1,2

Number of combinations that are possible when placing teams ranked #1 to #4*N in a single elimination tournament where there are four columns of N teams (as in the NCAA Men's Division-1 basketball tournament that is played in March), and each column is a separate regional tournament that produces one of the four semi-finalists. (The teams in the columns appear in sorted order, and the relative positions of the four columns is irrelevant.)

binomial(4*n,n)*binomial(3*n,n)*binomial(2*n,n)/24. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 25 2006

8 ranked teams (n=2) in a four region, single elimination tournament generates 105 different possible tournament orderings, where the teams in each region are ordered from best to worst. (Teams would be matched up from top to bottom, and continue towards the middle two for other matchups, when more than two teams are listed in each column.) 105 tournaments is too many to list here. As this formula applies to single elimination tournaments, this enumeration formula really only makes sense when n is even.

[seq(binomial(4*n, n)*binomial(3*n, n)*binomial(2*n, n)/24, n=1..17)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 25 2006

Cf. A005810, A005809, A000984.

Sequence in context: A075924 A094075 A018233 this_sequence A001546 A111647 A054862

Adjacent sequences: A082365 A082366 A082367 this_sequence A082369 A082370 A082371

easy,nonn

John A. Trono (jtrono(AT)smcvt.edu), May 10 2003

More terms from Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 25 2006