It's not impossible to deduce but besides arguing that the functions may combine to actually create something that may exist to give you and or present things to you, it does not, this function is a simple switch and return mechanism.
First, you must understand it is a computation. That makes us aware that we do not change what is in it. When that is clear, we will have the clear understanding for what this function is and how to make it.
When the function attempts factorials, it is inmediately offering the root to some other function. In simpler terms and keeping in mind they used grid paper when they needed to create computations, the function offering roots is a lot like saying that when we move our "cursor" on a grid, we are using a full block of information. When that full block of information is no longer being handled by the root functions, the second part, some function at n, takes over. The second part then moves the root to account for the full product of the entire function as the expected output, some dividened of the 1458 demonstrated, and when the function is pressed to move that value to another function, the inference of a polynomial as a full block without inference of the possible values and just as the geometric encounter, the whole function moves the cursor between things and offers the full value as a subset. And when that value is no longer a sub set, meaning we have removed all values to a root function, so that we can fill what is our "encounter", meaning we now have the right proportion to set the values facing the graph (like when you have a rectangle that needs to be cut into an uneven number of parts you cut into it with non same shaped cuts), the elasticity of the function seems to generate a sum that may be holding some other part of the function but does so without allowing the cursor to actually account for what is a geometric value because you are not rooted to the original graph, you simply have values available
