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.

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

Table of n, a(n) for n=0..102.

Xavier Gourdon, Largest component in random combinatorial structures, Disc. Math. 180 (1998) 185-209.

Ljuben Mutafchiev and Steven Finch, Large Components and Trees of Random Mappings, arXiv:2512.13662 [math.CO], 2025. See p. 4.

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

Cf. A084945, A143297, A244067, A244258, A244261, A261873.

Sequence in context: A395214 A300690 A193077 * A204993 A234001 A248946

Adjacent sequences: A271868 A271869 A271870 * A271872 A271873 A271874

Keyword

nonn,cons

Author

Jean-François Alcover, Apr 20 2016

Status

approved