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

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

znw(n) + ?j = n - m + 1n - 1 an - j + 1(j)zjw(j) + ?j = 0n - m ( an - j - m + 1(j)zm + an - j + 1(j) )zjw(j) = 0, {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,
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