On properties of entire solutions of linear differential equations with polynomial coefficients

We investigate properties of entire solutions of differential equations of the form

$$ {z^n}{w^{(n)}} + \sum\limits_{j = n - m + 1}^{n - 1} {a_{n - j + 1}^{(j)}{z^j}{w^{(j)}}} + \sum\limits_{j = 0}^{n - m} {\left( {a_{n - j - m + 1}^{(j)}{z^m} + a_{n - j + 1}^{(j)}} \right){z^j}{w^{(j)}}} = 0, $$

where n ≥ 3, 2 ≤ m ≤ n , and $a_k^{(j)}$ are complex numbers.