I want to know if there is a package in Mathematica or maple that can give back some recursion given a list of polynomial in $f_{n}(h)$. I want a recursion of the from $$ \sum_{k=0}^{N}a_{k}(h)f(n+k) =0 $$ where $a_{k}(h)$ is a rational function in $h$
For example I know there exists package RISC guess that where I give some list of rational numbers it can give me the recursion it satisfies. Here instead of rational number its polynomials. The following gives the list of polynomials in $h$ the numbers denote the on the extreme left the index of the element in the my list. I have proved that there exist a $N$ such that $$ \sum_{k=0}^{N}a_{k}(h)f(n+k) =0 $$ this will hold still wondering for an example.