Problem #8

A prawn is a piece that is a cross between a pawn and a rook. It can only move upward in the vertical direction (the pawn-like move) but can move either left or right in the horizontal direction (the rook-like move). On a board with m rows and n columns, how many routes can a prawn take from the lower left-hand corner to the upper right-hand corner without revisiting a square? For example on a 3×3 board there are nine paths as shown in the figure below.

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