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An equivalence relation on permutations.
(Formerly M1510)
2

%I M1510 #29 Jan 31 2022 06:47:43

%S 1,1,2,5,17,67,352,1969,13295,97619,848354,7647499,82862683,897904165,

%T 11226063188,146116260203,2089038231953,30230018309161,

%U 508450431515290,8318618236423861,154636109939564681,2896102013935844771,59056861862689101272

%N An equivalence relation on permutations.

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

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

%H Vincenzo Librandi, <a href="/A003510/b003510.txt">Table of n, a(n) for n = 0..200</a>

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

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

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

%t 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 *)

%Y Cf. A000010.

%K nonn,easy,nice

%O 0,3

%A _N. J. A. Sloane_