A node rather than n!/(k! (n - k)!): that quotient is correct and useless as a
spelling -- it loses the integrality, it is undefined for a negative n where
the falling factorial n (n - 1) ... (n - k + 1)/k! is not, and no rule can
recognise Pascal's identity or Vandermonde's in a ratio of three factorials. The
falling factorial is the definition for a whole k, whatever n is; a
whole k below zero gives 0; and for a k that is not whole the
value is Γ(n + 1)/(Γ(k + 1) Γ(n - k + 1)), which has no value where n is a negative whole number. What cannot be settled is left as this node.
https://github.com/asc-community/AngouriMath/issues/1409
https://github.com/asc-community/AngouriMath/issues/809