\[2\sum_{k=1}^{\infty}k^2f^{(k)}(x)=3f(x),\hspace{10mm}f(0)=2016\]

Find the function \(f:\mathbb{R}\rightarrow\mathbb{R}\) that satisfies the differential equation above for all real \(x\). Return \(f'(0)\) as your answer.

If you come to the conclusion that no such function exists (or there is more than one), enter 666.

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

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