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A252765
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Number of distinct n-colored necklaces with n beads per color.
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2
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1, 1, 2, 188, 3941598, 24934429725024, 74171603795480180204640, 150277870737901828652705825755721760, 283839436431731355577562936415156522873876247241520, 655934428473920614716696820356119117524334608980167506174657536026880
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = Sum_{d|n} phi(n/d)*(n*d)!/(d!^k*n^2) for n>0, a(0) = 1.
a(n) ~ (n^2)! / (n^2 * (n!)^n).
a(n) ~ n^(n^2 - n/2 - 1) / (exp(1/12) * (2*Pi)^((n-1)/2)).
(End)
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MAPLE
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with(numtheory):
a:= n-> `if`(n=0, 1, add(phi(n/d)*(n*d)!/(d!^n*n^2), d=divisors(n))):
seq(a(n), n=0..10);
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MATHEMATICA
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a[n_] := If[n == 0, 1, DivisorSum[n, EulerPhi[n/#]*(n*#)!/(#!^n*n^2)&]];
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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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