Zeros of meromorphic functions of the form $\sum _n{\displaystyle \frac{c_n}{(z-t_n{)}^2}}$

We study zeros distribution for meromorphic functions of the form $\sum _n{\displaystyle \frac{c_n}{(z-t_n{)}^2}}$, where $\sum _n{\displaystyle \frac{\mathrm{\mid }{c}_n\mathrm{\mid }}{\mathrm{\mid }{t}_n{\mathrm{\mid }}^2}}<\mathrm{\infty }$. We prove an analog of the classical Keldysh theorem and discuss a relation between zero-free functions of this form and second order differential equtions with polynomial coefficients.