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A271871
Decimal expansion of a constant related to the expected number of vertices of the largest tree associated with a random mapping on n symbols.
1
4, 8, 3, 4, 9, 8, 3, 4, 7, 1, 5, 4, 4, 2, 5, 5, 0, 0, 9, 2, 4, 0, 2, 6, 3, 6, 0, 8, 5, 0, 7, 5, 6, 1, 9, 4, 4, 4, 9, 2, 4, 6, 6, 7, 9, 5, 4, 1, 3, 3, 8, 1, 0, 4, 3, 2, 9, 2, 6, 4, 9, 4, 1, 5, 5, 2, 4, 7, 0, 9, 3, 3, 5, 1, 1, 4, 0, 3, 2, 9, 5, 9, 9, 2, 3, 7, 3, 2, 3, 1, 9, 6, 0, 8, 7, 7, 0, 1, 8, 9, 4, 8, 8
OFFSET
0,1
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.4.2 Random Mapping Statistics, p. 289.
LINKS
Xavier Gourdon, Largest component in random combinatorial structures, Discrete Mathematics 180, 1998, Pages 185-209.
EXAMPLE
0.48349834715442550092402636085075619444924667954133810432926494155247...
MATHEMATICA
digits = 98; F[x_] := 1 - Exp[-x]/Sqrt[Pi*x] - Erf[Sqrt[x]]; Clear[f]; f[m_] := f[m] = 2 NIntegrate[1-(1-F[x])^-1, {x, 0, m}, WorkingPrecision -> digits+10]; f[m = 100]; f[m = 2 m]; Print["m = ", m]; While[ RealDigits[ f[m], 10, digits + 5][[1]] != RealDigits[f[m/2], 10, digits + 5][[1]], m = 2 m; Print["m = ", m]]; RealDigits[f[m/2], 10, digits + 5][[1]]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
STATUS
approved