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Search: id:A000183
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| A000183 |
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Number of discordant permutations of length n.
(Formerly M2121 N0838)
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+0
5
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| 0, 0, 0, 1, 2, 20, 144, 1265, 12072, 126565, 1445100, 17875140, 238282730, 3407118041, 52034548064, 845569542593, 14570246018686, 265397214435860, 5095853023109484, 102877234050493609, 2178674876680100744
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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a(n)=ways to reseat n diners at circular table, none in or next to original chair.
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
J. Riordan, Discordant permutations, Scripta Math., 20 (1954), 14-23.
Anthony C. Robin, Circular Wife Swapping, The Mathematical Gazette, November 2006.
R. P. Stanley, Enumerative Combinatorics I, Example 4.7.17.
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.
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FORMULA
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a(n) = Sum_{m=0..n} (-1)^m*(n-m)!*A061702(n, m), n>2.
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EXAMPLE
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a(5)=2: [ 1 2 3 4 5 ] -> [ 3 4 5 1 2 ] or [ 4 5 1 2 3 ].
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CROSSREFS
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Cf. A061702, A061703, A000338, A000561-A000565.
Sequence in context: A003490 A003481 A081006 this_sequence A081159 A105489 A093302
Adjacent sequences: A000180 A000181 A000182 this_sequence A000184 A000185 A000186
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KEYWORD
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nonn,nice,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Jun 18 2001
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