Proof methods / preserver_image

Image under a real-rootedness preserver

8,704 sequences

• A128100 → basis A007318 → θ+1
  1 · 1 · 3, 2 · 5, 4 … Σ 1, 1, 5, 9, 28, 62, 165, 391, …
  (−∞, 0]nonnegative
• A038226 → basis A013610 → D
  528, 1152 · 8712, 38016, 41472 … Σ 1680, 88200, 4116000, 180075000, …
  (−∞, 0]nonnegativerational roots
• narayana → basis A013609 → θ+1
  1 · 2, 4 · 5, 20, 12 · 14, 84, 108, 32 … Σ 1, 6, 37, 238, 1578, 10684, 73429, …
  (−∞, 0]nonnegative
• A013622 → x ↦ x/(x+1) → (θ+1)²
  1 · 3, 32 · 9, 192, 576 · 27, 864, 5184, 8192 … Σ 1, 35, 777, 14267, 235345, 3621651, …
  (−∞, 0]nonnegative
• A173018 → reverse (shift +1) → reverse → x ↦ x+1
  1 · 1 · 2, 1 · 6, 6, 1 … Σ 1, 1, 3, 13, 75, 541, 4683, 47293, …
  (−∞, −1]nonnegative
• A028326 → x ↦ x/(x+1)
  2 · 2, 4 · 2, 8, 8 · 2, 12, 24, 16 … Σ 2, 6, 18, 54, 162, 486, 1458, 4374, …
  [−1, 0]nonnegativerational roots
• A100862 → x ↦ x+1
  1 · 2, 1 · 5, 5, 1 · 14, 21, 9, 1 … Σ 1, 3, 11, 45, 201, 963, 4899, 26253, …
  (−∞, −1]nonnegative
• A112007 → (θ+1)²
  1 · 2, 4 · 6, 32, 9 · 24, 232, 198, 16 … Σ 1, 6, 47, 470, 5705, 81270, 1327095, …
  (−∞, 0]nonnegative
• A038271 → θ+1
  1 · 7, 10 · 49, 140, 75 · 343, 1470, 1575, 500 … Σ 1, 17, 264, 3888, 55296, 767232, …
  (−∞, 0]nonnegativerational roots
• A125662 → basis A013609 → θ+1
  1 · 4, 4 · 15, 32, 12 · 56, 184, 144, 32 … Σ 1, 8, 59, 416, 2845, 19032, 125207, …
  (−∞, 0]nonnegative
• A156992 → basis A007318 → D+1
  1 · 6, 2 · 48, 36, 6 · 480, 576, 216, 24 … Σ 1, 8, 90, 1296, 22680, 466560, …
  (−∞, 0]nonnegativerational roots
• A110441 → basis A007318
  1 · 4, 1 · 14, 8, 1 · 48, 44, 12, 1 … Σ 1, 5, 23, 105, 479, 2185, 9967, 45465, …
  (−7, −1)nonnegative
• A257621 → (θ+1)²
  1 · 3, 12 · 9, 168, 81 · 27, 1572, 3537, 432 … Σ 1, 15, 258, 5568, 143040, 4255440, …
  (−∞, 0]nonnegative
• A147716 → basis A013611 → D
  4 · 120, 32 · 2700, 1440, 192 … Σ 0, 4, 152, 4332, 109744, 2606420, …
  (−∞, 0]nonnegativerational roots
• A008277 → x ↦ x+1 → x ↦ x+1
  1 · 3, 1 · 11, 7, 1 · 47, 43, 12, 1 … Σ 1, 4, 19, 103, 622, 4117, 29521, …
  (−∞, −1]nonnegative
• A013613 → θ+1
  1 · 1, 12 · 1, 24, 108 · 1, 36, 324, 864 … Σ 1, 13, 133, 1225, 10633, 88837, 722701, …
  (−∞, 0]nonnegativerational roots
• A038259 → basis A013610 → (θ+1)²
