If $\sum_{k=1}^{31} \left({}^{31}C_k\right)\left({}^{31}C_{k-1}\right) - \displaystyle \sum_{k=1}^{30} \left({}^{30}C_k\right)\left({}^{30}C_{k-1}\right) = \frac{\alpha(60!)}{(30!)(31!)}$, where $\alpha \in R$, then the value of $16\alpha$ is equal to:
