I'm having trouble with a proof:
Let $a_{n} = \sum_{k=1}^{n}{k{n\choose{k}}{n \choose{k-1}}}$. Given $\beta \gt 4$, show that $\lim_{n \to \infty}{\frac{a_{n}}{\beta^{n}}} = 0$
I'm struggling to find an approach to this question due to the double binomial in the summation. Could anyone give me a hint or tip on how to start?