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

1, 24, 11352, 11211216, 15277017432, 24934429725024, 45695805591924048, 90784545100668913392, 191417861328837588057432, 422458626725600682518100816, 966695515158024410709527456352, 2277925055026596846727033776223440, 5499697195473757755182168765034005328

Offset: 0

Author

Alois P. Heinz, Feb 24 2012

Keywords

• nonn

Examples

			a(0) =  1: the empty necklace.
a(1) = 24: {01234, 01243, ..., 04321}.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..100

Crossrefs

Column k=5 of A208183.

Cf. A000010, A000142.

Programs

Maple

with(numtheory):
a:= n-> `if`(n=0, 1, add(phi(n/d) * (5*d)!/(d!^5 *5*n), d=divisors(n))):
seq(a(n), n=0..14);

Formula

a(n) = Sum_{d|n} phi(n/d)*(5*d)!/(d!^5*5*n) if n>0 and a(0) = 1.

a(n) ~ 5^(5*n-1/2) / (4 * Pi^2 * n^3). - Vaclav Kotesovec, Aug 23 2015