Ab initio calculations have been performed for the Hn+ clusters (n=3–17; odd) at Møller–Plesset second order (MP2)/6-311G(mp), Møller–Plesset complete fourth order (MP4)/6-311G(mp), and coupled-cluster single-double-triple [CCSD(T)/6-311G(1p)] levels of calculations. Such hydrogen clusters are constituted by an H3+ core in which H2 units are bound. In order to understand the features of these bindings, enthalpy and entropy variations upon cluster formation, binding energies, and charge distributions have been computed, and a molecular orbital analysis, based on localized orbital, was performed. Our results show that the way the first three H2 units bind to the H3+ core is fundamentally different from the others, providing an explanation for the binding energies observed for these molecules. For the H13+, H15+, and H17+ clusters, the way in which the external H2 units are distributed around the H3+ plane leads to the formation of different isomers with very close energies, but with a rotational barrier large enough to inhibit the interconversions.