Ab initio post Hartree-Fock studies were performed on the title species. Their structures consist of a tightly bound H-3(+) core ion which generates progressively weaker bonded distinct shells of Ar atoms. The predicted structures of H3+Arn (n = 1-9) clusters explain the experimental pattern of changes in the stepwise enthalpies and entropies of dissociation. The subtle changes in thermodynamic properties reproduced by calculations indicate an accurate location of the global minimum geometries of the clusters and the proper determination of the shells for coordinating argon atoms. The nature of chemical bonding is studied based on the interaction energy decomposition. The importance of the covalent component in the interaction forces is revealed.