A167406 Sequence a(n) gives the number of ways to seat 2n people around a circular table so that person i does not sit across from person n+i for any 1 <= i <= n.

0, 4, 64, 2880, 208896, 23193600, 3640688640, 768126320640, 209688566169600, 71921062285148160, 30278182590480384000, 15350836256712740044800, 9225766813653105691852800, 6485670333458406942179328000, 5272823572160895949091320627200

Offset

1,2

Links

Table of n, a(n) for n=1..15.

Formula

a(n) = (n!)^2/(2*n)*sum{k = 0..n+1}((-1)^k/k!*binomial(2*n-2*k, n-k)*2^k).

Example

When n=2, there are four people seated around a circular table. Person 1 can sit across from either person 2 or person 4, and person 3 can sit either to the left or to the right of person 1. Thus a(2) = 2*2=4.

Prog

(PARI) a(n) = n!^2/(2*n)*sum(k = 0, n+1, (-1)^k/k!*binomial(2*n-2*k, n-k)*2^k) \\ Michel Marcus, Jul 11 2013

Crossrefs

Sequence in context: A002454 A013043 A296741 * A156631 A088065 A053718

Adjacent sequences: A167403 A167404 A167405 * A167407 A167408 A167409

Keyword

nonn

Author

Steven Klee (klees(AT)math.washington.edu), Nov 03 2009

Extensions

More terms from Michel Marcus, Jul 11 2013

Status

approved