cp's OEIS Frontend

A208193 Number of distinct 8-colored necklaces with n beads per color.

%I A208193 #13 Aug 23 2015 03:57:08
%S A208193 1,5040,5108105520,15391623287043360,74701932179186551241520,
%T A208193 474389544274867071519255599040,3581026866351385580856518554063502880,
%U A208193 30495546426686489361833408314854897254404320,283839436431731355577562936415156522873876247241520
%N A208193 Number of distinct 8-colored necklaces with n beads per color.
%C A208193 In general, column k > 1 of A208183 is asymptotic to k^(k*n-1/2) / ((2*Pi)^((k-1)/2) * n^((k+1)/2)). - _Vaclav Kotesovec_, Aug 23 2015
%H A208193 Alois P. Heinz, <a href="/A208193/b208193.txt">Table of n, a(n) for n = 0..50</a>
%F A208193 a(n) = Sum_{d|n} phi(n/d)*(8*d)!/(d!^8*8*n) if n>0 and a(0) = 1.
%F A208193 a(n) ~ 8^(8*n-1/2) / ((2*Pi)^(7/2) * n^(9/2)). - _Vaclav Kotesovec_, Aug 23 2015
%e A208193 a(0) =    1: the empty necklace.
%e A208193 a(1) = 5040: {01234567, 01234576, ..., 07654321}.
%p A208193 with(numtheory):
%p A208193 a:= n-> `if`(n=0, 1, add(phi(n/d) *(8*d)!/(d!^8 *8*n), d=divisors(n))):
%p A208193 seq(a(n), n=0..10);
%Y A208193 Column k=8 of A208183.
%Y A208193 Cf. A000010, A000142.
%K A208193 nonn
%O A208193 0,2
%A A208193 _Alois P. Heinz_, Feb 24 2012