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

1,4

Comments

For labeled version, see A277257.

Links

Table of n, a(n) for n=1..30.

Formula

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

Example

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.

Sequence in context: A227830 A299521 A167164 * A263631 A010239 A320975

Adjacent sequences: A277262 A277263 A277264 * A277266 A277267 A277268

Keyword

nonn,tabl

Author

Max Alekseyev, Oct 07 2016

Status

approved