The numbers $1,2,3, \ldots, 20$ are written on a board. It is allowed to erase any two numbers $a$ and $b$ and replace them with their sum $ab + a + b$. What number can result after 19 such operations?
Note that the equality $a b+a+b=(a+1)(b+1)-1$ holds. Let's carefully calculate the result after applying two such operations, that is, for three numbers $a, b, c$. After the first operation, the remaining numbers are $(a+1)(b+1)-1, c$. After the second operation, we need to take the product of the new numbers, each increased by 1, and subtract 1 from the product, i.e.,

$(((a+1)(b+1)-1)+1)(c+1)-1=(a+1)(b+1)(c+1)-1$.

Similarly, for any number of numbers.

## Answer

$21!-1$.