%I
%S 1,2,7,40,355,3678,37263,361058,3403613,31653377,292547199,2696619716
%N Football tournament numbers: the number of possible point series for a tournament of n teams playing each other once where 3 points are awarded to the winning team and 1 to each in the case of a tie.
%C This sequence reflects the now common 3point rule of international football where the sum of total points awarded depends on the outcome of each match. The classical 2point rule is equivalent to that for chess tournaments (A007747).
%H A. Ivanyi, L. Lucz, T. Matuszka, and S. Pirzada, <a href="http://www.acta.sapientia.ro/actainfo/C42/info427.pdf">Parallel enumeration of degree sequences of simple graphs</a>, Acta Univ. Sapientiae, Informatica, 4, 2 (2012) 260288.  From _N. J. A. Sloane_, Feb 15 2013
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Three_points_for_a_win">Three points for a win</a>
%e For 2 teams there are 2 possible outcomes: [0, 3] and [1, 1], so a(2) = 2.
%e For 3 teams the outcomes are [0, 3, 6], [1, 3, 4], [3, 3, 3], [1, 1, 6], [1, 2, 4], [0, 4, 4] and [2, 2, 2], so a(3) is 7. Note that the outcome [3, 3, 3] can be obtained in two ways: (A beats B, B beats C, C beats A) or (B beats A, A beats C, C beats B).
%Y Cf. A007747, A047730, A064422, A152789.
%K nonn,nice,more,hard,changed
%O 1,2
%A Thomas Schulze (jazariel(AT)tiscalenet.it), Sep 30 2001
%E a(8) and a(9) from _Jon E. Schoenfield_, May 05 2007
%E a(10) from Ming Li (dawnli(AT)ustc.edu), Jun 20 2008
%E a(11) from _Jon E. Schoenfield_, Sep 04 2008
%E a(12) from _Jon E. Schoenfield_, Dec 12 2008
