Rosen example ( generating function)

Question

Let the alphabet consist of {0,1,2} find the number of r digit binary sequence that contain an even number of 0's.

Comments

The exponential generating function required.

---

Yes ,but I couldn't understand given explanation in book ..if possible then give detail approach ... Thanks

And an = 1/( n+1) for n=0,1,2...closed form will be e^x/x ? Verify this one also thanks