We work on a GRB sample whose initial Lorentz factors (Gamma(0)) are constrained by the afterglow onset method and the jet opening angles (theta j) are determined by the jet break time. We confirm the Gamma(0)-E-gamma,E-iso correlation by Liang etal.(2010), and the Gamma(0)-L-gamma,L-iso correlation by Lu etal.(2012). Furthermore, we find correlations between Gamma(0) and the beaming corrected gamma-ray energy (E-gamma) and mean gamma-ray luminosity (L-gamma). By also including the kinetic energy of the afterglow, we find rough correlations (with larger scatter) between Gamma(0) and the total (gamma- ray plus kinetic) energy and the total mean luminosity, both for isotropic values and beaming corrected values: these correlations allow us to test the data with GRB central engine models. Limiting our sample to the GRBs that likely have a black hole central engine, we compare the data with theoretical predictions of two types of jet launching mechanisms from BHs, i. e. the nonmagnetized v (v) over bar -annihilation mechanism, and the strongly magnetized Blandford- Znajek (BZ) mechanism. We find that the data are more consistent with the latter mechanism, and discuss the implications of our findings for GRB jet composition. (C) 2017 Elsevier B.V. All rights reserved.