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Search: id:A094047
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| A094047 |
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a(n) is the number of arrangements of n couples around a round table so that each person sits between two members of the opposite sex and no couple is seated together. |
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+0
4
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| 0, 0, 2, 12, 312, 9600, 416880, 23879520, 1749363840, 159591720960, 17747520940800, 2363738855385600, 371511874881100800, 68045361697964851200, 14367543450324474009600, 3464541314885011705344000
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Also, the number of Hamiltonian directed circuits in the crown graph of order n.
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LINKS
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Eric Weisstein's World of Mathematics, Crown Graph
Eric Weisstein's World of Mathematics, Hamiltonian Circuit
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FORMULA
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For n>1, a(n) = (-1)^n * 2 * (n-1)! + n! * SUM[j=0..n-1] (-1)^j * (n-j-1)! * binomial(2*n-j-1,j).
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CROSSREFS
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Cf. A114939, A137729.
Adjacent sequences: A094044 A094045 A094046 this_sequence A094048 A094049 A094050
Sequence in context: A012425 A012422 A122767 this_sequence A091472 A012727 A088229
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KEYWORD
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nonn
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AUTHOR
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Matthijs Coster (matthijs(AT)coster.demon.nl), Apr 29 2004
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EXTENSIONS
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Better definition from Joel Lewis (jblewis(AT)post.harvard.edu), Jun 30 2007
Formula and further terms from Max Alekseyev (maxal(AT)cs.ucsd.edu), Feb 10 2008
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