A sequence

I'm having a rough time figuring out the next 3 terms of this sequence.
1/2,  1/3,  1/6,  1/15,  1/45,  2/315.......

\(\begin{array}{|rcll|} \hline \dfrac12 \times \boxed{\dfrac{2}{3}} &=& \dfrac13 \\\\ \dfrac13 \times \boxed{\dfrac{2}{4}} &=& \dfrac16 \\\\ \dfrac16 \times \boxed{\dfrac{2}{5}} &=& \dfrac{1}{15} \\\\ \dfrac{1}{15} \times \boxed{\dfrac{2}{6}} &=& \dfrac{1}{45} \\\\ \dfrac{1}{45} \times \boxed{\dfrac{2}{7}} &=& \dfrac{2}{315} \\\\ \dfrac{2}{315} \times \boxed{\dfrac{2}{8}} &=& \dfrac{1}{630} \\\\ \dfrac{1}{630} \times \boxed{\dfrac{2}{9}} &=& \dfrac{1}{2835} \\\\ \dfrac{1}{2835} \times \boxed{\dfrac{2}{10}} &=& \dfrac{1}{14175} \\ \hline \end{array}\)