proposition: Lemma coef_derivn n p i : p^`(n)`_i = p`_(n + i) *+ (n + i) ^_ n.
proof: Proof. elim: n i => [|n IHn] i; first by rewrite ffactn0 mulr1n. by rewrite derivnS coef_deriv IHn -mulrnA ffactnSr addSnnS addKn. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype bigop finset tuple) mathcomp(div ssralg countalg binomial)