Sequences And Series

Let \(\alpha=\sum_\limits{r=0}^n\left(4 r^2+2 r+1\right){ }^n C_r\) and \(\beta=\left(\sum_\limits{r=0}^n \frac{{ }^n C_r}{r+1}\right)+\frac{1}{n+1}\). If \(140<\frac{2 \alpha}{\beta}<281\), then the value of \(n\) is _________.