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A246849 Decimal expansion of 1-delta_0, where delta_0 is the Hall-Montgomery constant (A143301). 3
8, 2, 8, 4, 9, 9, 5, 0, 6, 8, 5, 8, 4, 6, 3, 9, 3, 4, 1, 3, 9, 5, 6, 0, 0, 2, 8, 4, 4, 4, 7, 8, 7, 8, 9, 0, 3, 7, 7, 7, 3, 7, 0, 9, 5, 7, 7, 0, 4, 4, 9, 1, 5, 8, 2, 8, 5, 7, 8, 8, 9, 0, 8, 1, 7, 6, 3, 0, 1, 3, 9, 4, 4, 0, 5, 6, 9, 1, 4, 2, 2, 0, 1, 2, 0, 2, 8, 8, 0, 1, 9, 1, 3, 1, 9, 9, 1, 8, 2, 6, 9 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

This constant, by coincidence, is also a limiting probability concerning the number of cycles of a given length in a random permutation.

One has P_1(xi) = 1-delta_0 = Pi^2/6 - log(xi) - log(xi)^2 - 2*Li_2(xi), where xi = 1/(1+sqrt(e)) (see A246848 and the references).

LINKS

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

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

Steven R. Finch, Errata and Addenda to Mathematical Constants, January 22, 2016. [Cached copy, with permission of the author]

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

Eric Weisstein's MathWorld, Hall-Montgomery Constant

FORMULA

Pi^2/6 + log(1 + sqrt(e)) - log(1 + sqrt(e))^2 - 2*Li_2(1/(1 + sqrt(e))), where Li_2 is the dilogarithm function.

EXAMPLE

0.82849950685846393413956002844478789037773709577...

MATHEMATICA

Pi^2/6 + Log[1 + Sqrt[E]] - Log[1 + Sqrt[E]]^2 - 2*PolyLog[2, 1/(1 + Sqrt[E])] // RealDigits[#, 10, 101]& // First

PROG

(PARI) Pi^2/6 + log(exp(1/2)+1) - log(exp(1/2)+1)^2 - 2*polylog(2, 1/(exp(1/2)+1)) \\ Charles R Greathouse IV, Sep 08 2014

(Python)

from mpmath import *

mp.dps=102

print map(int, list(str(pi**2/6 + log(exp(1/2)+1) - log(exp(1/2)+1)**2 - 2*polylog(2, 1/(exp(1/2)+1)))[2:-1])) # Indranil Ghosh, Jul 04 2017

CROSSREFS

Cf. A143301, A246848.

Sequence in context: A303326 A085967 A163960 * A143531 A211269 A278809

Adjacent sequences:  A246846 A246847 A246848 * A246850 A246851 A246852

KEYWORD

nonn,cons

AUTHOR

Jean-Fran├žois Alcover, Sep 05 2014

STATUS

approved

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Last modified October 18 02:23 EDT 2019. Contains 328135 sequences. (Running on oeis4.)