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I'm trying to figure out the generating function for this power series.. I have a few ideas but can't get any result..

$$\sum_{n=2}^\infty \left(\sum_{k=1}^{n} ((n-k)(k-1)M_{k-1}) z^n\right) $$

$M(k)$ is my recursive function.. my problem is with the $(n-k)(k-1)$ part..

I was thinking that it can be extracted from the summation and it should become

$$n(n+1)(n+2)/6$$

but I'm still unable to solve this..

  • 2
    A generating function and a (formal) power series are the same thing, so it's not clear what you're asking.2011-11-21
  • 1
    Have you tried applying convolution backwards?2011-11-21
  • 1
    If you want to solve for $M_k$, you should give the original recursion in your question.2011-11-21

2 Answers 2