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%I A134295 #6 Jun 06 2021 19:22:12
%S A134295 2,2,6,16,65,312,1813,12288,95617,840960,8254081,89441280,1060369921,
%T A134295 13649610240,189550368001,2824077312000,44927447040001,
%U A134295 760034451456000,13622700994560001,257872110354432000,5140559166898176001
%N A134295 a(n) = Sum_{k=1..n} ((n-k)!*(k-1)! - (-1)^k).
%C A134295 According to the Generalized Wilson-Lagrange Theorem, a prime p divides (p-k)!*(k-1)! - (-1)^k for all integers 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}.
%F A134295 a(n) = Sum_{k=1..n} ((n-k)!*(k-1)! - (-1)^k).
%t A134295 Table[ Sum[ (n-k)!*(k-1)! - (-1)^k, {k,1,n} ], {n,1,30} ]
%Y A134295 Cf. A007540, A007619 (Wilson quotients: ((p-1)!+1)/p).
%Y A134295 Cf. A134296 (quotients a(p)/p).
%K A134295 nonn
%O A134295 1,1
%A A134295 _Alexander Adamchuk_, Oct 17 2007

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