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A272430
Asymptotic variance (normalized by n^2) of the second largest connected component in a random mapping on n symbols.
0
0, 1, 8, 6, 2, 0, 2, 2, 3, 3, 0, 6, 7, 8, 1, 3, 8, 8, 7, 2, 1, 4, 0, 6, 5, 7, 0, 3, 6, 2, 3, 4, 3, 1, 5, 0, 4, 3, 1, 9, 3, 5, 6, 0, 1, 4, 4, 9, 5, 7, 4, 9, 9, 8, 2, 3, 1, 8, 4, 2, 5, 9, 1, 9, 9, 9, 2, 8, 1, 2, 3, 3, 6, 1, 8, 7, 8, 5, 3, 1, 2, 2, 6, 5, 3, 0, 2, 3, 5, 7, 0, 3, 1, 1, 2, 3, 1, 6, 5
OFFSET
0,3
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.4.2 Random mapping statistics, p. 290.
LINKS
Xavier Gourdon, Combinatoire, Algorithmique et Géométrie des Polynomes, Ecole Polytechnique, Paris 1996, page 152 (in French).
Eric Weisstein's World of Mathematics, Flajolet-Odlyzko Constant
FORMULA
(8/3)*integral_{0..infinity} x*(1 - e^(Ei(-x)/2)*(1 - Ei(-x)/2)) dx - 4*(integral_{0..infinity} 1 - e^(Ei(-x)/2)*(1 - Ei(-x)/2) dx)^2, where Ei is the exponential integral.
EXAMPLE
0.01862022330678138872140657036234315043193560144957499823184259199928...
MATHEMATICA
digits = 98; Ei = ExpIntegralEi; (8/3)*NIntegrate[x*(1 - E^(Ei[-x]/2)*(1 - Ei[-x]/2)), {x, 0, 200}, WorkingPrecision -> digits + 5] - 4*NIntegrate[1 - E^(Ei[-x]/2)*(1 - Ei[-x]/2), {x, 0, 200}, WorkingPrecision -> digits + 5]^2 // Join[{0}, RealDigits[#, 10, digits][[1]]]&
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
STATUS
approved