I am having as problem with inverting a relation of the form
$f(i)=\sum_{j=0}^i g(i,j)h(j)$
I would like to have h in terms of f and g. I know that if my formula was of the form $f(i)=∑_j^ih(j)$ I could just use a generalized Möbius inversion formula, but since g depends on both i and j I don't think the method applies. Is there a more general one? Any help would be appreciated! Thanks
EDIT: $g(i,j)=\binom{i}{j}$