  In this paper we continue the perturbative analysis of the quartic Kontsevich
model. We investigate meromorphic functions $\Omega^{(0)}_m$ with $m=1,2$, that
obey blobbed topological recursion. We calculate their expansions and check
their equivalence to sums of ribbon graph weights, which are obtained with
common methods of perturbation theory in QFT, up to fifth order in the coupling
using Mathematica.
  Furthermore, we provide a catalog of permutation pairs $(\alpha,\sigma)$,
which encode all 5660 vacuum ribbon graphs that contribute to the free energy
$\mathcal{F}^{(g)}$ with genus $g\geq 0$ up to fifth order and begin to expand
upon the used methods to also consider ribbon graphs of general correlation
functions $G_{\dots}$. This is a first step towards automation of the
calculation of ribbon graph expansions in the quartic Kontsevich model.
