Proof methods / preserver_image

Image under a real-rootedness preserver

8,704 sequences

• A166961 → (θ+1)²
  1 · 1, 4 · 1, 36, 9 · 1, 236, 378, 16 … Σ 1, 5, 46, 631, 12259, 312022, 10028171, …
  (−∞, 0]nonnegative
• A038331 → basis A013609 → x ↦ x/(x+1)
  289, 918, 729 · 4913, 23409, 37179, 19683 … Σ 1936, 85184, 3748096, 164916224, …
  [−1, 0]nonnegativerational roots
• A327997 → x ↦ x+1
  1 · 4, 1 · 17, 9, 1 · 78, 65, 15, 1 … Σ 1, 5, 27, 159, 1029, 7353, 58095, …
  (−∞, −1]nonnegative
• A272867 → x ↦ x+1 → D
  6, 2 · 72, 96, 36, 4 · 648, 1512, 1296, 504, 90, 6 … Σ 0, 8, 208, 4056, 70304, 1142440, …
  (−∞, 0]nonnegative
• A371259 → θ+1
  1 · 36, 2 · 1764, 200, 3 · 112896, 19728, 600, 4 … Σ 1, 38, 1967, 133228, 11446741, …
  (−∞, 0]nonnegative
• A126351 → x ↦ x+1 → reverse
  1 · 2, 3 · 4, 13, 10 · 8, 43, 71, 37 … Σ 1, 5, 27, 159, 1025, 7221, 55307, …
  (−∞, 0]nonnegative
• basis-map coefficients of A021012 → basis A008277 → reverse
  1 · -1, -1 · 2, 6, 2 · -6, -36, -42, -6 … Σ 1, -2, 10, -90, 1248, -24360, 631440, …
  (−∞, 0]
• A137320 → basis A013611 → basis A007318
  1 · 10, 8 · 110, 168, 64 · 1320, 2896, 2112, 512 … Σ 1, 18, 342, 6840, 143640, 3160080, …
  (−∞, −1]nonnegativerational roots
• A145324 → basis A013609 → x ↦ x/(x+1)
  1 · 3, 7 · 12, 58, 70 · 60, 446, 1104, 910 … Σ 1, 10, 140, 2520, 55440, 1441440, …
  [−1, 0]nonnegativerational roots
• A039991 → x ↦ x+1
  1 · 1 · 1, -2, -1 · 1, -6, -3 … Σ 1, 1, -2, -8, -8, 16, 64, 64, …
  (−∞, ∞)
• A085880 → basis A013610 → x ↦ x+1
  1 · 5, 3 · 50, 60, 18 · 625, 1125, 675, 135 … Σ 1, 8, 128, 2560, 57344, 1376256, …
  (−∞, −1]nonnegativerational roots
• A099093 → reverse → D+1
  1 · 3 · 12, 3 · 45, 18 … Σ 1, 3, 15, 63, 270, 1134, 4725, 19521, …
  (−∞, 0]nonnegative
• A132393 → θ+1 → x ↦ x+1
  1 · 2, 2 · 5, 8, 3 · 17, 34, 21, 4 … Σ 1, 4, 16, 76, 428, 2808, 21096, 178848, …
  (−∞, −1]nonnegative
• A322944 → D
  1 · 6, 2 · 38, 30, 3 · 272, 376, 84, 4 … Σ 0, 1, 8, 71, 736, 8805, 119496, …
  (−∞, 0]nonnegative
