If for positive intergers r >1, n >2, the coefficients of the (3 r )^th and ( r +2)^th powers of x in the expansion of (1+x)^2 n are equal, then n is…

If for positive intergers $\displaystyle \mathrm{r}>1, \mathrm{n}>2$, the coefficients of the $\displaystyle (3 \mathrm{r})^{\text {th }}$ and $\displaystyle (\mathrm{r}+2)^{\text {th }}$ powers of $\displaystyle x$ in the expansion of $\displaystyle (1+x)^{2 \mathrm{n}}$ are equal, then n is equal to :