  We introduce an algorithm to obtain coefficients of fractional parentage for
light $p$-shell nuclei. The coefficients enable to use Jacobi coordinates in
no-core shell model calculations separating off the center-of-mass motion.
Fully antisymmetrized basis states are given together with recoupling
coefficients that allow one to apply two- and three-nucleon operators. As an
example, we study the dependence on the harmonic oscillator frequency of $^3$H,
$^4$He, $^6$He, $^6$Li and $^7$Li and extract their binding and excitation
energies. The coefficients will be made openly accessible as HDF5 data files.
