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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. 2

%I

%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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Last modified May 15 16:02 EDT 2021. Contains 343920 sequences. (Running on oeis4.)