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I would like to find all the possible hypergeometric solutions for the recurrence relation defined as $$ (n+2)a_{n+2} - 2(4n+5)a_{n+1} + 8(2n+1)a_n = 0.$$

Is there any way to approach this problem in an elegant way? As far as I have looked into the book suggested in some other question (A=B), one can use the algorithm hyper to solve these problems. However, I would like a faster way to find all the possible solutions for this concrete recurrence.

Any ideas?

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    Excuse me for the newbie question, but what do you mean by hypergeometric solution? I dind't find easily something on google...2011-06-27
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    Can you clarify what you mean by "faster"? Does Hyper really run too slowly on your computer or do you mean that you want a simpler method than the full algorithm because you think that this is a simpler case?2011-10-04

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