Broadband THz pulses have been generated in 2-[3-(4- hydroxystyryl)-5,5-dimethylcyclohex-2-enylidene]malononitrile (OH1) by optical rectification of sub-picosecond laser pulses. We show that OH1 crystals allow velocity-matched generation and detection of THz frequencies in the whole range between 0.3 and 2.5 THz for a pump laser wavelength range from 1200 to 1460 nm. OH1 crystals show a higher figure of merit for THz generation and detection in the optimized range compared to the benchmark inorganic semiconductor crystals ZnTe and GaAs and the organic ionic salt crystal 4-N,N-dimethylamino-4'-N'-methyl stilbazolium tosylate (DAST). The material shows a low THz absorption coefficient alpha3 in the range between 0.3 and 2.5 THz, reaching values lower than 0.2mm(-1) between 0.7 and 1.0 THz. This is similar as in ZnTe and GaAs, but much lower than in DAST in the respective optimum frequency range. A peak THz electric field of 100 kV/cm and a photon conversion efficiency of 11 percent have been achieved at a pump pulse energy of 45 microJ.