The Delannoy numbers D(a, b) are the number of lattice paths from (0, 0) to (b, a) in which only east (1, 0), north (0, 1), and northeast (1, 1) steps are allowed (i.e., ->, ↑, and ↗). They are given by the recurrence relation D(a, b) = D(a - 1, b) + D(a, b - 1) + D(a - 1, b - 1), with D(0, 0) = 1.
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