Higher order harmonic generation in a free-electron laser amplifier operating in the superradiant regime [R. H. Dicke, Phys. Rev. 93, 99 (1954).] has been observed. Superradiance has been induced by seeding a single-pass amplifier with the second harmonic of a Ti:sapphire laser, generated in a β-Barium borate crystal, at seed intensities comparable to the free-electron laser saturation intensity. Pulse energy and spectral distributions of the harmonics up to the 11th order have been measured and compared with simulations.