Transient-type stimulated emission in the terahertz (THz) frequency range has been achieved from phosphorus doped silicon crystals under optical excitation by a few-picosecond-long pulses generated by the infrared free electron lasers FELIX and CLIO. The analysis of the lasing threshold and emission spectra indicates that the stimulated emission occurs due to combined population inversion based lasing and stimulated Raman scattering. Giant gain has been obtained in the optically pumped silicon due to large THz cross sections of intracenter impurity transitions and resonant intracenter electronic scattering. The transient-type emission is formed under conditions when the pump pulse intervals exceed significantly the photon lifetime in the laser resonator.