%I #35 Mar 28 2016 18:46:43

%S 1,394,122601,8510140,210940745,2524556538,17167621086,72787256640,

%T 202996629360,382918536000,492133561920,424994169600,236107872000,

%U 76281004800,10897286400

%N Number of nonisomorphic edge colorings of the Petersen graph with exactly n colors.

%C This is zero when n is more than fifteen because only fifteen edges are available.

%C These are not colorings in the strict sense, since there is no requirement that adjacent edges have different colors. - _N. J. A. Sloane_, Mar 28 2016

%C The value for n=15 is 15!/120 because all orbits are the same size namely 120 (order of the symmetric group on five elements) when each of the 15 edges has a unique color. - _Marko Riedel_, Mar 28 2016

%H Math StackExchange, <a href="http://math.stackexchange.com/questions/1711016/">Edge colorings of the Petersen graph</a>

%F Cycle index of the automorphisms acting on the edges is (1/120)*S[1]^15+(5/24)*S[2]^6*S[1]^3+(1/4)*S[4]^3*S[2]*S[1]+(1/6)*S[3]^5+(1/6)*S[3]*S[6]^2+(1/5)*S[5]^3.

%F Inclusion-exclusion yields a(n) = sum(C(n, q)*(-1)^q*A270842(n - q), q = 0 .. n)

%Y Cf. A270842, A063843.

%K nonn,easy,fini,full

%O 1,2

%A _Marko Riedel_, Mar 24 2016