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Oct 17th, 2017
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RSolve[{p[n, m] == m/n p[n - 1, m - 1] + (n - m - 1)/n p[n - 1, m],
p[n, n - 1] == 1/n, p[n, 1] == 1/2}, p[n, m], {n, m}]
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