A277876 a(n) = n!/(m*(n-m)) with m = floor(n/2).

2, 3, 6, 20, 80, 420, 2520, 18144, 145152, 1330560, 13305600, 148262400, 1779148800, 23351328000, 326918592000, 4940103168000, 79041650688000, 1351612226764800, 24329020081766400, 464463110651904000, 9289262213038080000, 195848611658219520000

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

Sequence in context: A168268 A340652 A361648 * A002078 A000372 A333445

Adjacent sequences: A277873 A277874 A277875 * A277877 A277878 A277879

Keyword

nonn

Author

Stanislav Sykora, Nov 03 2016

Status

approved