Exponential Generating functions , product rules Given sequences{an}n?0 and{bn}n?0, de?ne formal power series A(x) and B(x) as follows:

3. Given sequences {on}n20 and {baby}, dene formal power series A(:r) and B (3:) as follows: 14(3) : 2%: 3(3) z gang. 1120 1120 Note that A(3:)B(:r:) = 2 g 2 (2) akbmk, and ex = 2 E: (1) 1120 1120 For sequences {an}n20 and {an}n20, prove that if and only if