In the expansion of $\left( \left( 1 + x ^ { 2 } \right) ^ { 2 } ( 1 + x ) ^ { n } \right.$, coefficients of $x , x ^ { 2 }$ and $x ^ { 3 }$ are in A.P, then find sum of all possible values of $n \in N$.
In the expansion of $\left( \left( 1 + x ^ { 2 } \right) ^ { 2 } ( 1 + x ) ^ { n } \right.$, coefficients of $x , x ^ { 2 }$ and $x ^ { 3 }$ are in A.P, then find sum of all possible values of $n \in N$.