IMO 1987 LL GBR25

Numbers d(n, m), with m, n integers, 0 \leqm \leqn, ae defined

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IMO 1987 LL GBR25

Origin: GBR

Problem

Numbers d(n, m), with m, n integers, 0 \leqm \leqn, ae defined by d(n, 0) = d(n, n) = 0 for all n \geq0 and md(n, m) = md(n −1, m) + (2n −m)d(n −1, m −1) for all 0 < m < n. Prove that all the d(n, m) are integers.