  The Exponential Formula allows one to enumerate any class of combinatorial
objects built by choosing a set of connected components and placing a structure
on each connected component which depends only on its size. There are multiple
variants of this result, including Speicher's result for noncrossing
partitions, as well as analogues of the Exponential Formula for series-reduced
planar trees and forests. In this paper we use these formulae to give
generating functions contracted Grassmannian trees and forests, certain graphs
whose vertices are decorated with a helicity. Along the way we enumerate
bipartite planar trees and forests, and we apply our results to enumerate
various families of permutations: for example, bipartite planar trees are in
bijection with separable permutations. Our generating function for Grassmannian
forests can be interpreted as the rank generating function for the boundary
strata of the momentum amplituhedron, an object which encodes the tree-level
S-matrix of maximally supersymmetric Yang-Mills theory. This allows us to
verify that the Euler characteristic of the momentum amplituhedron is 1.
