recursive formula

Hi all,
can anybody give me a hint about this problem?

I have a function (from N to N) defined in 'recursive form' as
follows:

n(0)=n0

n(i)= n(i-1) A^n(i-1) + N [ 1-A^n(i-1) ]

I know that n(i)->N when N-> INF,
so n(i) is the weighted mean between the previous value n(i-1) and the
last value N
Weigths are: A^n(i-1) and [ 1-A^n(i-1) ]

I need to obtain the 'close form' of this function (if it is
possible), that is, n(i)= f(A,i,n0 )
Do you think it is possible?

Do you know if n(i) has 'interesting' proprieties?

Thanks!
.

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