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Question: Recursive function definition does not work with sum

Question:Recursive function definition does not work with sum

Mircode 10 Maple 10
sum define
June 10 2011
1

Hi! Normally recursively defined functions work well, but if I use a sum inside, this happens:

> y:=n->sum(y(k),k=0..n-1);

                                   n - 1
                                   -----
                                    \
                     y := n ->   )   y(k)
                                    /
                                   -----
                                   k = 0

> y(0):=a;

                              y(0) := a

> y(4);
Error, (in y) too many levels of recursion

 

when it should be 6a.

What can I do? (This is just an example, I don't want an explicit solution to this particular problem)
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