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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