A272413 Asymptotic mean (normalized by n) of the second longest cycle in a random permutation on n symbols.

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

Offset

0,1

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..97.

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 - exp(Ei(-x))*(1 - Ei(-x)) dx, where Ei is the exponential integral.

Example

0.20958087428418581398902965781534955690113103201623433...

Mathematica

digits = 98; NIntegrate[1 - Exp[ExpIntegralEi[-x]]*(1 - ExpIntegralEi[-x]), {x, 0, 200}, WorkingPrecision -> digits+5] // RealDigits[#, 10, digits]& // First

Crossrefs

Cf. A084945, A247398.

Sequence in context: A262177 A136319 A176057 * A152566 A021481 A372910

Adjacent sequences: A272410 A272411 A272412 * A272414 A272415 A272416

Keyword

nonn,cons

Author

Jean-François Alcover, Apr 29 2016

Status

approved