I was messing around on Desmos, and I started plotting a function point-by-point which looks looks like the following:
$$\left(1,\ \frac{1}{2!}\right), \left(2,\ \frac{12}{3!}\right),...,\left(9,\ \frac{123456789}{10!}\right), \left(10,\ \frac{1234567890}{11!}\right),...,\left(20,\ \frac{12345678901234567890}{21!}\right)$$
I'm not sure if there's a function that can describe this, but here's the graph that was produced:
I think this is a pretty cool-looking result. In fact, it looks sort of like a right-skewed distribution. Is there anything particular about what I've run into or something similar that is known to describe this? Thanks!