Search: id:A033312
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%I A033312
%S A033312 0,0,1,5,23,119,719,5039,40319,362879,3628799,39916799,479001599,
%T A033312 6227020799,87178291199,1307674367999,20922789887999,355687428095999,
%U A033312 6402373705727999,121645100408831999,2432902008176639999
%N A033312 n! - 1.
%C A033312 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
%C A033312 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
%D A033312 Problem 598, J. Rec. Math., 11 (1978), 68-69.
%D A033312 A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of 
               combinatorial proof, M.A.A. 2003, id. 181.
%H A033312 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/
               matha1/matha105.htm">Factorizations of many number sequences</a>
%H A033312 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/
               matha1/matha103.htm">Factorizations of many number sequences</a>
%H A033312 Andrew Walker, <a href="http://www.uow.edu.au/~ajw01/ecm/curves.html">
               Factors of n! +- 1</a>
%H A033312 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Factorial.html">Link to a section of The World of Mathematics.</a>
%H A033312 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PermutationPattern.html">Link to a section of The World of Mathematics.</
               a>
%H A033312 R. G. Wilson v, <a href="a38507.txt">Explicit factorizations</a>
%H A033312 <a href="Sindx_Fa.html#factorial">Index entries for sequences related 
               to factorial numbers</a>
%H A033312 G. P. Michon, <a href="http://home.att.net/~numericana/wilson.htm">Wilson's 
               Theorem</a>
%F A033312 Equals Sum_{k=1..n} k*k!.
%F A033312 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
%t A033312 f[n_]:=n!-1;lst={};Do[AppendTo[lst,f[n]],{n,0,5!}];lst [From Vladimir 
               Orlovsky (4vladimir(AT)gmail.com), Jun 27 2009]
%Y A033312 Cf. A000142, A038507.
%Y A033312 Cf. A002582; A054415; A056110; A002982.
%Y A033312 Sequence in context: A167248 A005393 A162815 this_sequence A151881 A121636 
               A020032
%Y A033312 Adjacent sequences: A033309 A033310 A033311 this_sequence A033313 A033314 
               A033315
%K A033312 nonn
%O A033312 0,4
%A A033312 Eric Weisstein (eric(AT)weisstein.com)

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