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A059375 Number of seating arrangements for the ménage problem. 2
1, 0, 0, 12, 96, 3120, 115200, 5836320, 382072320, 31488549120, 3191834419200, 390445460697600, 56729732529254400, 9659308746908620800, 1905270127543015833600, 431026303509734220288000, 110865322076320374571008000, 32172949121885378686623744000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

The "probleme des menages" asks for the number of gender-alternating seating arrangements for n couples around a circular table with the condition that no two spouses are seated adjacently. - Paul C. Kainen and Michael Somos, Mar 11 2011

REFERENCES

Bogart, Kenneth P. and Doyle, Peter G., Nonsexist solution of the menage problem, Amer. Math. Monthly 93 (1986), no. 7, 514-519.

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 184, mu*(n).

Alexander Guterman, Pólya permanent problem: 100 years after, http://www.law05.si/law14/presentations/Guterman.pdf, 2014.

H. J. Ryser, Combinatorial Mathematics. Mathematical Association of America, Carus Mathematical Monograph 14, 1963, p. 32. equation (2.3).

LINKS

Table of n, a(n) for n=0..17.

FORMULA

a(n) = 2 * n! * A000179(n).

EXAMPLE

a(3) = 12 because there is a unique seating arrangement up to circular and clockwise / counterclockwise symmetry. - Paul C. Kainen and Michael Somos, Mar 11 2011

PROG

(PARI) {a(n) = local(A); if( n<3, n==0, A = vector(n); A[3] = 1; for(k=4, n, A[k] = (k * (k - 2) * A[k-1] + k * A[k-2] - 4 * (-1)^k) / (k-2)); 2 * n! * A[n])} /* Michael Somos, Mar 11 2011 */

CROSSREFS

Cf. A000179.

Sequence in context: A155620 A219438 A219139 * A251430 A027255 A121791

Adjacent sequences:  A059372 A059373 A059374 * A059376 A059377 A059378

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jan 28 2001

STATUS

approved

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Last modified December 22 07:03 EST 2014. Contains 252328 sequences.