OFFSET
1,1
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.6 Otter's tree enumeration constants, p. 303.
LINKS
A. Meir and J. W. Moon, On the altitude of nodes in random trees, Canad. J. Math. 30(1978), 997-1015 Published:1978-10-01, page 1011.
E. M. Palmer and A. J. Schwenk, On the Number of Trees in a Random Forest, Journal of Combinatorial Theory, Series B, volume 27, number 2, October 1979, pages 109-121, see page 119 expected number of rooted trees in a rooted forest.
FORMULA
EXAMPLE
2.19183740319712630647869950285753649110618350758245...
MATHEMATICA
Clear[th]; digits = 100; m0 = 100; dm = 100; th[max_] := th[max] = (Clear[T, s, a]; T[0] = 0; T[1] = 1; T[n_] := T[n] = Sum[Sum[d*T[d], {d, Divisors[j]} ] * T[n-j], {j, 1, n-1}]/(n-1); 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}]; alpha = c /. FindRoot[eq, {c, 3}, WorkingPrecision -> digits + 5]; 2+Sum[T[j]*1/(alpha^j*(alpha^j-1)), {j, 1, max}]); th[m0]; th[max = m0 + dm]; While[Print["max = ", max]; RealDigits[th[max], 10, digits] != RealDigits[th[max - dm], 10, digits], max = max + dm]; theta = th[max]; RealDigits[theta, 10, digits] // First
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Jean-François Alcover, Aug 09 2015
STATUS
approved