Find the values of the coefficients $a$, $b$ and $c$ so that the conditions

$$f(0) = 1, \quad f'(0) = 2, \quad \mbox{ and } \quad \ f''(0) = 3$$

hold for the function

$$f(x) = a e^{2 x} + b e^{- x} + c x e^{- x}.$$

$a =$
$b =$
$c =$