Let n ∈ N and [x] denote the greatest integer less than or equal to x. If the sum of ( n +1) terms ^n C_0, 3 ·^n C_1, 5 ·^n C_2, 7 ·^n C_3, ….. is…

Let $\displaystyle \mathrm{n} \in \mathrm{N}$ and $\displaystyle [x]$ denote the greatest integer less than or equal to $\displaystyle x$. If the sum of $\displaystyle (\mathrm{n}+1)$ terms $\displaystyle { }^{\mathrm{n}} \mathrm{C}_0, 3 \cdot{ }^{\mathrm{n}} \mathrm{C}_1, 5 \cdot{ }^{\mathrm{n}} \mathrm{C}_2, 7 \cdot{ }^{\mathrm{n}} \mathrm{C}_3, \ldots .$. is equal to $\displaystyle 2^{100} \cdot 101$, then $\displaystyle 2\left[\frac{\mathrm{n}-1}{2}\right]$ is equal to \_\_\_\_.