Multi-table menage numbers T(n,k) for n,k >= 1 equals the number of ways to seat the gentlemen from 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; provided that the ladies are already properly seated (i.e., no two ladies sit next to each other).

A277256

Multi-table menage numbers T(n,k) for n,k >= 1 equals the number of ways to seat the gentlemen from 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; provided that the ladies are already properly seated (i.e., no two ladies sit next to each other).