**Recurrence for the Right-Hand Side**

We obtain a recurrence for the right-hand side by applying
__Mgfun[sum_of_sys]__
on the system computed in the previous section.

`> `
**sum_of_sys(sys,k=-infinity..infinity,takayama_algo);**

This recurrence is different from the one obtained for the left-hand side.

`> `
**rec[right]:=op(collect(",h,factor));**

We thus need more work to prove that both sides agree.