MathDB

23

Part of PEN M Problems

Problems(1)

M 23

Source:

5/25/2007
Define {d(n,0)=d(n,n)=1(n≥0),md(n,m)=md(n−1,m)+(2n−m)d(n−1,m−1)(0<m<n).\begin{cases}d(n, 0)=d(n, n)=1&(n \ge 0),\\ md(n, m)=md(n-1, m)+(2n-m)d(n-1,m-1)&(0<m<n).\end{cases} Prove that d(n,m)d(n, m) are integers for all m,n∈Nm, n \in \mathbb{N}.
inductionRecursive Sequences