• A099040 → x ↦ x−8
  1 · -16, 2 · 240, -62, 4 · -3584, 1408, -184, 8 … Σ 1, -14, 182, -2352, 30380, -392392, …
  (6, 8]
• A280580 → reverse
  1 · 1, 1 · 1, 6, 2 · 1, 15, 30, 5 … Σ 1, 2, 9, 51, 323, 2188, 15511, 113634, …
  (−∞, 0]nonnegative
• A116414 → D
  1 · 8, 2 · 42, 24, 3 · 184, 174, 48, 4 … Σ 0, 1, 10, 69, 410, 2252, 11790, 59767, …
  (−∞, 0]nonnegative
• A038271 → basis A013609 → D+1
  1 · 22, 10 · 384, 440, 100 · 6048, 11520, 6600, 1000 … Σ 1, 32, 924, 25168, 660176, 16866432, …
  (−∞, 0]nonnegativerational roots
• A028326 → basis A013611 → θ+1
  2 · 4, 16 · 8, 64, 96 · 16, 192, 576, 512 … Σ 2, 20, 168, 1296, 9504, 67392, 466560, …
  (−∞, 0]nonnegativerational roots
• A008459 → (θ+1)²
  1 · 1, 4 · 1, 16, 9 · 1, 36, 81, 16 … Σ 1, 5, 26, 134, 670, 3262, 15540, 72732, …
  (−∞, 0]nonnegative
• A106246 → θ+1 → reverse
  1 · 2, 2 · 3, 8, 1 · 4, 18, 6 … Σ 1, 4, 12, 28, 55, 96, 154, 232, …
  (−∞, 0]nonnegative
• A088996 → reverse
  1 · 1 · 2, 1 · 6, 7, 2 … Σ 1, 1, 3, 15, 105, 945, 10395, 135135, …
  (−∞, −1]nonnegativerational roots
• basis-map coefficients of A297191, shifted → (θ+1)² → reverse
  1 · 9 · 25 · 49 … Σ 1, 9, 25, 49, 81, 121, 169, 225, …
  (−∞, 0]nonnegativerational roots
• A122848 → basis A007318 → D
  1 · 3, 2 · 9, 12, 3 · 28, 54, 30, 4 … Σ 0, 1, 5, 24, 116, 580, 3012, 16240, …
  (−∞, 0]nonnegative
• A123519 → basis A007318 → x ↦ x/(x+1)
  11, 36, 29 · 41, 199, 319, 169 … Σ 76, 728, 6976, 66848, 640576, 6138368, …
  [−1, −1/2)nonnegative
• A130534 → basis A013610 → D
  3 · 15, 18 · 78, 162, 81 · 462, 1278, 1134, 324 … Σ 0, 3, 33, 321, 3198, 33822, 383580, …
  (−∞, 0]nonnegative
• A038328 → x ↦ x+1 → D
  56, 8 · 1176, 336, 24 · 21952, 9408, 1344, 64 … Σ 64, 1536, 32768, 655360, 12582912, …
  (−∞, 0]nonnegativerational roots
• A132393 → D → (θ+1)²
  1 · 1, 8 · 2, 24, 27 · 6, 88, 162, 64 … Σ 0, 1, 9, 53, 320, 2134, 15918, 132474, …
  (−∞, 0]nonnegative
• A163936: Triangle related to the o.g.f.s. of the right-hand columns of A130534 (E(x,m=1,n)).
