Find the coefficient of $x^{29}$ in the given polynomial. The polynomial is :
$$
\left(x-\frac{1}{1\cdot3}\right) \left(x-\frac{2}{1\cdot3\cdot5}\right) \left(x-\frac{3}{1\cdot3\cdot5\cdot7}\right) \cdots \left(x-\frac{30}{1\cdot3\cdot5\cdots61}\right)
$$
What I've done so far : The given polynomial is an expression of degree $30$. Hence, the coefficient of $x^{29}$ will be the negative of the sum of the roots. But the resulting sum is too complicated to handle and I think I'm doing it wrong. 

HINT: The sum $S_k $ given by 
$$\sum_{n=1}^{k} \dfrac {n}{(2n+1)!!} $$
for  $k=1,2,3....$ gives 
$$S_1=\frac {1}{3} \\ =\frac {1}{2}-\frac {1/2}{ 1 \cdot 3}$$
$$S_2=\frac {1}{3} + \frac {2}{15} =\frac {7}{15} \\= \frac {1}{2}-\frac {1/2}{1 \cdot 3 \cdot 5 }$$
$$S_3=\frac {1}{3} + \frac {2}{15} +\frac {3}{105} =\frac {52}{105} \\= \frac {1}{2}-\frac {1/2}{1 \cdot 3 \cdot 5 \cdot 7 }$$
You can use induction to confirm this pattern. 
