  In the Color Glass Condensate formalism, we evaluate the 3-dipole correlator
up to the $\frac{1}{N_c^4}$ order with $N_c$ being the number of colors, and
compute the azimuthal cumulant $c_{123}$ for 3-particle productions. In
addition, we discuss the patterns appearing in the $n$-dipole formula in terms
of $\frac{1}{N_c}$ expansions. This allows us to conjecture the $N_c$ scaling
of $c_n\{m\}$, which is crosschecked by our calculation of $c_2\{4\}$ in the
dilute limit.
