In: Advanced Math
Create the generating functions in closed form ( not as an infinite sum) using the sequences:
example: 1,1,1,1,1,1,... = 1/(1-x)
1. 0,1,1,1,1,1,...
2. 1,0,0,1,0,0,1,0,0,1,0,0,1,...
3. 0, 0,0,0,1,1,1,1,1,1,1,1,1,...
4. 1, -1, 1, -1, 1,....
5. 1,1,1,0,0,1,1,1,1,1,1,1,1,1,...
6. 0,0,0,1,2,3,4,5,6,..
7. 3,2,4,1,1,1,1,1,...
8. 0,2,0,0,2,0,0,2,0,0,..