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A248080 Decimal expansion of P_0(xi), the maximum limiting probability that a random n-permutation has no cycle exceeding a given length. 1
0, 9, 8, 7, 1, 1, 7, 5, 4, 4, 8, 0, 7, 1, 4, 6, 9, 2, 4, 9, 3, 7, 2, 1, 3, 0, 8, 2, 3, 7, 0, 2, 0, 6, 7, 9, 9, 3, 3, 3, 3, 3, 3, 5, 4, 7, 8, 0, 8, 4, 4, 0, 0, 0, 2, 5, 6, 6, 9, 7, 9, 0, 8, 3, 6, 2, 2, 5, 2, 5, 3, 6, 4, 2, 7, 4, 0, 6, 3, 0, 1, 5, 8, 6, 2, 6, 3, 0, 0, 2, 1, 5, 7, 5, 9, 2, 4, 5, 4, 6, 1, 6 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..101.

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] 2009.

FORMULA

(1/2)*log(1 + sqrt(e))^2 - log(1 + sqrt(e)) + Li_2(1/(1 + sqrt(e))) - Pi^2/12 + 1.

EXAMPLE

0.098711754480714692493721308237020679933333354780844...

MATHEMATICA

xi = 1/(1 + Sqrt[E]); P0[x_] := Log[x]^2/2 + Log[x] + PolyLog[2, x] - Pi^2/12 + 1; Join[{0}, RealDigits[P0[xi], 10, 101] // First]

PROG

(Python)

from mpmath import *

mp.dps=102

xi=1/(1 + sqrt(e))

print map(int, list(str(log(xi)**2/2 + log(xi) + polylog(2, xi) - pi**2/12 + 1)[2:-1])) # Indranil Ghosh, Jul 04 2017

CROSSREFS

Cf. A143301, A246849.

Sequence in context: A129269 A094145 A002388 * A278828 A011116 A106334

Adjacent sequences:  A248077 A248078 A248079 * A248081 A248082 A248083

KEYWORD

nonn,cons,easy

AUTHOR

Jean-Fran├žois Alcover, Oct 14 2014

STATUS

approved

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Last modified June 24 09:37 EDT 2019. Contains 324323 sequences. (Running on oeis4.)