  By the work of Ferroni and Larson, Kazhdan-Lusztig polynomials and
Z-polynomials of complete graphs have combinatorial interpretations in terms of
quasi series-parallel matroids. We provide explicit formulas for the number of
series-parallel matroids and the number of simple series-parallel matroids of a
given rank and cardinality, extending results of Ferroni-Larson and
Gao-Proudfoot-Yang-Zhang.
