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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
Steven R. Finch, Errata and Addenda to Mathematical Constants, arXiv:2001.00578 [math.HO], 2020, p. 29.
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))
C = log(xi)**2/2 + log(xi) + polylog(2, xi) - pi**2/12 + 1
print([int(n) for n in list(str(C)[2:-1])]) # Indranil Ghosh, Jul 04 2017
CROSSREFS
Sequence in context: A129269 A094145 A002388 * A278828 A334448 A011116
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved

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Last modified May 26 13:56 EDT 2024. Contains 372826 sequences. (Running on oeis4.)