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.

0, 1, 0, 2, 12, 2, 9, 1200, 3280, 12, 44, 498960, 97193600, 5972400, 312, 265, 415981440, 14591060915200, 73866846715200, 31918489344, 9600, 1854, 615853022400, 7390721380256614400, 9022243072072662432000, 287350869074488547328, 393956489203200, 416880, 14833, 1477095102362880

Offset: 1

Author

Max Alekseyev, Oct 07 2016

Keywords

• nonn
• tabl

Comments

For labeled version, see A277257.

Examples

			Table T(n,k):
n=1: 0, 0, 2, 12, 312, 9600, ...
n=2: 1, 12, 3280, 5972400, ...
n=3: 2, 1200, 97193600, ...
n=4: 9, 498960, 14591060915200, ...
...
		

Crossrefs

Cf. A094047 (row n=1), A000166 (column k=1), A277256, A277257.

Formula

T(n,k) = A277256(n,k) * (n*k)! / n! / k^n.