Here is an interesting problem:
The number of distince resistances that can be produced from n equal resistance resisters is given below.
Surprisingly this is also equal to the number of terms in nth order differentiation of a function y(x) with respect to x. How do I connect that these facts? That these represent the same counting and are expected to be equal.
P.S. I have only checked a few first terms of the differentiation. It may not be correct.
Edited. differentiation of a $nth$ power of function $y(x)$ with respect to $x$. E.G. $$\frac{dy^n}{dx}=ny^{n-1}y'$$
$$({y^n})''=n(n-1)y^{n-2}y'+ny^{n-1}y''$$ $$\vdots$$
ADDED Ok, if this sequence does not necessarily, explain this, how can I determine number of terms in this iteration? I found first five terms, if not mistaken to be $1, 2, 4, 9, 22, ...$
Added Serious! Error detected! Question is incorrect. Sorry!
You say you've checked the first $5$ terms. Note that an OEIS search yields a full $36$ sequences containing these $5$ terms, many of which begin with those $5$ terms. You could be asking this question about any one of those sequences, with equal (lack of) justification. Unless you have a specific reason to believe that these two phenomena are related, there's nothing to explain here.