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%I #16 Apr 30 2019 08:23:03
%S 1,1,9,109,1641,27151,478341,8782075,166237161,3220837534,63562741159,
%T 1273237637706,25820645555109,529080420540114,10937268142896643,
%U 227824992158991334,4777204094770874857,100757627271124231383,2136117417348870713646,45496022230420668679932
%N Number of necklaces with n white beads and 8*n black beads.
%H Alois P. Heinz, <a href="/A261502/b261502.txt">Table of n, a(n) for n = 0..730</a>
%H F. Ruskey, <a href="http://combos.org/necklace">Necklaces, Lyndon words, De Bruijn sequences, etc.</a>
%H F. Ruskey, <a href="/A000011/a000011.pdf">Necklaces, Lyndon words, De Bruijn sequences, etc.</a> [Cached copy, with permission, pdf format only]
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Necklace.html">Necklace</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Necklace_(combinatorics)">Necklace (combinatorics)</a>
%H <a href="/index/Ne#necklaces">Index entries for sequences related to necklaces</a>
%F a(n) = 1/(9*n) * Sum_{d|n} C(9*n/d,n/d) * A000010(d) for n>0, a(0) = 1.
%F a(n) ~ 9^(9*n-1/2) / (sqrt(2*Pi) * 8^(8*n+1/2) * n^(3/2)). - _Vaclav Kotesovec_, Aug 22 2015
%p with(numtheory):
%p a:= n-> `if`(n=0, 1, add(binomial(9*n/d, n/d)
%p *phi(d), d=divisors(n))/(9*n)):
%p seq(a(n), n=0..25);
%Y Column k=8 of A261494.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Aug 21 2015