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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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9
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0, 0, 2, 12, 312, 9600, 416880, 23879520, 1749363840, 159591720960, 17747520940800, 2363738855385600, 371511874881100800, 68045361697964851200, 14367543450324474009600, 3464541314885011705344000
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OFFSET
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1,3
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COMMENTS
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Also, the number of Hamiltonian directed circuits in the crown graph of order n.
Or the number of those 3Xn Latin rectangles (cf. A000186) the second row of which is a full cycle. [From Vladimir Shevelev, Mar 22 2010]
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REFERENCES
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V. S. Shevelev, Reduced Latin rectangles and square matrices with equal row and column sums, Diskr.Mat.(J. of the Akademy of Sciences of Russia) 4(1992),91-110. [From Vladimir Shevelev, Mar 22 2010]
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LINKS
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Table of n, a(n) for n=1..16.
Eric Weisstein's World of Mathematics, Crown Graph
Eric Weisstein's World of Mathematics, Hamiltonian Cycle
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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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MATHEMATICA
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Join[{0}, Table[(-1)^n 2(n-1)!+n!Sum[(-1)^j (n-j-1)!Binomial[2n-j-1, j], {j, 0, n-1}], {n, 2, 20}]] (* From Harvey P. Dale, Mar 07 2012 *)
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CROSSREFS
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Cf. A114939, A137729.
Sequence in context: A012425 A012422 A122767 * A091472 A156518 A012727
Adjacent sequences: A094044 A094045 A094046 * A094048 A094049 A094050
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KEYWORD
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nonn
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AUTHOR
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Matthijs Coster, Apr 29 2004
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EXTENSIONS
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Better definition from Joel B. Lewis, Jun 30 2007
Formula and further terms from Max Alekseyev, Feb 10 2008
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STATUS
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approved
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