# Two questions about generating functions

I'm very interested in the topic of generating functions, so I have two questions:

1. I just realized that when I have exponential generating function for example $F(x)=e^{e^x-1}$, I can take n-th derivative and count the value in $x=0$ to get n-th element of sequence that this function represents. It's very useful I think :-) but are the ordinary generating functions that useful too? Is there any operation on ordinary generating function that can help me count the n-th element of sequence that this function represents?
2. Here: http://en.wikipedia.org/wiki/Generating_function#Examples we have got exponential generating function for sequence $a_n=n^2$. It's simple to find the ordinary generating function for this sequence (taking derivatives and subtracting something) but how can I deduce that $\displaystyle \sum_{n=0}^{+\infty}n^2\frac{x^n}{n!}=x(x+1)e^x$?
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(1) Just do the same and divide by $n!$ then.