A089179 - OEIS

A089179

Number of equivalence classes of permutations of n letters, where the relation is that f and g are equivalent if every cycle of f is a power of some cycle of g.

%I #9 Jun 05 2019 09:46:26

%S 1,2,6,20,85,402,2464,15752,119655,976190,9331894,91769988,1077214879,

%T 12570658310,168390947820,2337860163248,35513649943201,

%U 544140329564898,9660558198790510,166372364728477220

%N Number of equivalence classes of permutations of n letters, where the relation is that f and g are equivalent if every cycle of f is a power of some cycle of g.

%H Albert Nijenhuis, <a href="https://www.jstor.org/stable/2319149">Solution to Problem 5932</a>, Amer. Math. Monthly, 82 (1975), pp. 86-87.

%H R. P. Stanley, <a href="https://www.jstor.org/stable/2319419">Problem 5932</a>, Amer. Math. Monthly, 80 (1973), p. 949.

%F E.g.f. x*exp(Sum( x^n/(n*phi(n)), n=1..infinity )) (phi is Euler's totient function). a(n) = n* A003510(n-1). - _Vladeta Jovovic_, Apr 15 2006

%t yy[nn_] := CoefficientList[Normal[Series[Exp[Sum[x^n t[n]/(n), {n, 1, nn}]], {x, 0, nn}]], x]; zz[nn_] := Table[Simplify[yy[nn][[m]] m! ], {m, 1, nn}]; zz[10] (* will then give the first 10 values *)

%K easy,nonn

%O 1,2

%A Herbert S. Wilf, Dec 08 2003

%E More terms from _Vladeta Jovovic_, Apr 15 2006