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%I #9 Apr 02 2017 12:39:48
%S 0,1,4,54,1794,99990,7955460,848584800,116816051520,20167501253760,
%T 4268024125243200,1086711068022148800,327759648421871635200,
%U 115567595710587359539200,47104362677165542792243200,21978200228619432098036736000,11639211300056830532862403584000,6943663015969522875618267601920000
%N Number of proper colorings of the 2n-gon with 2 instances of each of n colors under dihedral (rotational and reflectional) symmetry.
%H Omar Sehlouli, Marko Riedel, <a href="http://math.stackexchange.com/questions/2209954/">Hexagon coloring</a>
%F For n>=2, (1/4)(n-1)! + (1/4)n! + (1/(4n)) * Sum_{p=0..n} C(n,p) ((-1)^p/2^(n-p)) ((2n-p)! + p(2n-p-1)!).
%e When n=2 the coloring of the nodes of the square with two instances each of black and white must alternate and a rotation by Pi/4 takes one coloring to the other, so there is just one coloring.
%Y Cf. A274634, A284664.
%K nonn
%O 1,3
%A _Marko Riedel_, Apr 01 2017
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