cp's OEIS Frontend

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.

%I A270174 #35 Sep 19 2017 21:30:48
%S A270174 0,0,0,0,240,8640,584640,40239360,3493808640,364941158400,
%T A270174 45683021260800,6754660222464000,1166167699041945600,
%U A270174 232618987254682828800,53114643986227439616000,13768242163527512973312000,4021980517038414919532544000,1315337131173516220415213568000
%N 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.
%C A270174 We assume that the chairs are uniform and indistinguishable.
%C A270174 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}.
%H A270174 Feng Jishe, <a href="/A270174/a270174.jpg">The board B4</a>
%H A270174 D. Zeilberger, <a href="http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/menages.html">Automatic Enumeration of Generalized Ménage Numbers</a>
%H A270174 D. Zeilberger, <a href="http://arxiv.org/abs/1401.1089">Automatic Enumeration of Generalized Menage Numbers</a>, arXiv preprint arXiv:1401.1089 [math.CO], 2014.
%F A270174 a(n) = 2*n! * A292574(n). - _Andrew Howroyd_, Sep 19 2017
%Y A270174 Cf. A267060, A292574.
%K A270174 nonn
%O A270174 1,5
%A A270174 _Feng Jishe_, Mar 12 2016
%E A270174 a(11)-a(18) from _Andrew Howroyd_, Sep 19 2017