A270174 a(n) is the number of different ways to seat a set of n married male-female couples at a straight table so that men and women alternate and every man is separated by at least two men from his wife.

0, 0, 0, 0, 240, 8640, 584640, 40239360, 3493808640, 364941158400, 45683021260800, 6754660222464000, 1166167699041945600, 232618987254682828800, 53114643986227439616000, 13768242163527512973312000, 4021980517038414919532544000, 1315337131173516220415213568000

Offset

1,5

Comments

We assume that the chairs are uniform and indistinguishable.

First we arrange the women in alternating seats, in 2*n! ways. Second, we find the number, G_{n} say, of ways of arranging men in the remaining seats such that every husband cannot sit at the left or right next 1, 2, ..., h male's seats from his wife. Note that here h = 2. We give the board B4, where X denotes the seat cannot be set at, where there are h X's in first column, and h+1 X's in first row, ..., 2h X's in the h column, ..., other entries are 1's. Thus the number of different ways to seat a set of n married male-female couples at a straight table is a_{n}=2*n!*G_{n}.

Links

Table of n, a(n) for n=1..18.

Feng Jishe, The board B4

D. Zeilberger, Automatic Enumeration of Generalized Ménage Numbers

D. Zeilberger, Automatic Enumeration of Generalized Menage Numbers, arXiv preprint arXiv:1401.1089 [math.CO], 2014.

Formula

a(n) = 2*n! * A292574(n). - Andrew Howroyd, Sep 19 2017

Crossrefs

Cf. A267060, A292574.

Sequence in context: A218131 A268637 A264317 * A008340 A252183 A251434

Adjacent sequences: A270171 A270172 A270173 * A270175 A270176 A270177

Keyword

nonn

Author

Feng Jishe, Mar 12 2016

Extensions

a(11)-a(18) from Andrew Howroyd, Sep 19 2017

Status

approved