Dear SeqFans, numbers n such that: (i) C(2n,n) - n^2 is prime: 2, 3, 5, 9, 13, 27, 47, 59, 111, 547, 923, ... (ii) C(n^2,n) - n^n is squarefree: 2, 3, 5, 7, 13, 17, 19, 23, 29, 31, 33, 35, 37, 41, 43, 47, 53,... What tn the next one? Thanks. JSG