  1 · 11, 60 · 121, 1320, 2025 … Σ 1, 71, 3466, 143936, 5445856, …
  (−∞, 0]nonnegative
• A008459 → basis A013611 → x ↦ x/(x+1)
  1 · 2, 6 · 6, 36, 46 · 20, 180, 492, 396 … Σ 1, 8, 88, 1088, 14176, 190208, 2600704, …
  [−1, 0]nonnegative
• A075500 → D+1
  40, 17, 1 · 300, 235, 33, 1 · 2500, 3125, 775, 54, 1 … Σ 58, 569, 6455, 82506, 1166887, …
  (−∞, 0]nonnegative
• A225472 → x ↦ x+1
  1 · 5, 3 · 43, 57, 18 · 557, 1143, 756, 162 … Σ 1, 8, 118, 2618, 77482, 2866418, …
  (−2, −1)nonnegative
• A249253 → (θ+1)²
  1 · 3, 4 · 12, 20 · 60, 112, 9 … Σ 1, 7, 32, 181, 1179, 8761, 73324, …
  (−∞, 0]nonnegative
• A128813 → basis A007318 → x ↦ x/(x+1)
  1 · 2, 3 · 8, 26, 21 · 56, 286, 485, 273 … Σ 1, 5, 55, 1100, 35200, 1654400, …
  [−1, 0]nonnegativerational roots
• A137597 → reverse → x ↦ x/(x+1)
  1 · 1, 3 · 1, 7, 11 · 1, 12, 43, 47 … Σ 1, 4, 19, 103, 622, 4117, 29521, …
  [−1, 0]nonnegative
• A081580 → basis A013611 → reverse
  1 · 4, 2 · 16, 36, 9 · 64, 256, 168, 28 … Σ 1, 6, 61, 516, 4621, 40626, 359281, …
  (−∞, 0]nonnegative
• A008292 → γ (scale 1/4) (shift +1) → D → x ↦ x+1
  2 · 16 · 120, 32 · 960, 544 … Σ 0, 0, 2, 16, 152, 1504, 16608, 201216, …
  (−∞, −1]nonnegative
• A082985 → x ↦ x/(x+1)
  1 · 1, 4 · 1, 7, 11 · 1, 10, 31, 29 … Σ 1, 5, 19, 71, 265, 989, 3691, 13775, …
  [−1, 0]nonnegative
• A099040 → basis A013610 → basis A007318
  1 · 8, 6 · 72, 102, 36 · 640, 1344, 936, 216 … Σ 1, 14, 210, 3136, 46844, 699720, …
  (−∞, −1]nonnegative
• A154986 → θ+1 → x ↦ x+1
  1 · 3, 2 · 12, 14, 3 · 60, 100, 45, 4 … Σ 1, 5, 29, 209, 1785, 17789, 201909, …
  (−∞, −1]nonnegative
• A327997 → x ↦ x/(x+1)
  1 · 3, 4 · 9, 25, 17 · 27, 119, 169, 78 … Σ 1, 7, 51, 393, 3273, 30231, 317547, …
  [−1, 0]nonnegative
• A038291 → basis A013610
  1 · 10, 3 · 100, 60, 9 · 1000, 900, 270, 27 … Σ 1, 13, 169, 2197, 28561, 371293, …
  (−∞, −1]nonnegativerational roots
• A013618 → basis A013610 → x ↦ x/(x+1)
  144, 1080, 2025 · 1728, 19440, 72900, 91125 … Σ 3249, 185193, 10556001, 601692057, …
  [−1, 0]nonnegativerational roots
• A225470 → x ↦ x+1 → x ↦ x+1
  1 · 4, 1 · 28, 11, 1 · 280, 138, 21, 1 … Σ 1, 5, 40, 440, 6160, 104720, 2094400, …
  (−∞, −1]nonnegativerational roots
• A075498 → D
  1 · 9, 2 · 63, 36, 3 · 405, 450, 90, 4 … Σ 0, 1, 11, 102, 949, 9311, 97782, …
  (−∞, 0]nonnegative
