RSolve not returning known solution

Question

I have the following recurrence relationship for which I know the solution is given by a binomial distribution:

reccurance =  A (i + 1) v[i + 1] + (n - i - 1) v[i - 1] == (n - i) v[i] + A i v[i]

But when I use RSolve I get

RSolve[{reccurance}, v, i]

{{v -> DifferenceRoot[
    Function[{\[FormalY], \[FormalN]}, {(-2 - \[FormalN] + 
           n) \[FormalY][\[FormalN]] + (1 + \[FormalN] (1 - A) - A - 
           n) \[FormalY][
          1 + \[FormalN]] + (2 A + \[FormalN] A) \[FormalY][
          2 + \[FormalN]] == 0, \[FormalY][0] == 
       C[1], \[FormalY][1] == C[2]}]]}}

Putting in the appropriate boundary conditions does not help things at all. e.g.

RSolve[{reccurance, v[-1] == 0, v[n + 1] == 0}, v, i]

Does not do anything at all (well, it returns the input). Nor does adding the constraint for all values to sum to one, or the first value equal to a yet-to-be-determined constant.

How do I make this result in something that is clearly a binomial distribution?