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A particle moves from (0, 0) to (n, n) directed by a fair coin. For each head it moves one step east and for each tail it moves one step north. At (n, y), y < n, it stays there if a head comes up and at (x, n), x < n, it stays there if a tail comes up. Letk be a fixed positive integer. Find the probability that the particle needs exactly 2n+k tosses to reach (n, n).

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