• A038271 → basis A013610 → x ↦ x/(x+1)
  1 · 12, 27 · 144, 648, 729 … Σ 1, 39, 1521, 59319, 2313441, 90224199, …
  [−1, 0]nonnegativerational roots
• A225470 → basis A013609 → θ+1
  1 · 3, 4 · 18, 36, 12 · 162, 396, 216, 32 … Σ 1, 7, 66, 806, 12164, 219108, 4591600, …
  (−∞, 0]nonnegative
• A185410 → (θ+1)²
  1 · 1 · 1, 8 · 1, 40, 36 … Σ 1, 1, 9, 77, 813, 10245, 150045, …
  (−∞, 0]nonnegative
• A132166 → x ↦ x+1
  379, 44, 1 · 5713, 1242, 66, 1 … Σ 424, 7022, 110812, 1717748, 26514880, …
  [−37, −1)nonnegative
• A056242 → reverse → (θ+1)²
  1 · 2, 4 · 4, 20, 9 · 8, 64, 81, 16 … Σ 1, 6, 33, 169, 810, 3690, 16184, 68952, …
  (−∞, 0]nonnegative
• A274496 → basis A013611 → θ+1
  1 · 2 · 4, 16 · 8, 32 … Σ 1, 2, 20, 40, 336, 672, 5184, 10368, …
  (−∞, 0]nonnegativerational roots
• A099040 → x ↦ x−12
  1 · -24, 2 · 552, -94, 4 · -12672, 3264, -280, 8 … Σ 1, -22, 462, -9680, 202796, -4248552, …
  (10, 12]
• A038303 → basis A013610 → basis A013610
  1 · 14, 9 · 196, 252, 81 · 2744, 5292, 3402, 729 … Σ 1, 23, 529, 12167, 279841, 6436343, …
  (−∞, −1]nonnegativerational roots
• A048993 → θ+1
  1 · 0, 2 · 0, 2, 3 · 0, 2, 9, 4 … Σ 1, 2, 5, 15, 52, 203, 877, 4140, …
  (−∞, 0]nonnegative
• A126216 → basis A007318 → x ↦ x/(x+1)
  1 · 3, 4 · 11, 29, 19 · 45, 177, 231, 100 … Σ 1, 7, 59, 553, 5541, 58107, 629799, …
  [−1, 0]nonnegative
• A132393 → Veronese 2 (j=1) → (θ+1)²
  1 · 1 · 2, 4 · 6, 24 … Σ 0, 1, 1, 6, 30, 173, 1155, 8807, …
  (−∞, 0]nonnegative
• A204420 → basis A013610 → D
  3 · 36, 54 · 1035, 2430, 1215 … Σ 0, 3, 90, 4680, 388080, 47355840, …
  (−∞, 0]nonnegative
• A008288 → (θ+1)²
  1 · 1, 4 · 1, 12, 9 · 1, 20, 45, 16 … Σ 1, 5, 22, 82, 283, 923, 2892, 8788, …
  (−∞, 0]nonnegative
• A131431 → x ↦ x+1 → θ+1
  1 · 4, 8 · 7, 28, 21 · 10, 60, 90, 40 … Σ 1, 12, 56, 200, 624, 1792, 4864, 12672, …
  (−∞, 0]nonnegativerational roots
• A038303 → basis A013609 → D
  2 · 44, 8 · 726, 264, 24 · 10648, 5808, 1056, 64 … Σ 0, 2, 52, 1014, 17576, 285610, 4455516, …
  (−∞, 0]nonnegativerational roots
• A075497 → x ↦ x+1 → D+1
  1 · 4, 1 · 19, 10, 1 · 104, 85, 18, 1 … Σ 1, 5, 30, 208, 1624, 14032, 132480, …
  (−∞, −1]nonnegative
• A225466 → reverse
  1 · 3, 2 · 9, 21, 4 · 27, 135, 117, 8 … Σ 1, 5, 34, 287, 2839, 31898, 399079, …
  (−∞, 0]nonnegative