A267386 - OEIS

%I #7 Feb 18 2017 08:36:09

%S 1,1,2,6,24,120,720,4320,30960,256320,2399760,25022880,287250480,

%T 3284869680,41344521840,566715682800,8391341277360,133348995238320,

%U 2262083352430320,38232720235613520,689864650481977200,13221780471876281040,268029961230742291440

%N Number of acyclic orientations of the Turán graph T(n,6).

%C 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.

%H Alois P. Heinz, <a href="/A267386/b267386.txt">Table of n, a(n) for n = 0..450</a>

%H Richard P. Stanley, <a href="http://dx.doi.org/10.1016/0012-365X(73)90108-8">Acyclic Orientations of Graphs</a>, Discrete Mathematics, 5 (1973), pages 171-178, doi:10.1016/0012-365X(73)90108-8

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Tur%C3%A1n_graph">Turán graph</a>

%F a(n) ~ n! / (5 * (1 - log(6/5))^(5/2) * 6^n * (log(6/5))^(n+1)). - _Vaclav Kotesovec_, Feb 18 2017

%Y Column k=6 of A267383.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Jan 13 2016