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?