A208186 Number of distinct n-colored necklaces with 5 beads per color.

1, 1, 26, 50452, 586637256, 24934429725024, 2961088201992945120, 823940558733748910598720, 474389544274867071519255599040, 515190840198859838606483730223480320, 982409170121762644481286121423409538362880, 3106878824601775580798512171862746898249905228800

Offset: 0

Author

Alois P. Heinz, Feb 24 2012

Keywords

• nonn

Examples

			a(0) =  1: the empty necklace.
a(1) =  1: {00000}.
a(2) = 26: {0000011111, ..., 0101010101}.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..50

Crossrefs

Row n=5 of A208183.

Cf. A000010, A000142.

Programs

Maple

with(numtheory);
a:= n-> `if`(n=0, 1, add(phi(5/d) *(n*d)!/(d!^n *5*n), d={1, 5})):
seq(a(n), n=0..12);

Formula

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