${ }^n{C}_0{}^{4n}{C}_n{-}^n{C}_1{}^{(4n-3)}{C}_n{+}^n{C}_2{}^{4n-6}{C_n}^{\_n}{C}_3{}^{4n-9}{C}_n+\mathrm{...}+$  to (n + 1) terms is equal to ${(1+k)}^n;$  then the value of k is  $(k\in N)$

Coefficient $x^n$ in   ${\{}^n{C}_0{{(1+x)}^{4n}}^{\_n}{C}_1{(1+x)}^{4n-3}{+}^n{C}_2{(1+x)}^{4n-6}\mathrm{......}+{{(-1)}^n}^n{C}_n{(1+x)}^n\}$
$\Rightarrow$ Coefficient  $x^n$ in  ${(1+x)}^n{\{{(1+x)}^3-1\}}^n\Rightarrow 3^n$