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