%I A125032
%S A125032 1,1,2,6,2,24,8,8,24,120,40,40,120,40,120,240,280,24,720,240,240,720,
%T A125032 240,720,1440,1680,144,240,80,720,1440,2880,1680,1680,1680,8640,2400,
%U A125032 144,2400,2640,5040,1680,1680,5040,1680,5040,10080,11760,1008,1680,560
%N A125032 Triangle read by rows: T(n,k) = number of tournaments with n players 
               which have the k-th score sequence. The score sequences are in the 
               same order as A068029 and start with the empty score sequence.
%C A125032 The score sequences are sorted by number of players and then lexicographically.
%C A125032 There are A000571(m) score sequences for m players. The sum of all the 
               a(n) for m players is A006125(m)=2^(m(m-1)/2).
%H A125032 Martin Fuller, <a href="b125032.txt">Table of n, a(n) for n = 1..2242</
               a>
%H A125032 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               ScoreSequence.html">Score Sequence</a>
%H A125032 <a href="Sindx_To.html#tournament">Index entries for sequences related 
               to tournaments</a>
%e A125032 There are two score sequences with 3 players: [0,1,2] from 6 tournaments 
               and [1,1,1] from 2 tournaments. These score sequences come 4th and 
               5th respectively, so a(4)=6 and a(5)=2.
%Y A125032 Cf. A000571, A006125, A068029, A125031 (number of highest scorers), A123553.
%Y A125032 Other sequences that can be calculated using this one: A013976, A125031.
%Y A125032 Sequence in context: A126287 A008556 A096485 this_sequence A131980 A076743 
               A141056
%Y A125032 Adjacent sequences: A125029 A125030 A125031 this_sequence A125033 A125034 
               A125035
%K A125032 nonn,tabf
%O A125032 1,3
%A A125032 Martin Fuller (martin_n_fuller(AT)btinternet.com), Nov 16 2006