Tired of Sequences. This one is Nice

Number Theory Level pending

Let \(a_{0},a_{1},a_{2},\ldots\) be a sequence such that \(a_{0}=1\) and \(a_{n+1}=(n+1)a_{n}\), for integer \(n>0\). Which element of this sequence is equal to \(123!\) ?

Notation: \(!\) denotes the factorial notation. For example, \(8! = 1\times2\times3\times\cdots\times8 \).

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