Consider this restricted lattice bounded by [0,0];[x,0];[x,y];[y,0]. One can move from any point to another by a path , sequence of adjacent lattice points ( like one in the bad diagram I have written). Enumerate the number of paths from [0,0] to [x,y] ( obviously within the restricted grid). What about the paths that have loops? By a loop I mean the path coming back to the point that has already been traversed. (This diagram does not have loops)
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