Generating series for Hochschild-arbor invariants

Derive and prove the four conjectural generating-series identities, in the variable s, for the Zeta polynomials, M-triangles, Ehrhart polynomials, and Laplace transforms of volume functions associated with the arbor family t_n.

Background

For the arbor family t_n related to Hochschild polytopes, the paper gives guessed generating functions for four different invariant families. Each identity is marked with a conjectural symbol, indicating that the formulas were inferred using computer algebra rather than proved. The requested problem is to establish these identities rigorously.