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%I #12 Aug 23 2015 03:46:21
%S 1,120,623760,7623616080,135277939358160,2961088201992945120,
%T 74171603795480180204640,2041012695880532470281654960,
%U 60192781171721237282811209918160,1872173374511564116503341160073744080,60735890264793885272652711347090416733760
%N Number of distinct 6-colored necklaces with n beads per color.
%H Alois P. Heinz, <a href="/A208191/b208191.txt">Table of n, a(n) for n = 0..70</a>
%F a(n) = Sum_{d|n} phi(n/d)*(6*d)!/(d!^6*6*n) if n>0 and a(0) = 1.
%F a(n) ~ 6^(6*n-1/2) / (2^(5/2) * Pi^(5/2) * n^(7/2)). - _Vaclav Kotesovec_, Aug 23 2015
%e a(0) = 1: the empty necklace.
%e a(1) = 120: {012345, 012354, ..., 054321}.
%p with(numtheory):
%p a:= n-> `if`(n=0, 1, add(phi(n/d) *(6*d)!/(d!^6 *6*n), d=divisors(n))):
%p seq(a(n), n=0..12);
%Y Column k=6 of A208183.
%Y Cf. A000010, A000142.
%K nonn
%O 0,2
%A _Alois P. Heinz_, Feb 24 2012
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