Are these below a "standard" (i.e. not-obscure) piece one can see in textbooks:

$\displaystyle n_{(r)}=\frac{n^{(r)}}{r!}$ [$\displaystyle n_{(3)}=\frac{n(n-1)(n-2)}{3!}$] and $\displaystyle n_{r}=\frac{n^r}{r!}$

($\displaystyle n!!$, I presume, is "standard".)

Pretty please post more "alike".