  We calculate the rate of double open charm production in the forward
kinematics studied recently in the LHCb experiment. We find that the mean field
approximation for the double parton GPD (Generalized parton distributions),
which neglects parton - parton correlations, underestimates the rate by a
factor of two. The enhancement due to the perturbative QCD correlation \12
mechanism which explains the rate of double parton interactions at the central
rapidities is found to explain 60 $\div$ 80 \% of the discrepancy. We argue
that the nonperturbative fluctuations leading to non-factorized (correlated)
contributions to the initial conditions for the DGLAP collinear evolution of
the double parton GPD play an important role in this kinematics. Combined, the
two correlation mechanisms provide a good description of the rate of double
charm production reported by the LHCb. We also give predictions for the
variation of the \effs (i.e. the ratio of double and square of single inclusive
rates) in the discussed kinematics as a function of $p_t$. The account for two
correlation mechanisms strongly reduces sensitivity of the results to the
starting point of the QCD evolution.
