The rook problem is related to the number of nonattacking rooks that can be placed on a Ferrers Board. A Ferrers board is a board in which the number of cells in a column is always nondecreasing from left to right until it terminates. A rectangular board is a simple example of a Ferrers board.
Dr. Johnson showed how the Rook problem on the Ferrers board generates various polynomial coefficients which are in turn related to several examples of well known number sequences in mathematics and combinatorial number theory.
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