Getting recurrence relations using generating functions

Question

In Wilf's "Generatingfunctionology", it is mentioned that generating functions sometimes help in finding other recurrence relations of the sequence. However, as far as I've seen, the only example in the book is the xDlog method, so are there any other methods for getting recurrences from generating functions? Also, what are other examples of using the xDlog method apart from the Bell numbers and $A(x)=B(x)^k$ (when the explicit formula of coefficients of $A(x)$ is known)?