A272415 - OEIS

%I #5 Apr 29 2016 10:16:35

%S 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,

%T 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,

%U 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

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

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

%H Xavier Gourdon, <a href="http://algo.inria.fr/gourdon/thesis.html">Combinatoire, Algorithmique et Géométrie des Polynomes</a> Ecole Polytechnique, Paris 1996, page 152 (in French)

%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/Golomb-DickmanConstant.html">Golomb-Dickman Constant</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Golomb%E2%80%93Dickman_constant">Golomb-Dickman constant</a>

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

%e 0.0883160988831536310105425664298767011723643204511633304667874093...

%t 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]]]&

%Y Cf. A084945, A247398, A272413, A272414.

%K nonn,cons

%O 0,2

%A _Jean-François Alcover_, Apr 29 2016