Irrationality and transcendence of continued fractions with algebraic integers

We extend a result of Hančl, Kolouch and Nair on the irrationality and transcendence of continued fractions. We show that for a sequence $\{\alpha_n\}$ of algebraic integers of degree bounded by $d$, each attaining the maximum absolute value among their conjugates and satisfying certain growth conditions, the condition $$ \limsup_{n\rightarrow\infty}\vert\alpha_n\vert^{\frac{1}{Dd^{n-1}\prod_{i=1}^{n-2}(Dd^i+1)}}=\infty $$ implies that the continued fraction $\alpha=[0;\alpha_1,\alpha_2,\dots]$ is not an algebraic number of degree less than or equal to $D$.