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A261495
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Number of necklaces with n white beads and n^2 black beads.
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2
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1, 1, 3, 19, 245, 4751, 124936, 4141383, 166237161, 7847250409, 426342182761, 26219808548110, 1801378010581175, 136784412621194274, 11378390032696241010, 1029218687419565103111, 100592759623604055645649, 10565465772302876757883823, 1186893721789951847976898669
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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/((n+1)*n) * Sum_{d|n} C((n+1)*n/d,n/d) * A000010(d) for n>0, a(0) = 1.
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MAPLE
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with(numtheory):
a:= n-> `if`(n=0, 1, add(binomial((n^2+n)/d, n/d)
*phi(d), d=divisors(n))/(n^2+n)):
seq(a(n), n=0..20);
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MATHEMATICA
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a[n_] := If[n==0, 1, DivisorSum[n, Binomial[(n^2+n)/#, n/#]*EulerPhi[#]&]/ (n^2 + n)];
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PROG
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(PARI) a(n) = if(n<1, 1, sumdiv(n, d, binomial((n^2 + n)/d, n/d) * eulerphi(d)) / (n^2 + n));
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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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