  We present new sum rules for $3jm$ coefficients, which involve, in addition
to the usual weighting factor $(2j + 1)$ where $j$ is an angular momentum, the
quantity $[j(j + 1)]^k$ with $k \ge 1$. The sum rules appear for instance in
the statistical modeling of rotational spectra within the theory of moments,
and enable one to deduce the expectation values of $r^k$ (used in the theory of
Stark effect for hydrogenic ions) in parabolic coordinates from the expectation
values of $r^k$ in spherical coordinates.
