cp's OEIS Frontend

A208190 Number of distinct 5-colored necklaces with n beads per color.

%I A208190 #12 Aug 23 2015 03:36:43
%S A208190 1,24,11352,11211216,15277017432,24934429725024,45695805591924048,
%T A208190 90784545100668913392,191417861328837588057432,
%U A208190 422458626725600682518100816,966695515158024410709527456352,2277925055026596846727033776223440,5499697195473757755182168765034005328
%N A208190 Number of distinct 5-colored necklaces with n beads per color.
%H A208190 Alois P. Heinz, <a href="/A208190/b208190.txt">Table of n, a(n) for n = 0..100</a>
%F A208190 a(n) = Sum_{d|n} phi(n/d)*(5*d)!/(d!^5*5*n) if n>0 and a(0) = 1.
%F A208190 a(n) ~ 5^(5*n-1/2) / (4 * Pi^2 * n^3). - _Vaclav Kotesovec_, Aug 23 2015
%e A208190 a(0) =  1: the empty necklace.
%e A208190 a(1) = 24: {01234, 01243, ..., 04321}.
%p A208190 with(numtheory):
%p A208190 a:= n-> `if`(n=0, 1, add(phi(n/d) * (5*d)!/(d!^5 *5*n), d=divisors(n))):
%p A208190 seq(a(n), n=0..14);
%Y A208190 Column k=5 of A208183.
%Y A208190 Cf. A000010, A000142.
%K A208190 nonn
%O A208190 0,2
%A A208190 _Alois P. Heinz_, Feb 24 2012