On some identities and generating functions for Pell-Lucas numbers

Generating functions for Pell and Pell-Lucas numbers are obtained. Applications are given for some results recently obtained by Mansour [Mansour12]; by using an alternative approach that considers the action of the operator \(\delta_{e_1 e_2}^k\) to the series \(\sum_{j=0}^\infty a_j (e_1 z)^j\).