\displaystile f^{(n)}(0) = \left\{ 
\begin{array}{l l}
\displaystile (n-1)!!\cdot (-4)^{\frac{n}{4}}\cdot f(0) & \quad n\equiv_4 0\\
\displaystile (n-1)!!\cdot (-4)^{\frac{n-1}{4}}\cdot f'(0) & \quad n\equiv_4 1\\
\displaystile (n-1)!!\cdot (-4)^{\frac{n-2}{4}}\cdot f''(0) & \quad n\equiv_4 2\\
\displaystile \frac{(n-1)!!\cdot (-4)^{\frac{n-3}{4}}\cdot f'''(0)}{2} & \quad n\equiv_4 3\\
\end{array} \right.