Exercise 7. The Catalan numbers Cn are defined by (2n)! n!(n + 1)!' 1 n+ 1 (2n) Cn := for n = N, forming a sequence Co = 1, C = 1, 2, 5, 14, 42, 132,.... For each n 1 prove that 2(2n-1) Cn n-1 n+1