Given a $n\times n$ chessboard with the $n$ rows(ranks) and $n$ columns(files) labelled. Now we would like to place $2n$ (similar/ unlabeled) pawns on the board so that both rows(rank) and columns(file) has exactly 2 pawns on it.
How many ways are there to place the pawns?
Call this function $f(n)$, I counted that $f(0)=1$, $f(1)=0$, $f(2)=1$, $f(3)=6$, and then it doesn't show a simple way out...
