{"id":"e-3fbe5bf8626421ec","operation":{"map":"A013610","operation":"basis_map"},"operation_detail":"A013610","conclusion_id":"n-e1099b1c979335bc","premise_count":1,"theorem":"geometric family P_k = g(t) (a + d t)^k: T(p) = g(t) p(a + d t), so the roots of T(p) are those of g and the points (r - a)/d for the roots r of p (elementary)","lean_route":null,"lean_declarations":[],"certificate_hash":"adf8ce9956f50671f190e7bdce4a68993ce2206cb77adbae2e48dda65d409a10","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":14925,"certificate_compressed_size":2805,"conclusion_name":"basis_map_A013610 of theta_plus_one of a(n) = 1 if n is of the form m(m+3)/2, otherwise 0.","claims":[{"claim":"real_rooted","from_index":1,"region":{"upper":{"closed":true,"value":"0"}}},{"claim":"interlacing","from_index":2,"kind":"weak","orientation":"unordered"}],"premises":[{"position":0,"node_id":"n-e177181dad825c00","role":"sequence","name":"derivative of basis-map coefficients of A scaled Hermite triangle.","uses":{"claim":"real_rooted","from_index":1,"region":{"upper":{"closed":true,"value":"0"}}},"uses_text":"Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 0]"}],"cited_by":[{"node_id":"n-e1099b1c979335bc","claim":"real_rooted"},{"node_id":"n-e1099b1c979335bc","claim":"one_signed_coefficients"},{"node_id":"n-e1099b1c979335bc","claim":"hadamard_kernel"},{"node_id":"n-e1099b1c979335bc","claim":"interlacing"}]}