If Σ_k=1^31(^31 C_k)(^31 C_k-1)-Σ_k=1^30(^30 C_k)(^30 C_k-1)=(α(60!))/((30!)(31!)), where α ∈ R, then the value of 16 α is equal to

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