Here is a link where people describe how one can generate the entries of the Slater Koster parameter table seen here as Table of interatomic matrix elements.
The authors mention Mathematica packages one can use to generate these table entries, namely factor.m and wigner.m. However, since this paper is rather old I was wondering if there is a nice way to generate these table elements with Mathematica today without the need for external packages. Because as it is right now I hard-coded the entire table -.- .