This site is supported by donations to The OEIS Foundation.



Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A277876 a(n) = n!/(m*(n-m)) with m = floor(n/2). 1


%S 2,3,6,20,80,420,2520,18144,145152,1330560,13305600,148262400,

%T 1779148800,23351328000,326918592000,4940103168000,79041650688000,

%U 1351612226764800,24329020081766400,464463110651904000,9289262213038080000,195848611658219520000

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

%C 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.

%H Stanislav Sykora, <a href="/A277876/b277876.txt">Table of n, a(n) for n = 2..201</a>

%p a:= n-> (m->n!/(m*(n-m)))(floor(n/2)):

%p seq(a(n), n=2..30); # _Alois P. Heinz_, Nov 04 2016

%t Table[n! / (Floor[n/2] (n - Floor[n/2])), {n, 2, 25}] (* _Vincenzo Librandi_, Nov 04 2016 *)

%o (MAGMA) [Factorial(n)/(Floor(n/2)*(n-Floor(n/2))): n in [2..30]]; // _Vincenzo Librandi_, Nov 04 2016

%K nonn

%O 2,1

%A _Stanislav Sykora_, Nov 03 2016

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 18 06:34 EST 2019. Contains 319269 sequences. (Running on oeis4.)