I am learning about generating function now, and I am quite confused about where to use EGF and where to use OGF. You know, I could do the exercises following each section, but if there are some mixed exercises, I often don't know whether I should choose OGF or EGF...
In addition, I read this article just now, and I feel also confused about some words in it. Qiaochu said, "In the language of exponential generating functions, differentiation corresponds to a shift in index (this is what we're really going after) and the above($s^n=s\times s^{n-1}$) is equivalent to the identity $\frac{d}{dx} e^{sx}=se^{sx}$." And I don't know how to understand that they are "equivalent".
Thanks in advance.