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A059375
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Number of seating arrangements for the menage problem.
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1
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1, 0, 0, 12, 96, 3120, 115200, 5836320, 382072320, 31488549120, 3191834419200, 390445460697600, 56729732529254400, 9659308746908620800, 1905270127543015833600, 431026303509734220288000, 110865322076320374571008000, 32172949121885378686623744000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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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
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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).
H. J. Ryser, Combinatorial Mathematics. Mathematical Association of America, Carus Mathematical Monograph 14, 1963, p. 32. equation (2.3).
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FORMULA
| a(n) = 2 * n! * A000179(n).
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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
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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 */
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CROSSREFS
| Cf. A000179.
Sequence in context: A038845 A204623 A155620 * A027255 A121791 A016753
Adjacent sequences: A059372 A059373 A059374 * A059376 A059377 A059378
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jan 28 2001
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