%I #12 Jan 17 2020 16:11:26

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

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

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

%N Decimal expansion of 1/(1+sqrt(e)), a constant appearing in the computation of a limiting probability concerning the number of cycles of a given length in a random permutation.

%C 1/(1+sqrt(e)) is the value of x that maximizes the expression Pi^2/6 - log(x) - log(x)^2 - 2*Li_2(x), where Li_2 is the dilogarithm function.

%H Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants</a>, p. 29.

%H Michael Lugo, <a href="http://arxiv.org/abs/0909.2909">The number of cycles of specified normalized length in permutations</a>, arXiv:0909.2909 [math.CO]

%e 0.37754066879814543536109943425449152124672063469108983694...

%t RealDigits[1/(1 + Sqrt[E]), 10, 101] // First

%o (PARI) 1/(1+sqrt(exp(1))) \\ _Michel Marcus_, Sep 05 2014

%Y Cf. A143301, A246849.

%K nonn,cons

%O 0,1

%A _Jean-François Alcover_, Sep 05 2014