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d(m,n) are integers

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September 5, 2010
inductionnumber theory unsolvednumber theory

Problem Statement

Numbers d(n,m)d(n,m), with m,nm, n integers, 0≤m≤n0 \leq m \leq n, are defined by d(n,0)=d(n,n)=0d(n, 0) = d(n, n) = 0 for all n≥0n \geq 0 and md(n,m)=md(n−1,m)+(2n−m)d(n−1,m−1) for all 0<m<n.md(n,m) = md(n-1,m)+(2n-m)d(n-1,m-1) \text{ for all } 0 < m < n. Prove that all the d(n,m)d(n,m) are integers.
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