Hey! 
I'm trying to wrap my head about generating functions and how we go about getting the coefficients.
One problem I have at the moment is simplifying a generating function and then applying the correct identities.
E.g. I have a generating function: (x1 + x2 + x3) (1 + x + x2 + x3 + ...)2
First off, does (x1 + x2 + x3) need to have an x taken out, so that it becomes: x ( 1 + x1 + x2) before I can apply an identity ? And if so, would this identity result in: ( x ( 1- x2)(1 + x1 + x2 + ...)) ?
Thanks for any advice on how to go forward!
I'm trying to wrap my head about generating functions and how we go about getting the coefficients.
One problem I have at the moment is simplifying a generating function and then applying the correct identities.
E.g. I have a generating function: (x1 + x2 + x3) (1 + x + x2 + x3 + ...)2
First off, does (x1 + x2 + x3) need to have an x taken out, so that it becomes: x ( 1 + x1 + x2) before I can apply an identity ? And if so, would this identity result in: ( x ( 1- x2)(1 + x1 + x2 + ...)) ?
Thanks for any advice on how to go forward!