OFFSET
0,4
COMMENTS
A tournament is a directed digraph obtained by assigning a direction for each edge in an undirected complete graph. In a transitive tournament all nodes can be strictly ordered by their reachability.
LINKS
Paul Erdős, On a problem in graph theory, The Mathematical Gazette, 47: 220-223 (1963).
FORMULA
EXAMPLE
Triangle begins:
1
1, 1
2, 4, 2
8, 24, 24, 6
64, 256, 384, 192, 24
1024, 5120, 10240, 7680, 1920, 120
MAPLE
T := (n, k) -> 2^(((n-1)*n - (k-1)*k)/2) * n! / (n-k)!:
seq(seq(T(n, k), k = 0..n), n = 0..8); # Peter Luschny, Nov 02 2023
PROG
(PARI) T(n, k) = binomial(n, k)*k!*2^(binomial(n, 2) - binomial(k, 2))
CROSSREFS
KEYWORD
AUTHOR
Thomas Scheuerle, Sep 14 2023
STATUS
approved