On the asymptotics of the number of states for the Bose-Maslov gas

For a given sequence λ _j of positive numbers whose counting function ρ(λ) has the asymptotics ρ(λ) = c ₀ λ ^1+γ (1 + O(λ ^?? )) with γ > ?1 and ? > 0 as λ → ∞, we consider sequences {N _j } of nonnegative integers such that $\sum\limits_{j = 1}^\infty {\lambda _j N_j \leqslant E} ,$ where E > 0, and find the asymptotics as E → ∞ of the number N(E) of such sequences.