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%I #15 Jul 04 2019 14:31:17
%S 0,8,0,96,384,12,3456,460800,236160,96,168960,3065610240,125962905600,
%T 764467200,3120,12211200,51115799347200,453840358706380800,
%U 226918953109094400,6383697868800,115200,1196052480,1816224465420288000,6896429934345052028928000
%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 round tables with 2*k seats each, such that (i) the gender of persons alternates around each table; and (ii) spouses do not sit next to each other.
%C Tables and seats are labeled. For unlabeled version, see A277265.
%F T(n,k) = A277256(n,k) * 2^n * (n*k)!.
%e Table T(n,k):
%e n=1: 0, 0, 12, 96, 3120, 115200, ...
%e n=2: 8, 384, 236160, 764467200, ...
%e n=3: 96, 460800, 125962905600, ...
%e n=4: 3456, 3065610240, 453840358706380800, ...
%e ...
%Y Cf. A059375 (row n=1), A277265.
%K nonn,tabl
%O 1,2
%A _Max Alekseyev_, Oct 07 2016