# Limited Proxies

Algebra Level 4

$\large{ a }_{ n }=\frac { f ( n ) ! }{ { a }_{ n-1 }{ a }_{ n-2 }{ a }_{ n-3 }{ a }_{ n-4 } }$

The recurrence relation above has the initial condition of $${ a }_{ 0 }={ a }_{ 1 }={ a }_{ 2 }={ a }_{ 3 }=1.$$ If $$f\left( n \right) =n-2$$ for $$n \ge 2$$, find the largest value of $$n$$ such that $${ a }_{ n }=f\left( n \right).$$

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