A246848 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.

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, 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, 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

Offset

0,1

Comments

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.

Links

Table of n, a(n) for n=0..100.

Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 29.

Michael Lugo, The number of cycles of specified normalized length in permutations, arXiv:0909.2909 [math.CO]

Example

0.37754066879814543536109943425449152124672063469108983694...

Mathematica

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

Prog

(PARI) 1/(1+sqrt(exp(1))) \\ Michel Marcus, Sep 05 2014

Crossrefs

Cf. A143301, A246849.

Sequence in context: A021730 A153844 A197476 * A019634 A123879 A193016

Adjacent sequences: A246845 A246846 A246847 * A246849 A246850 A246851

Keyword

nonn,cons

Author

Jean-François Alcover, Sep 05 2014

Status

approved