A272415 Asymptotic mean (normalized by n) of the third longest cycle in a random permutation on n symbols.

0, 8, 8, 3, 1, 6, 0, 9, 8, 8, 8, 3, 1, 5, 3, 6, 3, 1, 0, 1, 0, 5, 4, 2, 5, 6, 6, 4, 2, 9, 8, 7, 6, 7, 0, 1, 1, 7, 2, 3, 6, 4, 3, 2, 0, 4, 5, 1, 1, 6, 3, 3, 3, 0, 4, 6, 6, 7, 8, 7, 4, 0, 9, 3, 0, 9, 4, 2, 7, 0, 2, 2, 3, 9, 5, 7, 4, 6, 0, 9, 9, 0, 6, 0, 9, 6, 5, 9, 4, 8, 5, 1, 3, 9, 9, 7, 1, 5, 5

Offset

0,2

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.4 Golomb-Dickman Constant, p. 285.

Links

Table of n, a(n) for n=0..98.

Xavier Gourdon, Combinatoire, Algorithmique et Géométrie des Polynomes Ecole Polytechnique, Paris 1996, page 152 (in French)

Eric Weisstein's MathWorld, Golomb-Dickman Constant

Wikipedia, Golomb-Dickman constant

Formula

Integral_{0..infinity} 1 - e^Ei(-x)*(1 - Ei(-x) + (1/2)*Ei(-x)^2) dx, where Ei is the exponential integral.

Example

0.0883160988831536310105425664298767011723643204511633304667874093...

Mathematica

digits = 98; NIntegrate[1 - E^ExpIntegralEi[-x]*(1 - ExpIntegralEi[-x] + (1/2)*ExpIntegralEi[-x]^2), {x, 0, 100}, WorkingPrecision -> digits + 5] // Join[{0}, RealDigits[#, 10, digits][[1]]]&

Crossrefs

Cf. A084945, A247398, A272413, A272414.

Sequence in context: A210630 A377008 A265292 * A010530 A289915 A021535

Adjacent sequences: A272412 A272413 A272414 * A272416 A272417 A272418

Keyword

nonn,cons

Author

Jean-François Alcover, Apr 29 2016

Status

approved