7th Balkan Mathematical Olympiad Problems 1990

7th Balkan Mathematical Olympiad Problems 1990A1.  The sequence un is defined by u1 = 1, u2 = 3, un = (n+1) un-1 - n un-2. Which members of the sequence which are divisible by 11? A2.  Expand (x + 2x2 + 3x3 + ... + nxn)2 and add the coefficients of xn+1 through x2n. Show that the result is n(n+1)(5n2 + 5n + 2)/24.