  The scalar curvature equation for rotation invariant K\"ahler metrics on
$\mathbb{C}^n \backslash \{0\}$ is reduced to a system of ODEs of order 2. By
solving the ODEs, we obtain complete lists of rotation invariant zero or
positive csck on $\mathbb{C}^n \backslash \{0\}$ in lower dimensions. We also
prove that there does not exist negative csck on $\mathbb{C}^n \backslash
\{0\}$ for $n=2,3$.
