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.

1, 2, 6, 20, 85, 402, 2464, 15752, 119655, 976190, 9331894, 91769988, 1077214879, 12570658310, 168390947820, 2337860163248, 35513649943201, 544140329564898, 9660558198790510, 166372364728477220

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..20.

Albert Nijenhuis, Solution to Problem 5932, Amer. Math. Monthly, 82 (1975), pp. 86-87.

R. P. Stanley, Problem 5932, Amer. Math. Monthly, 80 (1973), p. 949.

FORMULA

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

MATHEMATICA

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 *)

CROSSREFS

Sequence in context: A372987 A177480 A365229 * A177483 A004104 A304932

Adjacent sequences: A089176 A089177 A089178 * A089180 A089181 A089182

KEYWORD

easy,nonn

AUTHOR

Herbert S. Wilf, Dec 08 2003

EXTENSIONS

More terms from Vladeta Jovovic, Apr 15 2006

STATUS

approved