This is documentation for Mathematica 6, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.1)

ButcherBetaBar

ButcherBetaBar[tree]
gives the number of ways of labeling tree with ButcherOrder[tree] distinct labels such that every vertex is labeled.
ButcherBetaBar[n, tree]
gives the number of ways of labeling n of the vertices of tree with n distinct labels such that every leaf is labeled.