Tent

Let us assume for simplicity that a person lying in a sleeping bag inside a tent occupies a rectangle of size 1 \times m on the floor. Accordingly, the floor of a classic $n$-person tent is a rectangle of size n \times m, where people are meant to lie parallel to the side whose length equals the person's height.

However, in practice, there are other, more complex ways to arrange $n$ people in an $n$-person tent. Your task is to count the number of such ways. Ways that differ by symmetry or rotation are considered different. For example, when m = 2, there are $3$ ways to arrange three people in a three-person tent: