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%I #36 Apr 25 2021 02:14:22
%S 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,
%T 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,
%U 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
%N Decimal expansion of P_0(xi), the maximum limiting probability that a random n-permutation has no cycle exceeding a given length.
%H Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants</a>, arXiv:2001.00578 [math.HO], 2020, p. 29.
%H Michael Lugo, <a href="http://arxiv.org/abs/0909.2909">The number of cycles of specified normalized length in permutations</a>, arXiv:0909.2909 [math.CO], 2009.
%F (1/2)*log(1 + sqrt(e))^2 - log(1 + sqrt(e)) + Li_2(1/(1 + sqrt(e))) - Pi^2/12 + 1.
%e 0.098711754480714692493721308237020679933333354780844...
%t 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]
%o (Python)
%o from mpmath import *
%o mp.dps=102
%o xi=1/(1 + sqrt(e))
%o C = log(xi)**2/2 + log(xi) + polylog(2, xi) - pi**2/12 + 1
%o print([int(n) for n in list(str(C)[2:-1])]) # _Indranil Ghosh_, Jul 04 2017
%Y Cf. A143301, A246849.
%K nonn,cons,easy
%O 0,2
%A _Jean-François Alcover_, Oct 14 2014
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