How do I calculate the infinite series:
$\frac{1^2\cdot 2^2}{1!}+\frac{2^2\cdot 3^2}{2!}+\dots \quad?$ I tried to find the nth term $t_n$. $t_n=\frac{n^2\cdot (n+1)^2}{n!}.$ So, $\sum_{n=1}^{\infty}t_n=\sum_{n=1}^{\infty}\frac{n^4}{n!}+2\sum_{n=1}^{\infty}\frac{n^3}{n!}+\sum_{n=1}^{\infty}\frac{n^2}{n!}$ after expanding. But I do not know what to do next.
Thanks.