For the following function f with domain N determine a formula for f(n) and use mathematical induction to prove your conclusion:

For a1,a2 in R, arbitrary, let f(1)=a1 and f(2)=a2. For n>2 f(n)=-^{f(n-2)}/_{n(n-1)}

I calculated the first few values as :

f(3)=-^{a1}/_{6 }f(4)=-^{a2}/12

f(5)=^{a1}/120

f(6)=^{a2}/360

I was going to define this piecewise, since a1 goes with the odd n and a2 is paired with even ones. I've come up with

^{a1}/_{n(n-1)(n-2)(n-3) }for even n

^{a2}/_{n(n-1)(n-2)(n-3) }for odd n

I'm not really sure how to address the changing sign however. I feel like I should use -1 to some power, but I'm not sure how to approach it.