Let \( n \in \mathbb{N} \) and \( [ x ] \) denote the greatest integer less than or equal to \( x \). If the sum of \( (n+1) \) terms \( \, {^{n}C_{0}},\, 3\cdot {^{n}C_{1}},\, 5\cdot {^{n}C_{2}},\, 7\cdot {^{n}C_{3}}, \ldots \\, \) is equal to \( 2^{100}\cdot 101 \), then \( 2\left[ \dfrac{n-1}{2} \right] \) is equal to _______.
