Delannoy Numbers

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What is the Delannoy number D(n, m)?

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The number of paths from (0, 0) to (n, m) in the grid, where each step is either right or up.

The number of paths from (0, 0) to (n, m) in the grid, where each step is either right or down.

The number of paths from (0, 0) to (n, m) in the grid, where each step is either right or diagonal.

The number of paths from (0, 0) to (n, m) in the grid, where each step is either up or diagonal.

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