%I A119743
%S A119743 1,1,1,6,3,1,15,45,15,1,28,210,420,105,1,45,630,3150,4725,945,1,66,1485,
%T A119743 13860,51975,62370,10395,1,91,3003,45045,315315,945945,945945,135135,1,
%U A119743 120,5460,120120,1351350,7567560,18918900,16216200,2027025,1,153,9180
%N A119743 Triangle read by rows: row n gives number of matchings of size 0<=k<=n 
               (edges) in the complete graph on 2*n >= 2 vertices.
%D A119743 The special case m(n,n) appears in: Flajolet, P. and Noy, M., "Analytic 
               Combinatorics of Chord Diagrams", INRIA Research Report, ISRN INRIA/
               RR-3914-FR+ENG, March 2000.
%F A119743 T(n,k)=(2*n)! / ((2*n-2*k)!*k!*2^k).
%e A119743 For example, T(3,2) is the number of matchings composed of any two edges 
               of the complete graph on 6 vertices. Then T(3,2) = a(3*(3+1)/2+2) 
               = a(8) = 45. Similarly, T(2,2)=a(5)=3 since the only matchings of 
               size 2 on the K_4 are {{0,1},{2,3}}, {{0,3}{1,2}} and {{0,2},{1,3}}.
%Y A119743 Sequence in context: A092151 A066717 A154969 this_sequence A108451 A122178 
               A126445
%Y A119743 Adjacent sequences: A119740 A119741 A119742 this_sequence A119744 A119745 
               A119746
%K A119743 nonn,tabl
%O A119743 1,4
%A A119743 Swapnil P. Bhatia (sbhatia(AT)cs.unh.edu), Jul 29 2006