%I #15 Jun 12 2016 04:49:02

%S 1,7,9,3,7,4,0,7,8,7,3,4,0,1,7,1,8,1,9,6,1,9,8,9,5,8,7,3,1,8,3,1,6,4,

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

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

%N Decimal expansion of 1/exp(exp(1)-1).

%C This is the limiting value of the probability that a random n-permutation will have no cycles of length less than k (for any k) as n goes to infinity. For example, the probability (as n goes to infinity) that a random n-permutation has no fixed points is 1/exp(1). The probability that it has no cycles of length 1 or 2 is 1/exp(1+1/2). The probability that it has no cycles of length 1 or 2 or 3 is 1/exp(1+1/2+1/3!)...

%H P. Flajolet and R. Sedgewick, <a href="http://algo.inria.fr/flajolet/Publications/books.html">Analytic Combinatorics</a>, 2009; see page 228.

%F Equals 1/A234473. - _Michel Marcus_, Jun 12 2016

%e 0.1793740787340171819619895873183164984596816...

%p Digits:=100: evalf(1/exp(exp(1)-1)); # _Wesley Ivan Hurt_, Jun 11 2016

%t RealDigits[1/E^(E - 1), 10, 50][[1]]

%o (PARI) 1/exp(exp(1)-1) \\ _Michel Marcus_, Jun 12 2016

%Y Cf. A000166, A038205, A047865, A234473.

%K nonn,cons

%O 0,2

%A _Geoffrey Critzer_, Jun 11 2016