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%I #9 Jul 04 2019 14:30:27
%S 0,1,0,2,12,2,9,1200,3280,12,44,498960,97193600,5972400,312,265,
%T 415981440,14591060915200,73866846715200,31918489344,9600,1854,
%U 615853022400,7390721380256614400,9022243072072662432000,287350869074488547328,393956489203200,416880,14833,1477095102362880
%N 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 For labeled version, see A277257.
%F T(n,k) = A277256(n,k) * (n*k)! / n! / k^n.
%e Table T(n,k):
%e n=1: 0, 0, 2, 12, 312, 9600, ...
%e n=2: 1, 12, 3280, 5972400, ...
%e n=3: 2, 1200, 97193600, ...
%e n=4: 9, 498960, 14591060915200, ...
%e ...
%Y Cf. A094047 (row n=1), A000166 (column k=1), A277256, A277257.
%K nonn,tabl
%O 1,4
%A _Max Alekseyev_, Oct 07 2016
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