(** The falling factorial *)
Definition falling_factorial := nosimpl ffact_rec.
Notation "n ^_ m" := (falling_factorial n m)
(at level 30, right associativity) : nat_scope.

Theorem Pascal a b n :
(a + b) ^ n = \sum_(i < n.+1) 'C(n, i) * (a ^ (n - i) * b ^ i).