  1 · 1 · 2, 1 · 6, 8, 1 … Σ 1, 1, 3, 15, 105, 945, 10395, 135135, …
  (−∞, 0)nonnegative
• A008955 → basis A007318 → x ↦ x/(x+1)
  1 · 2, 3 · 10, 33, 27 · 100, 520, 897, 513 … Σ 1, 5, 70, 2030, 101500, 7815500, …
  [−1, 0]nonnegativerational roots
• A130534 → D²∘x (shift +1) → D+1
  1 · 6, 3 · 29, 30, 6 · 155, 225, 90, 10 … Σ 1, 9, 65, 480, 3829, 33439, 319976, …
  (−∞, 0]nonnegative
• A108299 → x ↦ x+1
  1 · 0, -1 · -1, -3, -1 · -1, -2, 1, 1 … Σ 1, -1, -5, -1, 19, 23, -53, -145, …
  (−∞, ∞)
• A008278 → D
  1 · 3, 2 · 6, 14, 3 · 10, 50, 45, 4 … Σ 0, 1, 5, 23, 109, 544, 2876, 16113, …
  (−∞, 0]nonnegative
• A099040 → basis A013609 → (θ+1)²
  1 · 2, 16 · 6, 80, 144 · 16, 320, 1152, 1024 … Σ 1, 18, 230, 2512, 25052, 235224, …
  (−∞, 0]nonnegative
• A178822 → basis A013610 → (θ+1)²
  1 · 12, 72 · 84, 1008, 1701 · 448, 8064, 27216, 24192 … Σ 1, 84, 2793, 59920, 985950, 13545000, …
  (−∞, 0]nonnegative
• basis-map coefficients of A112227 → D
  0, 2 · 0, 0, 3 · 0, 0, 0, 4 · 0, 0, 0, 0, 5 … Σ 2, 3, 4, 5, 6, 7, 8, 9, …
  (−∞, 0]nonnegativerational roots
• A069466 → γ → θ+1
  1 · 2 · 6, 24 · 20, 240 … Σ 1, 2, 30, 260, 3010, 33012, 379764, …
  (−∞, 0]nonnegative
• A128099 → basis A013610 → θ+1
  1 · 1 · 3, 12 · 5, 24 … Σ 1, 1, 15, 29, 203, 537, 2695, 8341, …
  (−∞, 0]nonnegative
• A145324 → x ↦ x/(x+1)
  1 · 1, 3 · 1, 7, 12 · 1, 12, 47, 60 … Σ 1, 4, 20, 120, 840, 6720, 60480, …
  [−1, 0]nonnegativerational roots
• A156366 → (θ+1)²
  1, 48, 81 · 1, 132, 891, 432 … Σ 130, 1456, 18916, 279784, 4638880, …
  (−∞, 0]nonnegative
• A088729 → D
  9, 2 · 79, 36, 3 · 765, 530, 90, 4 … Σ 11, 118, 1389, 18231, 266062, 4287459, …
  (−∞, 0]nonnegative
• A136124 → basis A013611 → D+1
  1 · 7, 4 · 40, 60, 16 · 248, 572, 384, 64 … Σ 1, 11, 116, 1268, 14696, 181816, …
  (−∞, 0]nonnegative
• A286718 → basis A013610 → D
  3 · 21, 18 · 198, 270, 81 · 2418, 4158, 2106, 324 … Σ 0, 3, 39, 549, 9006, 171582, 3745800, …
  (−∞, 0]nonnegative
• A126216 → basis A013610 → x ↦ x+1
  1 · 6, 3 · 41, 39, 9 · 306, 423, 189, 27 … Σ 1, 9, 89, 945, 10577, 123129, 1476841, …
  (−∞, −1]nonnegative
• A028338 → basis A013611 → D+1
  1 · 6, 4 · 32, 56, 16 · 224, 560, 384, 64 … Σ 1, 10, 104, 1232, 16704, 256896, …
  (−∞, 0]nonnegative
• A013610 → basis A013610 → D+1
  1 · 13, 9 · 88, 234, 81 · 496, 2376, 3159, 729 … Σ 1, 22, 403, 6760, 107653, 1656538, …
  (−∞, 0]nonnegativerational roots
• A038281 → basis A013611 → x ↦ x/(x+1)
  121, 506, 529 · 1331, 8349, 17457, 12167 … Σ 1156, 39304, 1336336, 45435424, …
  [−1, 0]nonnegativerational roots
• A249247 → D+1
  1 · 2, 1 · 5, 3 · 16, 12, 1 … Σ 1, 3, 8, 29, 129, 691, 4348, 31509, …
  (−∞, 0]nonnegative
• A131431 → D+1 → D
  4 · 14, 14 · 0, 60, 30 · 0, 0, 156, 52 … Σ 0, 4, 28, 90, 208, 400, 684, 1078, …
  (−∞, 0]nonnegativerational roots
• A103327 → D+1
  1 · 4, 1 · 15, 12, 1 · 42, 77, 24, 1 … Σ 1, 5, 28, 144, 704, 3328, 15360, 69632, …
  (−∞, 0]nonnegative