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 A208191 Number of distinct 6-colored necklaces with n beads per color. 2
 1, 120, 623760, 7623616080, 135277939358160, 2961088201992945120, 74171603795480180204640, 2041012695880532470281654960, 60192781171721237282811209918160, 1872173374511564116503341160073744080, 60735890264793885272652711347090416733760 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..70 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 EXAMPLE a(0) =   1: the empty necklace. a(1) = 120: {012345, 012354, ..., 054321}. 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); CROSSREFS Column k=6 of A208183. Cf. A000010, A000142. Sequence in context: A325026 A046987 A127232 * A166351 A147964 A172857 Adjacent sequences:  A208188 A208189 A208190 * A208192 A208193 A208194 KEYWORD nonn AUTHOR Alois P. Heinz, Feb 24 2012 STATUS approved

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Last modified August 12 22:46 EDT 2022. Contains 356077 sequences. (Running on oeis4.)