Photoionization spectra and Rydberg-state-resolved threshold-ionization spectra of the gerade triplet np Rydberg states of He-4(2) located in the vicinity of the X+2 Sigma(+)(u) (v(+) = 0) ionization threshold were recorded from the 2s sigma a(3)Sigma(+)(u) metastable state. An accuracy of 0.01 cm(-1) was achieved for the experimental term values of the observed Rydberg states. The data were combined with spectroscopic data on low-lying triplet np and nf Rydberg states from the literature to derive energy-and internuclear-distance-dependent eigenquantum-defect parameters of multichannel quantum-defect theory (MQDT). The MQDT calculations reproduce the experimental data within their experimental uncertainties and enabled the derivation of potential-energy curves for the lowest triplet p Rydberg states (n = 2-5) of He-2. The eigenquantum-defect parameters describing the p - f interaction were found to be larger than 0.002 at the energies corresponding to the high-n Rydberg states, so that the p - f interaction plays an important role in the autoionization dynamics of np Rydberg states with v(+) = 0. By extrapolating the experimental term values of triplet np Rydberg states of He-4(2) in the range of principal quantum number n between 87 and 110, the positions of the (v(+) = 0, N+ = 3) and (v(+) = 0, N+ = 5) levels of the ground state of He-4(2)+ were determined to lie 70.937(3) cm(-1) and 198.369(6) cm(-1), respectively, above the (v(+) = 0, N+ = 1) ground rotational level. (C) 2014 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License.