I am not considering \((n!)!\).

\(1!! + 1\) is even.

\(3!! +1\) is even.

\(5!! + 1 \) is even.

\(7!! +1\) is even.

\(9!! +1\) is even.

Is it true that \(n!! + 1\) is always an even number for all positive odd integers \(n?\)

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