IMO 1984 LL GBR28

A “number triangle” (tnk) (0 \leqk \leqn) is defined by tn,0 =

IMO 1984 LL GBR28

Origin: GBR

Problem

A “number triangle” (tnk) (0 \leqk \leqn) is defined by tn,0 = tn,n = 1 (n \geq0), tn+1,m =  2 − \sqrt m tn,m +  2 + \sqrt n−m+1 tn,m−1 (1 \leqm \leqn). Prove that all tn,m are integers.