Holm studied modules of higher-order differential operators (generalizing derivations) on generic (central) hyperplane arrangements. We use his results to determine the Hilbert series of these modules. We also give a conjecture about the Poincaré-Betti series; these are known for the module of derivations through the work of Yuzvinsky and Rose and Terao.
"A Conjecture on Poincaré-Betti Series of Modules of Differential Operators on a Generic Hyperplane Arrangement." Experiment. Math. 14 (4) 445 - 456, 2005.