The closed form sum of 12 \left[ 1 \cdot 2^2 \cdot 3 + 2 \cdot 3^2 \cdot 4 + \dots + n (n + 1)^2 (n + 2) \right] for n \ge 1 is n(n + 1)(n + 2) p(n) for some polynomial p(n). Find p(n).
+1084 
