zscoder introduced Generating functions in Competitive Programming in his blog, which give a method to get the formula of general term of a array by it's generating function.
But sometime the generating function is somewhat complicated, for instance, the array http://oeis.org/A054726 which has generating function:
and we can calculate the first n term by poly sqrt with fft in $$$O(n \log n)$$$
But this array have a recurrence formula:
which will be much easy to calculate.
My question is how can I get recurrence formula by it's generating function in general(or some special form) ?