Find \(\dfrac{f^{(2016)}(0)}{2016!}\) for \(f(x)=\dfrac{x^3}{(1-x)^3(1+x+x^2)}\).

**Clarifications**:

\(f^{(k)}(x)\) denotes the \(k^\text{th}\) derivative of \(f(x) \).

\(!\) denotes the factorial notation. For example, \(8! = 1\times2\times3\times\cdots\times8 \).