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

Author

Jean-François Alcover, Sep 05 2014

Keywords

• nonn
• cons

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.

Examples

			0.37754066879814543536109943425449152124672063469108983694...
		

Links

• 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]

Crossrefs

Cf. A143301, A246849.

Programs

Mathematica

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

PARI

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