\sum_{n=0}^ \infty n(n-1) \frac{x^{n}}{n!}= \sum_{n=0}^ \infty n^{2} \frac{x^{n}}{n!}- \sum_{n=0}^ \infty n \frac{x^{n}}{n!} \ \Rightarrow \ \sum_{n=0}^ \infty n^{2} \frac{x^{n}}{n!}= \sum_{n=0}^ \infty n(n-1) \frac{x^{n}}{n!}+ \sum_{n=0}^ \infty n \frac{x^{n}}{n!}=x^{2}e^{x}+xe^{x}=xe^{x}(x+1)