Binomial coefficient
Generalization to negative integers n

For any n,

In particular, binomial coefficients evaluated at negative integers n are given by signed multiset coefficients. In the special case n = − 1 {\displaystyle n=-1}, this reduces to (− 1) k = (− 1 k) = ((− k k)). {\displaystyle (-1)^{k}={\binom {-1}{k}}=\left(\!\!{\binom {-k}{k}}\!\!\right).}

For example, if n = −4 and k = 7, then r = 4 and f = 10:
length_constraints:number_paragraphs[5]