Tessellate S.T.E.M.S. (2019) - Computer Science - School - Set 1 - Objective Problem 3

Remember the postman, from your childhood memory, he used to carry postcards, with envelopes. Here is the postman from my hometown, carrying $n$ -square-envelopes of different sizes. I unpretentiously asked the following counting problem: In how many different ways, can the envelopes be arranged by inclusion. Obviously the postman is confused, and needs your help. Could you help him in counting ? Here is a small instance: for $n=2$ , let the envelopes are labelled by $A,B$ and $A$ is larger than $B$ , and $I\in J$ denotes that the envelope $I$ is inside the envelope $J$ , then there are following two ways to arrange the envelopes by inclusion, namely:

1. $\Phi$ , keep them separately

2. $B$ in $A$ .

This problem is a part of Tessellate S.T.E.M.S (2019)