Chapter 8.4, Problem 49E

Find the sequence with each of these functions as its exponential generating function.

a) $f\left(x\right)=e^{-x}$b) $f\left(x\right)=3x^{2x}$c) $f\left(x\right)=e^{3x}-3e^{2x}$

d) $f\left(x\right)=\left(1-x\right)+e^{-2x}$e) $f\left(x\right)=e^{-2x}-\left(1/\left(1-x\right)\right)$f) $f\left(x\right)=e^{-3x}-\left(1+x\right)+\left(1/\left(1-2x\right)\right)$g) $f\left(x\right)=e^{x2}$