# Is it even odd?

Let a series be defined as $a_0=1$ $a_n=\frac{n!}{a_{n-1}},n>0$.

Now consider the following statements.

1. $$a_n$$ is an integer for $$n \ge 0$$.

2. $$a_n$$ is odd if and only if $$n$$ is odd.

3. $$a_n$$ is even, for positive $$n$$, if and only if $$n$$ is even

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