  We present sum rules for Clebsch-Gordan coefficients in the framework of
SO(4) group-theoretical description of the hydrogen atom. The main results are
obtained using properties of the Runge-Lenz- Pauli vector, in particular
expressing the matrix elements of the powers of its last component both in
spherical and parabolic basis. Connections with Stark effect and diamagnetism
of the hydrogen atom are outlined.
