A208192 Number of distinct 7-colored necklaces with n beads per color.

1, 720, 48648960, 8690922240480, 2374127830286012160, 823940558733748910598720, 333504309246734399617946903040, 150277870737901828652705825755721760, 73288704867601350013562616043249358012160, 37980016035292737119901943600678905519608160480

Offset: 0

Author

Alois P. Heinz, Feb 24 2012

Keywords

• nonn

Examples

			a(0) =   1: the empty necklace.
a(1) = 720: {0123456, 0123465, ..., 0654321}.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..60

Crossrefs

Column k=7 of A208183.

Cf. A000010, A000142.

Programs

Maple

with(numtheory):
a:= n-> `if`(n=0, 1, add(phi(n/d) *(7*d)!/(d!^7 *7*n), d=divisors(n))):
seq(a(n), n=0..12);

Formula

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

a(n) ~ 7^(7*n-1/2) / (8 * Pi^3 * n^4). - Vaclav Kotesovec, Aug 23 2015