Alternative Notation for Binomial Coefficient

Consider the binary operation $$ f(n,k) = \binom{n+k}{k} = \frac{(n+k)!}{n!k!}. $$ This binary operation is obviously ubiquitous in combinatorics (since it appears wherever the binomial coefficient does) and occasionally one encounters identities and arguments expressed using the binomial coefficient which are arguably simpler to express via this operation. It seems reasonably likely to me that there is some standard notation and name for $f$. Surely the most common notation is $\binom{n+k}{k}$, but I wonder if there is some pre-existing alternative notation which is not simply derived from the binomial coefficient notation, and which allows one to write $n,k$ only once instead of having to write one of them twice.

I don't think I would use such notation outside of personal notes, but I'm still curious: does such a notation already exist in the literature?

Yes. $$\displaystyle \left(\!\!{n \choose k}\!\!\right)=\binom{n+k-1}{k},$$ this is used in the context of compositions and multisets.