  We report an observation of coherent phonons of $E_g^1$, $E_u^1$, $A_{1g}^1$,
and $E_g^2$ symmetry generated in a single-crystal film of $Bi_2Se_3$ by an
intense single-cycle THz pulse. The atomic vibrations reveal themselves through
periodic modulation of the refractive index of the film. The largest signal is
detected at the frequency of 4.05 THz that corresponds to the $E_g^2$ mode. The
generation of $E_g^2$ phonons is interpreted as resonant excitation of the
Raman mode by the second harmonic of THz-driven nonlinear $E_u^1$ oscillator,
the fundamental frequency of which (2.05 THz) is approximately half that of
$E_g^2$. The origin of nonlinearity in this case is cubic lattice
anharmonicity, while generation of $E_g^1$ (1.1 THz) and $A_{1g}^1$ (2.25 THz)
phonons is a manifestation of quartic anharmonicity enhanced by the occasional
combination relations between phonon frequencies in $Bi_2Se_3$.
