A212809 Decimal expansion of radius of convergence of g.f. for unlabeled trees (A000055).

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

Offset

0,1

References

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 5.6, p. 296.

Links

Table of n, a(n) for n=0..93.

Michael Drmota and Bernhard Gittenberger, The shape of unlabeled rooted random trees, Eur. J. Comb. 31 (2010) no 8, 2028-2063.

E. M. Palmer and A. J. Schwenk, On the number of trees in a random forest, J. Combin. Theory, B 27 (1979), 109-121.

Formula

Equals 1/A051491. - Vaclav Kotesovec, Jul 29 2013

Example

0.338321856899208...

Mathematica

digits = 95; max = 200;
s[n_, k_] := s[n, k] = a[n + 1 - k] + If[n < 2*k, 0, s[n - k, k]];
a[1] = 1;
a[n_] := a[n] = Sum[a[k]*s[n - 1, k]*k, {k, 1, n - 1}]/(n - 1);
A[x_] := Sum[a[k]*x^k, {k, 0, max}];
eq = Log[c] == 1 + Sum[A[c^-k]/k, {k, 2, max}];
r = 1/c /. FindRoot[eq, {c, 3}, WorkingPrecision -> digits + 5];
RealDigits[r, 10, digits] // First (* Jean-François Alcover, Aug 10 2016 *)

Crossrefs

Cf. A000055.

Sequence in context: A154178 A276800 A332684 * A294643 A029614 A143615

Adjacent sequences: A212806 A212807 A212808 * A212810 A212811 A212812

Keyword

nonn,cons

Author

N. J. A. Sloane, May 29 2012

Extensions

More terms from Vaclav Kotesovec, Jul 29 2013

Status

approved