

A270174


a(n) is the number of different ways to seat a set of n married malefemale 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
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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 malefemale 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 MÃ©nage 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



