  We compare results of exact calculations of single parton scattering (SPS)
and double parton scattering (DPS) for production of $c \bar c c \bar c$ and
for $D$ meson correlations. The SPS calculations are performed in collinear
approximation with exact matrix element for $g g \to c \bar c c \bar c$ and $q
\bar q \to c \bar c c \bar c$ subprocesses. It is shown that the contribution
of gluon-gluon subprocess is about factor 50 larger than that for
quark-antiquark annihilation. The new results are compared with results of
previous calculation with the approximate matrix element for $g g \to c \bar c
c \bar c$ in the high-energy approximation. The cross section for the present
exact calculation is bigger only at small invariant masses and small rapidity
difference between two $c$ quarks (or two $\bar c$ antiquarks). We compare
correlations in rapidities of two $c$ (or two $\bar c$) for DPS and SPS
contributions. Finally we compare our predictions for $D$ mesons with recent
results of the LHCb collaboration for invariant mass, rapidity distance between
mesons and dimeson invariant mass. The predicted shapes are similar to the
measured ones, however, some strength seems to be lacking. Our new calulations
clearly confirm the dominance of DPS in the production of events with double
charm.
