A003510 An equivalence relation on permutations. (Formerly M1510)

1, 1, 2, 5, 17, 67, 352, 1969, 13295, 97619, 848354, 7647499, 82862683, 897904165, 11226063188, 146116260203, 2089038231953, 30230018309161, 508450431515290, 8318618236423861, 154636109939564681, 2896102013935844771, 59056861862689101272

Offset

0,3

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.18.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Richard Stanley and Albert Nijenhuis, Problem 5932, Amer. Math. Monthly, 82 (1975), 86-87.

Formula

E.g.f.: exp ( Sum_{j>=1} x^j / j*phi(j) ), where phi = Euler phi function (A000010).

Maple

with(numtheory); exp(add(x^n/(n*phi(n)), n=1..31));

Mathematica

max = 22; f[x_] := Exp[ Sum[ x^k/(k*EulerPhi[k]), {k, 1, max}]]; CoefficientList[ Series[ f[x], {x, 0, max}], x]*Range[0, max]! (* Jean-François Alcover, Oct 12 2011 *)

Crossrefs

Cf. A000010.

Sequence in context: A104082 A166474 A054769 * A051625 A056098 A239201

Adjacent sequences: A003507 A003508 A003509 * A003511 A003512 A003513

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Status

approved