Thought Process

This was quite an easy problem.

All you have to realise is that to find the number of configurations with n capacitors, you can think of it as adding x and n - x capacitors in series and in parallel. This means than you just slowly calculate for each n and use previous calculations, I keep track of the set of capacitances n capacitors can form. 

Also note that the value 60 is arbitrary, you can choose 1 just as well!

In order to overcome the precision problems from repeated divisions in the series connection case I ended up using the fractions module.

The answer can also be found in this OEIS sequence, but what fun is that!!