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A208190 Number of distinct 5-colored necklaces with n beads per color. 2
1, 24, 11352, 11211216, 15277017432, 24934429725024, 45695805591924048, 90784545100668913392, 191417861328837588057432, 422458626725600682518100816, 966695515158024410709527456352, 2277925055026596846727033776223440, 5499697195473757755182168765034005328 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

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

EXAMPLE

a(0) =  1: the empty necklace.

a(1) = 24: {01234, 01243, ..., 04321}.

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);

CROSSREFS

Column k=5 of A208183.

Cf. A000010, A000142.

Sequence in context: A239166 A065236 A074657 * A284985 A013729 A159729

Adjacent sequences:  A208187 A208188 A208189 * A208191 A208192 A208193

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Feb 24 2012

STATUS

approved

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Last modified February 19 12:09 EST 2019. Contains 320310 sequences. (Running on oeis4.)