A271948 Decimal expansion of a constant related to the variance of the number of vertices of the largest tree associated with a random mapping on n symbols.

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

Offset: 0

Author

Jean-François Alcover, Apr 20 2016

Keywords

• nonn
• cons

Examples

			0.049469852279228075333485464056253836603725107670028013295315781039...
		

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.

Crossrefs

Cf. A084945, A143297, A244067, A244258, A244261, A261873, A271871.

Programs

Mathematica

digits = 96; F[x_] := 1 - Exp[-x]/Sqrt[Pi*x] - Erf[Sqrt[x]]; Clear[f, g];
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]];
g[m_] := g[m] = (8/3) NIntegrate[(1 - (1 - F[x])^-1)*x, {x, 0, m}, WorkingPrecision -> digits + 10]; g[m = 100]; g[m = 2 m]; Print["m = ", m]; While[RealDigits[g[m], 10, digits + 5][[1]] != RealDigits[g[m/2], 10, digits + 5][[1]], m = 2 m; Print["m = ", m]];
Join[{0}, RealDigits[g[m] - f[m]^2, 10, digits][[1]]]