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A267389
Number of acyclic orientations of the Turán graph T(n,9).
2
1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3265920, 33022080, 369774720, 4536362880, 60451816320, 869007242880, 13397819541120, 220448163358080, 3854801333416320, 67295207974942080, 1248445283166184320, 24512281966435294080, 507579925622189454720
OFFSET
0,3
COMMENTS
An acyclic orientation is an assignment of a direction to each edge such that no cycle in the graph is consistently oriented. Stanley showed that the number of acyclic orientations of a graph G is equal to the absolute value of the chromatic polynomial X_G(q) evaluated at q=-1.
LINKS
Richard P. Stanley, Acyclic Orientations of Graphs, Discrete Mathematics, 5 (1973), pages 171-178, doi:10.1016/0012-365X(73)90108-8
Wikipedia, Turán graph
FORMULA
a(n) ~ n! / (8 * (1 - log(9/8))^4 * 9^n * (log(9/8))^(n+1)). - Vaclav Kotesovec, Feb 18 2017
CROSSREFS
Column k=9 of A267383.
Sequence in context: A154657 A179361 A179368 * A152693 A152712 A152707
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jan 13 2016
STATUS
approved