1. Recall F(2) 1 = -T 1+x+r? + 1.1 neo 1 (4+* - -)" n=0 (4+ n-1 . G(x) = (1 - ) = (1+2+ 2? +...)" = The second generating function counts the number of ways to distribute n candies to 4 kids. 1 H2) = 5+n-1 = ( (1 - 2) Calculate the nth term of the product F(x)(1). It will be a summation. Verify your summation equals (5+n-1) (the nth term of H()) for n 3 and n = 6