What does the !! mean in trigonometric identity? What does the $!!$ mean in:
$$
\int_0^x \sin^n(t) \mathrm dt = \begin{cases}
\frac{(n-1)\color{red}{!!}}{n\color{red}{!!}}\Big[1-\cos(x)\sum_{j=0}^{(n-1)/2}\frac{(2j-1)\color{red}{!!}}{(2j)\color{red}{!!}}\sin^{2j}(x)\Big]&\text{for $n$ odd}\\
\frac{(n-1)\color{red}{!!}}{n\color{red}{!!}}\Big[x-\cos(x)\sum_{j=0}^{(n-2)/2}\frac{(2j)\color{red}{!!}}{(2j+1)\color{red}{!!}}\sin^{2j+1}(x)\Big]&\text{for $n$ even}\\
\end{cases}.
$$
Is it factorial applied twice?
This is from page 317 of An Atlas of Functions, Second edition: with Equator, the Atlas Function Calculator by Keith B. Oldham, Jan Myland, Jerome Spanier

In mathematics, the double factorial or semifactorial of a number $n$ (denoted by $n!!$) is the product of all the integers from $1$ up to $n$ that have the same parity (odd or even) as $n$.
Example: $9!! = 9 \cdot 7 \cdot 5 \cdot 3 \cdot 1$
