I'm working on this sum, I don't have to find out the actual value, I just have to simplify it as much as I can. But the problem is that I don't know how far I can simplify it before reaching the actual arithmetic value so I need help. Here is the sum, where ${n \brace k}$ stands for the Stirling Numbers of second kind:
$$\sum\limits_{i=0}^{30} \binom{30}{i}{i\brace 25}$$
We know that for $n < k$ we have ${n\brace k} = 0$ and ${n\brace n} = 1$ so we can simplify it into the following:
$$\binom{30}{25}+\sum\limits_{i=26}^{30}\binom{30}{i}{i\brace 25}$$
From now on, I don't know how to proceed. I could technically start breaking down the Stirling numbers and eventually get an arithmetic value but that's not quite the sense of the problem and as I'm new into combinatorics, I don't know how far I can simplify it. Any help from more advanced mathematicians is very welcome!