Generating functions with n term outside

[SpartanG345]

Homework Statement

Discrete mathematics

is it possible to have a generating function where there is an n term outside the sum?

such as

2^n SUM ( bn(0.5)^n * z^n)

eg the 1st turn would be 2^n bo z^0

when you evaluate the series it evaluates to the series which i am trying to create a generating function for. NB bn is another generating function.

I also have the closed formula for bn.

 

[HallsofIvy]

Assuming the sum itself is over the index n, that would be bad notation. It means the same as $2^n \sum_k (b_k(0.5)^k z^k)$ but NOT the same as $\sum_n 2^n(b_n(0.5)^n z^n)$ with which it could easily be confused. On the other hand if the sum is over, say, index i from 0 to n, it would be perfectly good.