[ Invariants $]$

On the board, the numbers $1,2, \ldots, 20$ are written. It is allowed to erase any two numbers $a$ and $b$ and replace them with the number $a b + a + b$.

What number can remain on the board after 19 such operations?
Note that $a b+a+b+1=(a+1)(b+1)$. This means that if all numbers are increased by 1, the product of the new numbers under the specified operation does not change. At the beginning (and therefore at the end), it is equal to $21!$.

## Answer

$21!-1$.