We present a dynamical model for photoassociation (PA) of ultracold alkali atoms with ultracold alkali molecules in their rovibrational ground state to create excited trimer molecules. The model involves the long-range multipolar interactions between the atom and the molecule calculated with the degenerate perturbation theory, connected to an arbitrary short-range potential. The rate is found significantly smaller than in the atom-atom case under typical MOT conditions, but is promising in the nanokelvin domain. We design a proposal for an experiment in the Mott insulator regime. Being a half-collision, PA could offer the possibility to probe the complex short-range dynamics along the lines developed by J. Bohn and coll.