0,4

a(n) gives the index number in any table of permutations of the entry in which the last n+1 items are reversed. - Eugene McDonnell (eemcd(AT)mac.com), Dec 03 2004

a(n), n>=1, has the factorial representation [n-1,n-2,...,1,0]. The (unique) factorial representation of a number m from {0,1,...n!-1} is m =sum(m_j(n)*j!,j=0..n-1) with m_j(n) from {0,1,..,j}, n>=1. This is encoded as [m_{n-1},m_{n-2},...,m+1,m_0] with m_0=0. This can be interpreted as (D. N.) Lehmer code for the lexicographic rank of permutations of the symmetric group S_n (see the W. Lang link under A136663). The Lehmer code [n-1,n-2,...,1,0] stands for the permutation [n,n-1,...,1] (the last in lexicographic order). - Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), May 21 2008

Problem 598, J. Rec. Math., 11 (1978), 68-69.

A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003, id. 181.

Hisanori Mishima, Factorizations of many number sequences

Hisanori Mishima, Factorizations of many number sequences

Andrew Walker, Factors of n! +- 1

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

R. G. Wilson v, Explicit factorizations

Index entries for sequences related to factorial numbers

G. P. Michon, Wilson's Theorem

Equals Sum_{k=1..n} k*k!.

a(n) = a(n-1)*(n-1) + a(n-1) + n-1, a(0)=0. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 03 2003

f[n_]:=n!-1; lst={}; Do[AppendTo[lst, f[n]], {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jun 27 2009]

Cf. A000142, A038507.

Cf. A002582; A054415; A056110; A002982.

Sequence in context: A167248 A005393 A162815 this_sequence A151881 A121636 A020032

Adjacent sequences: A033309 A033310 A033311 this_sequence A033313 A033314 A033315

nonn

Eric Weisstein (eric(AT)weisstein.com)