Two recent experimental studies by Zweiback et al. and by Gobet et al. have motivated us to study the ground-state geometry and the consequent electronic structure of the singly-charged cationic hydrogen cluster H3+(H2)m for m=2,5 and 14, using at first the Hartree-Fock approximation. For the H+7 cluster the fully optimized ground-state geometry yeilds an isosceles triangle H3, with charge ~ 0.85(e), and sides 0.852 and 0.884 Å flanked by two H2 molecules lying parallel to each other, wiht bond lengths of 0.740 Å. In contrast, for the H+13 cluster, the central 'building block' is equilateral H3 with bond length 0.861 Å, and with charge ~0.815(e). This configuration of H3 is flanked by three almost-parallel H2 molecules with bond length 0.739 A. MP2 refinements of geometry, charge distribution and normal mode vibrational frequencies of the cationic tritium cluster T+7 and the corresponding deuterium cluster D+13 are also reported. Finally, Hartree-Fock and MP2 results are recorded for H+13.