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.

1, 1, 2, 6, 2, 24, 8, 8, 24, 120, 40, 40, 120, 40, 120, 240, 280, 24, 720, 240, 240, 720, 240, 720, 1440, 1680, 144, 240, 80, 720, 1440, 2880, 1680, 1680, 1680, 8640, 2400, 144, 2400, 2640, 5040, 1680, 1680, 5040, 1680, 5040, 10080, 11760, 1008, 1680, 560

Offset: 1

Author

Martin Fuller, Nov 16 2006

Keywords

• nonn
• tabf

Comments

The score sequences are sorted by number of players and then lexicographically.

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).

Examples

			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.
		

Links

• Martin Fuller, Table of n, a(n) for n = 1..2242
• Eric Weisstein's World of Mathematics, Score Sequence
• Index entries for sequences related to tournaments

Crossrefs

Cf. A000571, A006125, A068029, A125031 (number of highest scorers), A123553.

Other sequences that can be calculated using this one: A013976, A125031.