First of all, sorry if this is in the wrong area, if so, please move it. Anyway

suppose I have a set of 3 elements. Computing by hand it is obvious to see that the answer is 5. But what if I have 20 elements? I know I need to use bell number to solve this, but I am not sure how to do this.

Note: I only need to know how to do this for very simple cases, such as

n = 20, 10, 7, etc.