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%I #11 Dec 01 2014 20:22:46
%S 1,1,810,394397776,3111284141045598,191417861328837588057432,
%T 60192781171721237282811209918160,
%U 73288704867601350013562616043249358012160,283839436431731355577562936415156522873876247241520,3019803425783983174717206845130801781814711776972408728524160
%N Number of distinct n-colored necklaces with 8 beads per color.
%H Alois P. Heinz, <a href="/A208189/b208189.txt">Table of n, a(n) for n = 0..30</a>
%F a(n) = Sum_{d|8} phi(8/d)*(n*d)!/(d!^n*n*8) if n>0 and a(0) = 1.
%e a(0) = 1: the empty necklace.
%e a(1) = 1: {00000000}.
%e a(2) = 810: {0000000011111111, ..., 0101010101010101}.
%p with(numtheory);
%p a:= n-> `if`(n=0, 1, add(phi(8/d) *(n*d)!/(d!^n *8*n), d={1, 2, 4, 8})):
%p seq(a(n), n=0..10);
%Y Row n=8 of A208183.
%Y Cf. A000010, A000142.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Feb 24 2012
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