generating functions

Which one of the following is the closed form for the generating function of the sequence (a n } n $$\ge$$ 0 defined below? $${a_n} = \left\{ {\matrix{ {n + 1,} & {n\,is\,odd} \cr...

Let $$G\left( x \right) = 1/\left( {1 - x} \right)2 = \sum\limits_{i = 0}^\infty {g\left( i \right)\,{x^1}} \,\,\,,$$ where $$\left| x \right| < 1$$ What is $$g(i)$$?