The function $f(x) = 3 x \ln(1 + x)$ is represented as a power series:
$$f(x) = \sum_{n=0}^\infty c_n x^n$$

Find the following coefficients in the power series.
$c_2 =$
$c_3 =$
$c_4 =$
$c_5 =$
$c_6 =$

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