Find the sum `sum_(r=0)^n^(n+r)C_r` .

Explanation

`sum_(r=0)^(n) ""^(n+r)C_(n) = ""^(n)C_(n) + ""^(n+1)C_(n) + ""^(n+2)C_(n) + ...+ ""^(2n)C_(n)`
= Coefficient of ` x^(n) ` in
` [(1 + x)^(n) + (1 + x)^(n+1) + (1 + x)^(n+2) + …+ …+ (1 + x)^(2n)]`
= Coefficient of ` x^(n) " in" [((1 + x)^(n) [(1 + x)^(n+1)-1])/((1 +x) -1)]`
= Coefficient of ` x^(n+1) " in " [(1 + x)^(2n +1) - (1 + x)^(n)]` ltbr. ` ""^(2n+1)C_(n+1) - 0 = ""^(2n + 1)C_(n)` .