A208192 - OEIS

%I #12 Aug 23 2015 03:49:33

%S 1,720,48648960,8690922240480,2374127830286012160,

%T 823940558733748910598720,333504309246734399617946903040,

%U 150277870737901828652705825755721760,73288704867601350013562616043249358012160,37980016035292737119901943600678905519608160480

%N Number of distinct 7-colored necklaces with n beads per color.

%H Alois P. Heinz, <a href="/A208192/b208192.txt">Table of n, a(n) for n = 0..60</a>

%F a(n) = Sum_{d|n} phi(n/d)*(7*d)!/(d!^7*7*n) if n>0 and a(0) = 1.

%F a(n) ~ 7^(7*n-1/2) / (8 * Pi^3 * n^4). - _Vaclav Kotesovec_, Aug 23 2015

%e a(0) =   1: the empty necklace.

%e a(1) = 720: {0123456, 0123465, ..., 0654321}.

%p with(numtheory):

%p a:= n-> `if`(n=0, 1, add(phi(n/d) *(7*d)!/(d!^7 *7*n), d=divisors(n))):

%p seq(a(n), n=0..12);

%Y Column k=7 of A208183.

%Y Cf. A000010, A000142.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Feb 24 2012