OFFSET
2,1
COMMENTS
Consider this practical problem: n > 1 people are to be seated at two labeled round tables (T1 and T2), m of them at table T1, the rest at table T2. Two such seatings (A and B) are considered distinct if at least one person does not sit at the same table in seating A as in seating B, or has a different left or right neighbor (while rotating the seatings around any of the two tables is irrelevant). The number of such seatings is clearly binomial(n,m)*(m-1)!*(n-m-1)! which simplifies to this a(n). The formula holds for any m satisfying 0 < 2*m <= n.
LINKS
Stanislav Sykora, Table of n, a(n) for n = 2..201
MAPLE
a:= n-> (m->n!/(m*(n-m)))(floor(n/2)):
seq(a(n), n=2..30); # Alois P. Heinz, Nov 04 2016
MATHEMATICA
Table[n! / (Floor[n/2] (n - Floor[n/2])), {n, 2, 25}] (* Vincenzo Librandi, Nov 04 2016 *)
PROG
(Magma) [Factorial(n)/(Floor(n/2)*(n-Floor(n/2))): n in [2..30]]; // Vincenzo Librandi, Nov 04 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Stanislav Sykora, Nov 03 2016
STATUS
approved