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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. 3
0, 0, 0, 0, 240, 8640, 584640, 40239360, 3493808640, 364941158400, 45683021260800, 6754660222464000, 1166167699041945600, 232618987254682828800, 53114643986227439616000, 13768242163527512973312000, 4021980517038414919532544000, 1315337131173516220415213568000 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 16 17:39 EDT 2021. Contains 348042 sequences. (Running on oeis4.)