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 A252765 Number of distinct n-colored necklaces with n beads per color. 2
 1, 1, 2, 188, 3941598, 24934429725024, 74171603795480180204640, 150277870737901828652705825755721760, 283839436431731355577562936415156522873876247241520, 655934428473920614716696820356119117524334608980167506174657536026880 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..25 FORMULA a(n) = Sum_{d|n} phi(n/d)*(n*d)!/(d!^k*n^2) for n>0, a(0) = 1. From Vaclav Kotesovec, Aug 23 2015: (Start) a(n) ~ (n^2)! / (n^2 * (n!)^n). a(n) ~ n^(n^2 - n/2 - 1) / (exp(1/12) * (2*Pi)^((n-1)/2)). (End) MAPLE with(numtheory): a:= n-> `if`(n=0, 1, add(phi(n/d)*(n*d)!/(d!^n*n^2), d=divisors(n))): seq(a(n), n=0..10); MATHEMATICA a[n_] := If[n == 0, 1, DivisorSum[n, EulerPhi[n/#]*(n*#)!/(#!^n*n^2)&]]; Table[a[n], {n, 0, 10}] (* Jean-François Alcover, Mar 25 2017, translated from Maple *) CROSSREFS Main diagonal of A208183. Cf. A000010, A000142. Sequence in context: A232703 A135126 A053936 * A172801 A318195 A307587 Adjacent sequences: A252762 A252763 A252764 * A252766 A252767 A252768 KEYWORD nonn AUTHOR Alois P. Heinz, Dec 21 2014 STATUS approved

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Last modified August 15 09:07 EDT 2024. Contains 375173 sequences. (Running on oeis4.)