### indicial equation

Let N be an integer. Let a, b, A_1,...,A_N be constant real numbers. Let g(n) be a real function of integer variable n.

g(n) satisfies the recurrence equation:

(n + 1)*(n + b)*g(n+1) = (n + ~~a)~~*g(n) **a)*g(n) + sum(i=1 to *~~N)(A_i~~N)(A_i * g(n-i))

with g(n)=0 for n<0 . g(0) is obtained through boundary conditions, so it can be considered a given constant.

I need to know the general functional form of the term g(n), as a function of the given constants of the problem: a,b,N,A_1,...,A_N and g(0).

Could you help me? ~~I could ~~Could I programm in SAGE the code to provide the searched general term g(n)?

Thanks for your attention.

Javier Garcia