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A094047 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. 9
0, 0, 2, 12, 312, 9600, 416880, 23879520, 1749363840, 159591720960, 17747520940800, 2363738855385600, 371511874881100800, 68045361697964851200, 14367543450324474009600, 3464541314885011705344000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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]

REFERENCES

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]

LINKS

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

FORMULA

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).

MATHEMATICA

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}]] (* Harvey P. Dale, Mar 07 2012 *)

CROSSREFS

Cf. A114939, A137729.

Sequence in context: A012425 A012422 A122767 * A091472 A156518 A012727

Adjacent sequences:  A094044 A094045 A094046 * A094048 A094049 A094050

KEYWORD

nonn

AUTHOR

Matthijs Coster, Apr 29 2004

EXTENSIONS

Better definition from Joel B. Lewis, Jun 30 2007

Formula and further terms from Max Alekseyev, Feb 10 2008

STATUS

approved

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Last modified October 25 19:24 EDT 2014. Contains 248557 sequences.