Let function f(z) ≠ 0 be analytic in the unit disk and have sparse nonzero Taylor coefficients. Then the rate of decay of the function f as x → 1 - 0 depends on the rate of sparseness of its nonzero Taylor coefficients. In this paper, we consider the case f(z) =, where n _k > A ₀(k + 2) ^plogb(k + 2).