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 A134295 Sum[ (n-k)!*(k-1)! - (-1)^k, {k,1,n} ]. 1
 2, 2, 6, 16, 65, 312, 1813, 12288, 95617, 840960, 8254081, 89441280, 1060369921, 13649610240, 189550368001, 2824077312000, 44927447040001, 760034451456000, 13622700994560001, 257872110354432000, 5140559166898176001 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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}. LINKS FORMULA a(n) = Sum[ (n-k)!*(k-1)! - (-1)^k, {k,1,n} ]. MATHEMATICA Table[ Sum[ (n-k)!*(k-1)! - (-1)^k, {k, 1, n} ], {n, 1, 30} ] CROSSREFS Cf. A007540, A007619 = Wilson quotients:((p-1)!+1)/p. Cf. A134296 = Quotients a(p)/p. Sequence in context: A034439 A230825 A060165 * A184845 A062833 A006250 Adjacent sequences:  A134292 A134293 A134294 * A134296 A134297 A134298 KEYWORD nonn AUTHOR Alexander Adamchuk, Oct 17 2007 STATUS approved

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Last modified January 26 21:01 EST 2021. Contains 340443 sequences. (Running on oeis4.)