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%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_
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