I'm currently struggling with ordinary generating functions(OGF) and was hoping somebody could point me in the direction of determining the OGF for the Stirling numbers of the second kind $\sum_{n=k}^\infty S(n,k) x^n$.

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    $\begingroup$ en.wikipedia.org/wiki/… $\endgroup$ – Austin Mohr May 5 '13 at 16:44
  • $\begingroup$ That's a perfect link for the OGF but I'm having problems with proving that it's the OGf not just what the OGF is. $\endgroup$ – Atom May 5 '13 at 16:48

Take a look at Wilf's "generatingfunctionology". There you'll learn much of what there is about generating functions. A next step could be Flajolet and Sedgewick's "Analytic combinatorics" (careful, that one is quite a bit heavier going).

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  • $\begingroup$ You can also read this post on how to apply a Norlund-Rice (contour) integral to a known identity for the Stirling numbers of the second kind to arrive at the same OGF. $\endgroup$ – mds May 30 '18 at 23:21

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