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A261499
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Number of necklaces with n white beads and 5*n black beads.
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3
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1, 1, 6, 46, 446, 4751, 54132, 642342, 7861662, 98480332, 1256569506, 16273981758, 213378976004, 2826867619109, 37782553160820, 508840821830546, 6898459216311582, 94070535317459018, 1289430373206452136, 17755914760643605782, 245518560760433583946
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OFFSET
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0,3
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LINKS
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Eric Weisstein's World of Mathematics, Necklace
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FORMULA
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a(n) = 1/(6*n) * Sum_{d|n} C(6*n/d,n/d) * A000010(d) for n>0, a(0) = 1.
a(n) ~ 6^(6*n) / (2 * sqrt(3*Pi) * 5^(5*n+1/2) * n^(3/2)). - Vaclav Kotesovec, Aug 22 2015
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MAPLE
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with(numtheory):
a:= n-> `if`(n=0, 1, add(binomial(6*n/d, n/d)
*phi(d), d=divisors(n))/(6*n)):
seq(a(n), n=0..25);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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