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%I #59 May 07 2021 19:09:45
%S 1,0,0,4,20,108,714,4992,40284,362480,3628790,39912648,479001588,
%T 6226974684,87178287120,1307673722880,20922789887984,355687417715904,
%U 6402373705727982,121645100223034480,2432902008175589664,51090942167993548700,1124000727777607679978,25852016738803204991232
%N Number of cyclic permutations of [n] with symmetry order s=1.
%H Saeed Zakeri, <a href="https://arxiv.org/abs/1909.03300">Cyclic Permutations: Degrees and Combinatorial Types</a>, arXiv:1909.03300 [math.DS], 2019. See Table 1 p. 8.
%F a(n) = (1/n)*Sum_{d|n} moebius(d)*phi(d)*d^(n/d)*(n/d)!.
%F a(n) = n*A064852(n). - _Andrew Howroyd_, May 07 2021
%t Table[(1/n) DivisorSum[n, MoebiusMu[#] EulerPhi[#] #^(n/#)*(n/#)! &], {n, 24}] (* _Michael De Vlieger_, May 07 2021 *)
%o (PARI) a(n) = sumdiv(n, d, moebius(d)*eulerphi(d)*d^(n/d)*(n/d)!)/n;
%Y Cf. A002619, A064852.
%K nonn
%O 1,4
%A _Michel Marcus_, Sep 10 2019
%E a(1)=1 prepended by _Andrew Howroyd_, May 07 2021
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