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Decimal expansion of the coefficient c appearing in the expression of the asymptotic expected shortest cycle in a random n-cyclation as c*sqrt(n).
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%I #57 Jan 17 2020 05:45:29

%S 1,4,5,7,2,7,0,8,7,9,2,7,3,6,5,3,8,5,3,6,9,4,4,5,4,0,6,8,1,2,0,0,4,7,

%T 0,5,9,6,6,0,5,3,0,0,2,0,2,3,5,2,2,4,6,5,9,2,1,3,2,9,7,0,8,0,7,3,9,7,

%U 9,8,3,7,3,9,7,3,2,2,0,0,0,1,8,2,0,5,8,7,9,5,8,3,0,9,6,8,4,0,3,4,5,1

%N Decimal expansion of the coefficient c appearing in the expression of the asymptotic expected shortest cycle in a random n-cyclation as c*sqrt(n).

%H Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants</a>, p. 35.

%H Nicholas Pippenger, <a href="http://arxiv.org/abs/math/0408031">Random cyclations</a>, arXiv:math /0408031 [math.CO]

%F (sqrt(Pi)/2)*integral_{0..infinity} exp(-x - Ei(-x)/2), where Ei is the exponential integral function.

%e 1.457270879273653853694454068120047059660530020235224659213297...

%t digits = 102; (Sqrt[Pi]/2)*NIntegrate[Exp[-x - ExpIntegralEi[-x]/2], {x, 0, Infinity}, WorkingPrecision -> digits+10] // RealDigits[#, 10, digits]& // First

%Y Cf. A143297 (analog in the case of the expected *longest* cycle in a random cyclation).

%K nonn,cons,easy

%O 1,2

%A _Jean-François Alcover_, Sep 08 2014