cp's OEIS Frontend

A277265 Multi-table menage seating arrangements: T(n,k) for n,k >= 1 equals the number of ways to seat n*k married couples at n unlabeled round tables with 2*k unlabeled seats each, such that (i) the gender of persons alternates around each table; and (ii) spouses do not sit next to each other.

%I A277265 #9 Jul 04 2019 14:30:27
%S A277265 0,1,0,2,12,2,9,1200,3280,12,44,498960,97193600,5972400,312,265,
%T A277265 415981440,14591060915200,73866846715200,31918489344,9600,1854,
%U A277265 615853022400,7390721380256614400,9022243072072662432000,287350869074488547328,393956489203200,416880,14833,1477095102362880
%N A277265 Multi-table menage seating arrangements: T(n,k) for n,k >= 1 equals the number of ways to seat n*k married couples at n unlabeled round tables with 2*k unlabeled seats each, such that (i) the gender of persons alternates around each table; and (ii) spouses do not sit next to each other.
%C A277265 For labeled version, see A277257.
%F A277265 T(n,k) = A277256(n,k) * (n*k)! / n! / k^n.
%e A277265 Table T(n,k):
%e A277265 n=1: 0, 0, 2, 12, 312, 9600, ...
%e A277265 n=2: 1, 12, 3280, 5972400, ...
%e A277265 n=3: 2, 1200, 97193600, ...
%e A277265 n=4: 9, 498960, 14591060915200, ...
%e A277265 ...
%Y A277265 Cf. A094047 (row n=1), A000166 (column k=1), A277256, A277257.
%K A277265 nonn,tabl
%O A277265 1,4
%A A277265 _Max Alekseyev_, Oct 07 2016