login
A134295
a(n) = Sum_{k=1..n} ((n-k)!*(k-1)! - (-1)^k).
1
2, 2, 6, 16, 65, 312, 1813, 12288, 95617, 840960, 8254081, 89441280, 1060369921, 13649610240, 189550368001, 2824077312000, 44927447040001, 760034451456000, 13622700994560001, 257872110354432000, 5140559166898176001
OFFSET
1,1
COMMENTS
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}.
FORMULA
a(n) = Sum_{k=1..n} ((n-k)!*(k-1)! - (-1)^k).
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: A230825 A060165 A303150 * A184845 A062833 A006250
KEYWORD
nonn
AUTHOR
Alexander Adamchuk, Oct 17 2007
STATUS
approved