cp's OEIS Frontend

A248791 Decimal expansion of P_2(xi), the maximum limiting probability that a random n-permutation has exactly two cycles exceeding a given length.

%I A248791 #21 Apr 22 2021 10:28:52
%S A248791 0,7,2,7,8,8,7,3,8,6,6,0,8,2,1,3,7,3,3,6,6,7,1,8,6,6,3,3,1,8,1,9,1,4,
%T A248791 2,9,6,8,8,9,2,9,5,4,9,4,4,8,7,0,6,8,4,1,4,5,7,5,1,3,1,8,3,4,6,1,4,4,
%U A248791 6,0,6,9,1,6,6,9,0,2,2,7,6,4,0,1,7,0,8,1,9,5,9,2,9,2,0,8,3,6,2,6,9
%N A248791 Decimal expansion of P_2(xi), the maximum limiting probability that a random n-permutation has exactly two cycles exceeding a given length.
%H A248791 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 A248791 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 A248791 -Pi^2/12 + (1/2)*log(1 + sqrt(e))^2 + Li_2(1/(1 + sqrt(e))).
%e A248791 0.0727887386608213733667186633181914296889295494487...
%t A248791 xi = 1/(1 + Sqrt[E]); P2[x_] := -Pi^2/12 + (1/2)*Log[x]^2 + PolyLog[2, x]; Join[{0}, RealDigits[P2[xi], 10, 100] // First]
%o A248791 (Python)
%o A248791 from mpmath import *
%o A248791 mp.dps=101
%o A248791 xi=1/(1 + sqrt(e))
%o A248791 C = -pi**2/12 + (1/2)*log(xi)**2 + polylog(2, xi)
%o A248791 print([int(n) for n in list(str(C)[2:-1])]) # _Indranil Ghosh_, Jul 03 2017
%Y A248791 Cf. A143301, A246849, A248080.
%K A248791 nonn,cons,easy
%O A248791 0,2
%A A248791 _Jean-François Alcover_, Oct 14 2014