● ax ax r=0 (1+x)y=∑C( n rX ∑m(n r=0 r=0 Definition 2 The exponential generating function for the sequence ao, aj,..., ang... of real numbers is the infinite series f(x)=∑x=ao+a1x+2x2+…+x”+… 0▪ C(n,r)=p(n,r)/r!   = = + = = n r n r r n r r x x C n r x p n r 0 0 ! (1 ) ( , ) ( , )  = n r r r r x a 0 ! Definition 2: The exponential generating function for the sequence a0 ,a1 ,…,an ,…of real numbers is the infinite series =  = + + ++ +  = n n r r r x n a x a x a a x r a f x ! 2! ! ( ) 2 2 0 1 0   = = 0 ! ( ) r r ax r ax e