proposition: Lemma bin_fact2n_a n : 'C(n.*2, n) * (n`!)^2 = (n.*2)`!.
proof: Proof. by rewrite - addnn - mulnn - (bin_fact (leq_addr n n)) addnK. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype) mathcomp(ssrnat seq path div) mathcomp(fintype tuple finfun bigop finset binomial)