Rooks Problem -- from Wolfram MathWorld

The rook is a chess piece that may move any number of spaces either horizontally or vertically per move. The maximum number of nonattacking rooks that may be placed on an n×n chessboard is n. This arrangement is achieved by placing the rooks along the diagonal (Madachy 1979). The total number of ways of placing n nonattacking rooks on an n×n board is n! (Madachy 1979, p. 47). In general, the polynomial R_(mn)(x)=sum_(k)r_k^((m,n))x^k whose coefficients r_k^((m,n)) give the

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