ (n-k)!*(k-1)! - (-1)^k, {k,1,n} ]. |
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2
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| 2, 2, 6, 16, 65, 312, 1813, 12288, 95617, 840960, 8254081, 89441280, 1060369921, 13649610240, 189550368001, 2824077312000, 44927447040001, 760034451456000, 13622700994560001, 257872110354432000, 5140559166898176001
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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According to the Generalized Wilson-Lagrange Theorem a prime p divides (p-k)!*(k-1)! - (-1)^k for all integer k>0. p divides a(p) for prime p. Quotients a(p)/p are listed in A134296(n) = {1, 2, 13, 259, 750371, 81566917, 2642791002353, 716984262871579, 102688143363690674087, ...}. p^2 divides a(p) for prime p = {7, 71}.
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FORMULA
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a(n) = Sum[ (n-k)!*(k-1)! - (-1)^k, {k,1,n} ].
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MATHEMATICA
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Table[ Sum[ (n-k)!*(k-1)! - (-1)^k, {k, 1, n} ], {n, 1, 30} ]
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CROSSREFS
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Cf. A007540, A007619 = Wilson quotients:((p-1)!+1)/p. Cf. A134296 = Quotients a(p)/p.
Sequence in context: A067136 A034439 A060165 this_sequence A062833 A006250 A006249
Adjacent sequences: A134292 A134293 A134294 this_sequence A134296 A134297 A134298
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KEYWORD
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nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 17 2007
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