That sure is ugly and totally impossible to understand. Makes me want to tear my few remaining hairs out ( check out my avatar ).
Please learn to latex up your math.
First kids generating function:
Which coefficient do you compute?
Looks like the first bit of intelligent journalism in ohh, about 100 years. Much better than their continued coverage of how much ole Bill G. is worth or the latest fashion trend painted on some rock star bimbo.
It looks like I am just doing your homework for you.
I have given you the first couple but in order for you to learn you must try to do them yourself what have you done?
You obviously are in a pretty advanced course where they are throwing generating functions at you what have you learned? What have you tried?