so basically I found this formula :

(sorry I tried using latex but I kept getting errors)

and I'm not quite sure if I understand how to use it, so if any of you could give me some examles of how it's used I would be much grateful.

I did use a different way to find the generating function for the sum starting at n=1.

but when I got the exact same thing for n=2, I wasn't sure anymore.

(I think it's 1 + x/(1-x)^2 ? -damn I'm having problems with this latex)

so if you could please show me how to use this formula for n=2 or for any n, it would be great.

p.s - it is possible that I'm also confused by the Leibniz notations since I'm used to Lagrange

thanks.