  In the Super-Transition-Array statistical method for the computation of
radiative opacity of hot dense matter, the moments of the absorption or
emission features involve partition functions with reduced degeneracies,
occurring through the calculation of averages of products of subshell
populations. In the present work, we discuss several aspects of the computation
of such peculiar partition functions, insisting on the precautions that must be
taken in order to avoid numerical difficulties. In a previous work, we derived
a formula for supershell partition functions, which takes the form of a
functional of the distribution of energies within the supershell and allows for
fast and accurate computations, truncating the number of terms in the
expansion. The latter involves coefficients for which we obtained a recursion
relation and an explicit formula. We show that such an expansion can be
combined with the recurrence relation for shifted partition functions. We also
propose, neglecting the effect of fine structure as a first step, a
positive-definite formula for the Super-Transition-Array moments of any order,
providing an insight into the asymmetry and sharpness of the latter. The
corresponding formulas are free of alternating sums. Several ways to speed up
the calculations are also presented.
