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A252765 Number of distinct n-colored necklaces with n beads per color.

%I A252765 #14 Mar 25 2017 06:39:35
%S A252765 1,1,2,188,3941598,24934429725024,74171603795480180204640,
%T A252765 150277870737901828652705825755721760,
%U A252765 283839436431731355577562936415156522873876247241520,655934428473920614716696820356119117524334608980167506174657536026880
%N A252765 Number of distinct n-colored necklaces with n beads per color.
%H A252765 Alois P. Heinz, <a href="/A252765/b252765.txt">Table of n, a(n) for n = 0..25</a>
%F A252765 a(n) = Sum_{d|n} phi(n/d)*(n*d)!/(d!^k*n^2) for n>0, a(0) = 1.
%F A252765 From _Vaclav Kotesovec_, Aug 23 2015: (Start)
%F A252765 a(n) ~ (n^2)! / (n^2 * (n!)^n).
%F A252765 a(n) ~ n^(n^2 - n/2 - 1) / (exp(1/12) * (2*Pi)^((n-1)/2)).
%F A252765 (End)
%p A252765 with(numtheory):
%p A252765 a:= n-> `if`(n=0, 1, add(phi(n/d)*(n*d)!/(d!^n*n^2), d=divisors(n))):
%p A252765 seq(a(n), n=0..10);
%t A252765 a[n_] := If[n == 0, 1, DivisorSum[n, EulerPhi[n/#]*(n*#)!/(#!^n*n^2)&]];
%t A252765 Table[a[n], {n, 0, 10}] (* _Jean-François Alcover_, Mar 25 2017, translated from Maple *)
%Y A252765 Main diagonal of A208183.
%Y A252765 Cf. A000010, A000142.
%K A252765 nonn
%O A252765 0,3
%A A252765 _Alois P. Heinz_, Dec 21 2014