chess tournaments:

[N. J. A. Sloane]

%I A047657
%S A047657 1,2,5,16,59,247
%N A047657 Number of score sequences in chess tournament with n players (with 3 outcomes for each game).
%D A047657 P. A. MacMahon, Chess tournamemts and the like treated by the calculus of symmetric functions, Coll. P
apers I, MIT Press, 344-375.
%O A047657 0,3
%K A047657 nonn,more,nice
%A A047657 njas
%Y A047657 This is probably the same as either A028333 or A007747.
%e A047657 With 3 players the possible scores are 420, 411, 330, 321, 222.

This is probably the same as either A028333 or A007747, maybe someone could check! 
It is not obvious from the descriptions.
Perhaps simplest thing would be if someone extended this sequence

MacMahon also discusses the case of tournaments where there
are n players and in each of the C(n,2) games one player gets
3,2,1 or 0 points and the other player gets 0,1,2 or 3.
How many different score sequences are there?
This begins 1, 2, 8, 37 - more terms, someone?

For 3 players the possible scores are
630 621 540 531 522 441 432 333

NJAs