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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
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
FORMULA
a(n) = 2*n! * A292574(n). - Andrew Howroyd, Sep 19 2017
CROSSREFS
Sequence in context: A218131 A268637 A264317 * A008340 A252183 A251434
KEYWORD
nonn
AUTHOR
Feng Jishe, Mar 12 2016
EXTENSIONS
a(11)-a(18) from Andrew Howroyd, Sep 19 2017
STATUS
approved