Optimized recursion relation for the computation of partition functions in the superconfiguration approach

Partition functions of a canonical ensemble of non-interacting bound electrons are a key ingredient of the super-transition-array approach to the computation of radiative opacity. A few years ago, we published a robust and stable recursion relation for the calculation of such partition functions. In this paper, we propose an optimization of the latter method and explain how to implement it in practice. The formalism relies on the evaluation of elementary symmetric polynomials, which opens the way to further improvements.