On the number of trees in a random forest

AbstractThe analytic methods of Pólya, as reported in [1, 6] are used to determine the asymptotic behavior of the expected number of (unlabeled) trees in a random forest of order p. Our results can be expressed in terms of η = .338321856899208 …, the radius of convergence of t(x) which is the ordinary generating function for trees. We have found that the expected number of trees in a random forest approaches 1 + Σk=1∞ t(ηk) = 1.755510 … and the form of this result is the sam