Combinatorial meaning of Euler's number

In this paper, we consider a new limit for the number e and give its rigorous proof using the apparatus of mathematical analysis. With the help of this limit, a combinatorial interpretation is given for Euler's number. It means that Euler's number is the ratio of the number of permutations (or combinations) of $n^2+n$ by $n$ to the number of permutations (or combinations) of $n^2$ by $n$ with an infinitely large number of elements $n$.