Ononot — Let Xn \sim \text{Binomial}(n, pn) where pn = \frac{\lambda}

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Let $X_n \sim \text{Binomial}(n, p_n)$ where $p_n = \frac{\lambda}{n} + o\left(\frac{1}{n}\right)$ as $n \to \infty$ . Let $Y_n = 2 X_n$ . What is the probability generating function $G_Y(s) = E[s^Y]$ of the limiting distribution of $Y_n$ as $n \to \infty$ ?