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