Project Euler 155 Counting Capacitor Circuits

It was very complicated and hard problem when I saw this problem for the first time.
at that time I thought I could not solve this one.
and actually gave up to solve it. because I can't come up with any idea and Algorithm.

after one year from that time with algorithm study.
I have confidence and retry to solve it.
I got an answer of that problem.

Hint is dynamic problem and bruteforce and hashset

that is all
If you have more detail of it reply plz~


https://projecteuler.net/problem=155

An electric circuit uses exclusively identical capacitors of the same value C.
The capacitors can be connected in series or in parallel to form sub-units, which can then be connected in series or in parallel with other capacitors or other sub-units to form larger sub-units, and so on up to a final circuit.

Using this simple procedure and up to n identical capacitors, we can make circuits having a range of different total capacitances. For example, using up to n=3 capacitors of 60 F each, we can obtain the following 7 distinct total capacitance values:

If we denote by D(n) the number of distinct total capacitance values we can obtain when using up to n equal-valued capacitors and the simple procedure described above, we have: D(1)=1, D(2)=3, D(3)=7 ...

Find D(18).

Reminder : When connecting capacitors C₁, C₂ etc in parallel, the total capacitance is C_T = C₁ + C₂ +...,
whereas when connecting them in series, the overall capacitance is given by: