  A natural class of weighted Bergman spaces on the symmetrized polydisc is
isometrically embedded as a subspace in the corresponding weighted Bergman
space on the polydisc. We find an orthonormal basis for this subspace. It
enables us to compute the kernel function for the weighted Bergman spaces on
the symmetrized polydisc using the explicit nature of our embedding. This
family of kernel functions include the Szeg\"{o} and the Bergman kernel on the
symmetrized polydisc.
