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%I #6 Apr 03 2014 11:35:07
%S 1,1,2,6,2,24,8,8,24,120,40,40,120,40,120,240,280,24,720,240,240,720,
%T 240,720,1440,1680,144,240,80,720,1440,2880,1680,1680,1680,8640,2400,
%U 144,2400,2640,5040,1680,1680,5040,1680,5040,10080,11760,1008,1680,560
%N 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 The score sequences are sorted by number of players and then lexicographically.
%C 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 Martin Fuller, <a href="/A125032/b125032.txt">Table of n, a(n) for n = 1..2242</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ScoreSequence.html">Score Sequence</a>
%H <a href="/index/To#tournament">Index entries for sequences related to tournaments</a>
%e 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 Cf. A000571, A006125, A068029, A125031 (number of highest scorers), A123553.
%Y Other sequences that can be calculated using this one: A013976, A125031.
%K nonn,tabf
%O 1,3
%A _Martin Fuller_, Nov 16 2006
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