OEIS A347913 is an extremely interesting sequence about multisets of integers. It is defined as the number of multisets one can get starting with a multiset of $n$ zeros and "splitting", that is, increasing one number with a duplicate by 1 and decreasing the duplicate by 1. What is the limiting ratio of two consecutive terms of this sequence, if it exists? If it doesn't exist, what is the limit of the nth root of the nth term? The post has a lower bound of $2$, and I have managed to upper-bound it by $4$ using a clever injection to A000571.
Here's an example to show A347913(4):
{{$0,0,0,0$}}
{{$-1,0,0,1$}}
{{$-1,-1,1,1$}}
{{$-1,-1,0,2$}}
{{$-2,0,1,1$}}
{{$-2,0,0,2$}}
{{$-2,-1,1,2$}}