Definition PS_derive_n (n : nat) (a : nat -> R) :=
  (fun k => (INR (fact (k + n)%nat) / INR (fact k)) * a (k + n)%nat).

Lemma Derive_n_coef (a : nat -> R) (n : nat) : Rbar_lt (Finite 0) (CV_radius a) -> Derive_n (PSeries a) n 0 = a n * (INR (fact n)).