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

Author

N. J. A. Sloane, May 29 2012

Keywords

• nonn
• cons

Examples

			0.338321856899208...
		

References

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

Links

• 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.

Crossrefs

Cf. A000055.

Programs

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 *)

Formula

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

Extensions

More terms from Vaclav Kotesovec, Jul 29 2013