A208191 Number of distinct 6-colored necklaces with n beads per color.

1, 120, 623760, 7623616080, 135277939358160, 2961088201992945120, 74171603795480180204640, 2041012695880532470281654960, 60192781171721237282811209918160, 1872173374511564116503341160073744080, 60735890264793885272652711347090416733760

Offset: 0

Author

Alois P. Heinz, Feb 24 2012

Keywords

• nonn

Examples

			a(0) =   1: the empty necklace.
a(1) = 120: {012345, 012354, ..., 054321}.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..70

Crossrefs

Column k=6 of A208183.

Cf. A000010, A000142.

Programs

Maple

with(numtheory):
a:= n-> `if`(n=0, 1, add(phi(n/d) *(6*d)!/(d!^6 *6*n), d=divisors(n))):
seq(a(n), n=0..12);

Formula

a(n) = Sum_{d|n} phi(n/d)*(6*d)!/(d!^6*6*n) if n>0 and a(0) = 1.

a(n) ~ 6^(6*n-1/2) / (2^(5/2) * Pi^(5/2) * n^(7/2)). - Vaclav Kotesovec, Aug 23 2015