

A261496


Number of necklaces with n white beads and n^2n black beads.


2



1, 1, 2, 10, 116, 2126, 54132, 1753074, 69159400, 3220837534, 173103115760, 10551652603526, 719578430426044, 54297978110913252, 4492502634679508204, 404469190271900056316, 39370123445405248353744, 4120204305690280446004838, 461365717080849798202175772
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OFFSET

0,3


LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..335
F. Ruskey, Necklaces, Lyndon words, De Bruijn sequences, etc.
F. Ruskey, Necklaces, Lyndon words, De Bruijn sequences, etc. [Cached copy, with permission, pdf format only]
Eric Weisstein's World of Mathematics, Necklace
Wikipedia, Necklace (combinatorics)
Index entries for sequences related to necklaces


FORMULA

a(n) = 1/(n^2) * Sum_{dn} C(n^2/d,n/d) * A000010(d) for n>0, a(0) = 1.
a(n) ~ exp(n1/2) * n^(n5/2) / sqrt(2*Pi).  Vaclav Kotesovec, Aug 22 2015


MAPLE

with(numtheory):
a:= n> `if`(n=0, 1, add(binomial(n^2/d, n/d)
*phi(d), d=divisors(n))/n^2):
seq(a(n), n=0..20);


CROSSREFS

Lower diagonal of A261494.
Cf. A000010.
Sequence in context: A132522 A187653 A131811 * A006121 A110951 A172477
Adjacent sequences: A261493 A261494 A261495 * A261497 A261498 A261499


KEYWORD

nonn


AUTHOR

Alois P. Heinz, Aug 21 2015


STATUS

approved



