The closed form sum of
\(12 \left[ 1^2 \cdot 2 + 2^2 \cdot 3 + \ldots + n^2 (n+1) \right]\)
for \(n \geq 1\) is \(n(n+1)(n+2)(an+b).\) Find \(an + b.\)
an + b is 4n - 1.
+79 
