Use exponential generating functions to prove that:
P(n) = P(n-1) + n, with n >= 1 and P(0) = 1
will result in this equation: P(n) = (1/2)n2 + (1/2)n + 1

I know how to do this with generating functions, you just plug in n=1, n=2, n=3,....
P(1) will result in (1/2)(1)2 + (1/2)(1) +1 which is 2
P(2) will result in P(2-1)+2 which is P(1) + 2.. and so on
but I'm kind of stuck on "exponential" generating functions.
Can someone help me out?
I found this link, but I'm still not getting it.
https://www.whitman.edu/mathematics/...tion03.02.html