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%I #22 Apr 05 2017 04:58:10
%S 0,1,5,96,3528,199620,15908400,1697149440,233631921600,40335000693120,
%T 8536048230528000,2173422135804796800,655519296840629760000,
%U 231135191421131129932800,94208725354330431747302400,43956400457238853734678528000,23278422600113660887881093120000
%N Number of proper colorings of the 2n-gon with 2 instances of each of n colors under rotational symmetry.
%H Omar Sehlouli, Marko Riedel, <a href="http://math.stackexchange.com/questions/2209954/">Hexagon coloring</a>
%H Marko Riedel, <a href="http://www.mathematik.uni-stuttgart.de/~riedelmo/images/noniso-circnoadj3.png">Image of the five colorings of the hexagon (n=3).</a>
%F For n>=2, (1/2)(n-1)! + (1/(2n)) * 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, A284747.
%K nonn
%O 1,3
%A _Marko Riedel_, Mar 31 2017