login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Table of n, a(n) for n=1..21.

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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