How many patterns $P_n$ are there to cross out $n^2/2$ squares on a $n\times n$ chessboard, so that the number of crossed out squares in each row and each column are all even?
Is there a way to get a general formula for $P_n$? Or, at least, a formula when $n$ is big?
For example, if $n = 4$, the answer could be found as $ P_4 = 246$ by listing all probabilities
