Exercice given at the end of Leure.
Ifτis a tree, denote byλ(τ) the number of leaves ofτ.
Ifn≥is an integer, set
Ln={τ;τ is a plane rooted tree that hasnleaves and no vertex has exaly one child}. Find an offspring diribution µ on the nonnegative integers such that a random tree chosen uniformly at random in the setLnhas lawPµ(· |λ(τ) =n).