Ab initio calculations have been performed for the H-n(+) clusters (n=3-17; odd) at Moller-Plesset second order (MP2)/6-311G(mp), Moller-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 H-3(+) core in which H-2 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 H-2 units bind to the H-3(+) core is fundamentally different from the others, providing an explanation for the binding energies observed for these molecules. For the H-13(+), H-15(+), and H-17(+) clusters, the way in which the external H-2 units are distributed around the H-3(+) plane leads to the formation of different isomers with very close energies, but with a rotational barrier large enough to inhibit the interconversions.