The closed form sum of for is Find an+b.

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.