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i have the following two variable recurrence:

$$f(i,n+1) = f(i-1,n)*\frac{n-i+1}{n} + f(i,n)*\frac{i}{n}$$

$$f(0,n) = (\frac{1}{n})^{n-2}$$

$$f(i,0) = 0$$

I'm not sure which method can I try to solve this.

How can i solve this equation for f(i,n+1)? thanks

user288271
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  • Generating functions? – Did Nov 08 '15 at 23:49
  • I have only used generating functions on single variable recursion, how would one use it to solve a 2 variable recursion? can you please show me how to solve this with generating functions? – user288271 Nov 09 '15 at 00:05

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