The function $f(x) = 3 x \arctan (6 x)$ is represented as a power series
$\displaystyle f(x) = \sum_{n=0}^\infty c_n x^n .$
Find the first few coefficients in the power series.
$c_0 =$
$c_1 =$
$c_2 =$
$c_3 =$
$c_4 =$

Find the radius of convergence $R$ of the series.

$R =$