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

to supplement N3buchadnezzar, some ways to work out the double factorial or semifactorial are as follows:

following this definition, these handy relations can be used
for even !!

and odd !!

