General formalism solving linear recursion relations
Adel F. Antippa, Alain J. Phares · Journal of Mathematical Physics · 1977
We give the general solution of multiterm linear homogeneous recursion relations with nonconstant coefficients, by introducing a new class of special combinatorics functions based on the partition of an interval into classes. This provides power series solutions, whenever they exist, of ordinary linear differential equations, of any order, with polynomial coefficients.