%I A062346
%S A062346 3,45,210,630,1485,3003,5460,9180,14535,21945,31878,44850,61425,82215,
%T A062346 107880,139128,176715,221445,274170,335790,407253,489555,583740,690900,
%U A062346 812175,948753,1101870,1272810,1462905,1673535,1906128,2162160,2443155
%N A062346 Consider 2n tennis players; a(n) is the number of matches needed to let 
               every possible pair play each other.
%C A062346 Number of matchings of size two (edges) in a complete graph on 2n vertices.
%F A062346 Superseeker suggests a(n) = (6+25n+35n^2+20n^3+4n^4)/2, but I cannot 
               see why this should be true.
%F A062346 a(n)=n*(4n^3 - 12n^2 + 11n -3)/2. - Swapnil P. Bhatia (sbhatia(AT)cs.unh.edu), 
               Jul 20 2006
%e A062346 a(2)=3: given players a,b,c,d, the matches needed are (ab,cd), (ac,bd), 
               (ad,bc).
%e A062346 For example, for the K_4 on vertices {0,1,2,3} the possible matchings 
               of size two are: {{0,1}, {2,3}}, {{0,3},{1,2}} and {{0,2},{1,3}}.
%Y A062346 Sequence in context: A093585 A062270 A069955 this_sequence A002682 A073595 
               A117972
%Y A062346 Adjacent sequences: A062343 A062344 A062345 this_sequence A062347 A062348 
               A062349
%K A062346 nonn
%O A062346 2,1
%A A062346 Michel ten Voorde (seqfan(AT)tenvoorde.org) Jul 06 2001
%E A062346 More terms from Swapnil P. Bhatia (sbhatia(AT)cs.unh.edu), Jul 20 2006