{"id":"e-e9da8c20b726baa3","operation":{"operation":"theorem_check","theorem":"liu_wang"},"operation_detail":"liu_wang","conclusion_id":"n-2b477f2aa77e3efc","premise_count":0,"theorem":"L. L. Liu and Y. Wang, A unified approach to polynomial sequences with only real zeros, Adv. in Appl. Math. 38 (2007) 542-560, Theorem 2.1 with g = f' (as in their Corollary 2.4), with nonnegativity of the coefficients replaced by an exact induction keeping every root in (-inf, 0)","lean_route":null,"lean_declarations":[],"certificate_hash":"a6ff62b4d79ddc1a31dacc0248c34cf36c835b4c62cb7a0e5e3d30efa2d9d229","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"theorem_check","certificate_raw_size":2755,"certificate_compressed_size":1045,"conclusion_name":"Triangle of coefficients in expansion of (1+x)*(1+3x)*(1+5x)*(1+7x)*...*(1+(2n-1)x).","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":false,"value":"0"}}},{"claim":"interlacing","from_index":1,"kind":"weak","orientation":"previous_interlaces_next"}],"premises":[],"cited_by":[{"node_id":"n-2b477f2aa77e3efc","claim":"real_rooted"},{"node_id":"n-2b477f2aa77e3efc","claim":"one_signed_coefficients"},{"node_id":"n-2b477f2aa77e3efc","claim":"hadamard_kernel"},{"node_id":"n-2b477f2aa77e3efc","claim":"interlacing"}]}