Calculus Level 5

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, $$8! = 1\times2\times3\times\cdots\times8$$.

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