{"id":"e-d32219abddaaed67","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-bb74f03367de3ec8","premise_count":0,"theorem":"all-index identity Q_n = P_n certified by exact Ore-algebra division and identifying rows (polytool preserver-image certificate of the identity map)","lean_route":null,"lean_declarations":[],"certificate_hash":"60bd659b632efdf877554c96dcda4778db90dfad179572f562d5447c275f1275","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":18236,"certificate_compressed_size":4359,"conclusion_name":"Generalized Narayana numbers, T(n, k) = 3/(n + 1)*binomial(n + 1, k + 2)*binomial(n + 1, k - 1), triangular array read by rows.","claims":[],"premises":[],"cited_by":[]}