%I A000183 M2121 N0838
%S A000183 0,0,0,1,2,20,144,1265,12072,126565,1445100,17875140,238282730,
%T A000183 3407118041,52034548064,845569542593,14570246018686,265397214435860,
%U A000183 5095853023109484,102877234050493609,2178674876680100744
%N A000183 Number of discordant permutations of length n.
%C A000183 a(n)=ways to reseat n diners at circular table, none in or next to original 
               chair.
%D A000183 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000183 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000183 J. Riordan, Discordant permutations, Scripta Math., 20 (1954), 14-23.
%D A000183 Anthony C. Robin, Circular Wife Swapping, The Mathematical Gazette, November 
               2006.
%D A000183 R. P. Stanley, Enumerative Combinatorics I, Example 4.7.17.
%D A000183 K. Yamamoto, Structure polynomial of Latin rectangles and its application 
               to a combinatorial problem, Memoirs of the Faculty of Science, Kyusyu 
               University, Series A, 10 (1956), 1-13.
%F A000183 a(n) = Sum_{m=0..n} (-1)^m*(n-m)!*A061702(n, m), n>2.
%e A000183 a(5)=2: [ 1 2 3 4 5 ] -> [ 3 4 5 1 2 ] or [ 4 5 1 2 3 ].
%Y A000183 Cf. A061702, A061703, A000338, A000561-A000565.
%Y A000183 Sequence in context: A003490 A003481 A081006 this_sequence A081159 A105489 
               A093302
%Y A000183 Adjacent sequences: A000180 A000181 A000182 this_sequence A000184 A000185 
               A000186
%K A000183 nonn,nice,easy
%O A000183 1,5
%A A000183 N. J. A. Sloane (njas(AT)research.att.com).
%E A000183 More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Jun 18 2001