  Motivated by a formula of A. Postnikov relating binary trees, we define the
hook length polynomials for m-ary trees and plane forests, and show that these
polynomials have a simple binomial expression. An integer value of this
expression is C_{k,m}(n)=\frac{1}{mn+1}{(mn+1)k \choose n}, which we call the
(k,m)-Catalan number. For proving the hook length formulas, we also introduce a
combinatorial family, (k,m)-ary trees, which are counted by the (k,m)-Catalan
numbers.
