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A325956
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Number of cyclic permutations of [n] with symmetry order s=1.
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0
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1, 0, 0, 4, 20, 108, 714, 4992, 40284, 362480, 3628790, 39912648, 479001588, 6226974684, 87178287120, 1307673722880, 20922789887984, 355687417715904, 6402373705727982, 121645100223034480, 2432902008175589664, 51090942167993548700, 1124000727777607679978, 25852016738803204991232
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OFFSET
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1,4
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LINKS
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FORMULA
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a(n) = (1/n)*Sum_{d|n} moebius(d)*phi(d)*d^(n/d)*(n/d)!.
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MATHEMATICA
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Table[(1/n) DivisorSum[n, MoebiusMu[#] EulerPhi[#] #^(n/#)*(n/#)! &], {n, 24}] (* Michael De Vlieger, May 07 2021 *)
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PROG
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(PARI) a(n) = sumdiv(n, d, moebius(d)*eulerphi(d)*d^(n/d)*(n/d)!)/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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EXTENSIONS
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STATUS
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approved
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