cp's OEIS Frontend

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.

%I A271948 #26 Apr 20 2016 10:35:12
%S A271948 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,
%T A271948 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,
%U A271948 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
%N 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.
%D A271948 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.4.2 Random Mapping Statistics, p. 289.
%H A271948 Xavier Gourdon, <a href="http://dx.doi.org/10.1016/S0012-365X(97)00115-5">Largest component in random combinatorial structures</a>, Discrete Mathematics 180, 1998, Pages 185-209.
%e A271948 0.049469852279228075333485464056253836603725107670028013295315781039...
%t A271948 digits = 96; F[x_] := 1 - Exp[-x]/Sqrt[Pi*x] - Erf[Sqrt[x]]; Clear[f, g];
%t A271948 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]];
%t A271948 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]];
%t A271948 Join[{0}, RealDigits[g[m] - f[m]^2, 10, digits][[1]]]
%Y A271948 Cf. A084945, A143297, A244067, A244258, A244261, A261873, A271871.
%K A271948 nonn,cons
%O A271948 0,2
%A A271948 _Jean-François Alcover_, Apr 20 2016