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A267388 Number of acyclic orientations of the Turán graph T(n,8). 2
1, 1, 2, 6, 24, 120, 720, 5040, 40320, 322560, 2943360, 30078720, 339696000, 4196666880, 56255149440, 812752093440, 12585067447680, 194465276369280, 3220308737573760, 56845456896816000, 1064856592650695040, 21087473349235547520, 440007278378842984320 (list; graph; refs; listen; history; text; internal format)
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

Alois P. Heinz, Table of n, a(n) for n = 0..450

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! / (7 * (1 - log(8/7))^(7/2) * 8^n * (log(8/7))^(n+1)). - Vaclav Kotesovec, Feb 18 2017

CROSSREFS

Column k=8 of A267383.

Sequence in context: A179354 A179360 A179367 * A152628 A152647 A152642

Adjacent sequences:  A267385 A267386 A267387 * A267389 A267390 A267391

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jan 13 2016

STATUS

approved

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Last modified October 28 04:43 EDT 2021. Contains 348313 sequences. (Running on oeis4.)