2. For two partitions u = (p1,...,pk) and A = (A1,...,)\\g), we say that p S A if k S E and n,- E Ag for each 1 S i g k. Consider the partition 5", = (11,71. 1,...,2,1) for n 2 1. Show that the nth Catalan number 0,, counts the number of partitions p, such that p. 5 6n