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)n^{2}+ (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