On the Distribution of Integer Random Variables Related by a Certain Linear Inequality. III

We consider tuples $\{N_{jk}\}$, $j=1,2,\dots$, $k=1,\dots,q_j$, of nonnegative integers such that
$$ \sum_{j=1}^\infty\sum_{k=1}^{q_j} jN_{jk}\le M. $$
Assuming that $q_j\sim j^{d-1}$, $1<d<2$, we study how the probabilities of deviations of the sums $\sum_{j=j_1}^{j_2}\sum_{k=1}^{q_j} N_{jk}$ from the corresponding integrals of the Bose–Einstein distribution depend on the choice of the interval $[j_1,j_2]$.