  Local convergence of bounded degree graphs was introduced by Benjamini and
Schramm. This result was extended further by Lyons to bounded average degree
graphs. In this paper, we study the convergence of a random tree sequence where
the probability of a given tree is proportional to $\prod_{v_i\in
V(T)}d(v_i)!$. We show that this sequence is convergent and describe the limit
object, which is a random infinite rooted tree.
