Proof methods / preserver_image

Image under a real-rootedness preserver

8,704 sequences

• A075502 → θ+1
  49, 42, 3 · 343, 686, 126, 4 … Σ 94, 1159, 16651, 271550, 4918823, …
  (−∞, 0]nonnegative
• A028246 → x ↦ x+1
  1 · 2, 1 · 6, 7, 2 · 26, 49, 30, 6 … Σ 1, 3, 15, 111, 1095, 13503, 199815, …
  [−2, −1)nonnegative
• A225470 → x ↦ x+1 → D+1
  1 · 4, 1 · 27, 11, 1 · 261, 135, 21, 1 … Σ 1, 5, 39, 418, 5714, 95064, 1864456, …
  (−∞, 0]nonnegative
• A178820 → basis A007318
  1 · 8, 4 · 40, 40, 10 · 160, 240, 120, 20 … Σ 1, 12, 90, 540, 2835, 13608, 61236, …
  (−∞, −1]nonnegativerational roots
• A145596 → D+1
  1 · 4, 2 · 11, 14, 3 · 24, 60, 32, 4 … Σ 1, 6, 28, 120, 495, 2002, 8008, 31824, …
  (−∞, 0]nonnegative
• A225471 → basis A008277 → x ↦ x/(x+1)
  1 · 4, 5 · 32, 77, 46 · 384, 1353, 1581, 613 … Σ 1, 9, 155, 3931, 131553, 5466041, …
  [−1, 0]nonnegative
• A060187 → γ → D+1
  1 · 1 · 5, 4 · 21, 20 … Σ 1, 1, 9, 41, 385, 3393, 40041, 508233, …
  (−∞, 0]nonnegative
• A269944 → basis A013609 → x ↦ x/(x+1)
  1 · 1, 3 · 2, 10, 12 · 10, 64, 130, 84 … Σ 1, 4, 24, 288, 6336, 228096, 12317184, …
  [−1, 0]nonnegativerational roots
• A099040 → basis A013609 → reverse
  1 · 4, 2 · 16, 20, 6 · 64, 128, 80, 16 … Σ 1, 6, 42, 288, 1980, 13608, 93528, …
  (−∞, 0]nonnegative
• A130123 → Veronese 2 → θ+1
  1 · 0, 8 · 0, 0, 48 · 0, 0, 0, 256 … Σ 1, 0, 8, 0, 48, 0, 256, 0, …
  (−∞, 0]nonnegativerational roots
• A133081 → reverse (shift +1) → θ+1
  1 · 0, 2, 3 · 0, 0, 0, 0, 5 · 0, 0, 0, 0, 0, 6, 7 … Σ 1, 5, 5, 13, 9, 21, 13, 29, …
  (−∞, 0]nonnegativerational roots
• A038320 → basis A013611 → x ↦ x/(x+1)
  289, 1394, 1681 · 4913, 35547, 85731, 68921 … Σ 3364, 195112, 11316496, 656356768, …
  [−1, 0]nonnegativerational roots
• A090582 → (θ+1)²
  1 · 2, 4 · 6, 24, 9 · 24, 144, 126, 16 … Σ 1, 6, 39, 310, 2935, 32186, 400855, …
  (−∞, 0]nonnegative
• A038281 → x ↦ x+1 → D+1
  187, 84, 9 · 2420, 1683, 378, 27 … Σ 280, 4508, 71344, 1114064, 17210368, …
  (−∞, 0]nonnegativerational roots
• A166343 → x ↦ x+1
  14, 14, 1 · 56, 84, 30, 1 · 280, 560, 342, 62, 1 … Σ 29, 171, 1245, 10827, 109629, 1267371, …
  (−∞, −1]nonnegative
• A249139 → D
  1 · 2 · 7, 2 · 16, 6 … Σ 0, 1, 2, 9, 22, 68, 174, 475, …
  (−∞, 0]nonnegative
• A249248 → θ+1
  1 · 1, 6 · 1, 14, 9 · 1, 24, 66, 12 … Σ 1, 7, 24, 103, 419, 1815, 7970, 36277, …
  (−∞, 0]nonnegative
• A110441 → basis A013610 → D+1
  1 · 7, 3 · 38, 42, 9 · 180, 348, 189, 27 … Σ 1, 10, 89, 744, 5975, 46670, 357181, …
  (−∞, 0]nonnegative
• A249251 → basis A007318 → reverse
  1 · 3, 4 · 6, 18, 13 · 12, 57, 87, 43 … Σ 1, 7, 37, 199, 1069, 5743, 30853, …
  (−∞, 0]nonnegative
• A064861 → x ↦ x+1 → basis A007318
  15, 11, 2 · 75, 85, 32, 4 · 225, 330, 181, 44, 4 … Σ 28, 196, 784, 5488, 21952, 153664, …
  (−∞, −1]nonnegativerational roots
• A132440 → θ+1 → D
  4 · 0, 18 · 0, 0, 48 · 0, 0, 0, 100 … Σ 0, 0, 4, 18, 48, 100, 180, 294, …
  (−∞, 0]nonnegativerational roots
• A038208 → basis A013610 → θ+1
  1 · 4, 12 · 16, 96, 108 · 64, 576, 1296, 864 … Σ 1, 16, 220, 2800, 34000, 400000, …
  (−∞, 0]nonnegativerational roots
• A028338 → basis A013609 → x ↦ x+1
  1 · 4, 2 · 24, 20, 4 · 192, 208, 72, 8 … Σ 1, 6, 48, 480, 5760, 80640, 1290240, …
  (−∞, −1]nonnegativerational roots
• A110441 → reverse → x ↦ x/(x+1)
  1 · 1, 4 · 1, 8, 14 · 1, 12, 44, 48 … Σ 1, 5, 23, 105, 479, 2185, 9967, 45465, …
  [−1, 0]nonnegative
• A038320 → basis A013609 → D
  408, 288 · 10404, 14688, 5184 … Σ 696, 30276, 1170672, 42436860, …
  (−∞, 0]nonnegativerational roots
• A038333 → θ+1
  144, 336, 147 · 1728, 6048, 5292, 1372 … Σ 627, 14440, 322373, 7037334, 151042039, …
  (−∞, 0]nonnegativerational roots
• basis-map coefficients of A297191, shifted → D+1
  1 · 0, 2, 1 · 0, 0, 0, 4, 1 · 0, 0, 0, 0, 0, 6, 1 … Σ 1, 3, 5, 7, 9, 11, 13, 15, …
  (−∞, 0]nonnegativerational roots
• A166343 → x ↦ x/(x+1)
  1, 14, 14 · 1, 30, 84, 56 · 1, 62, 342, 560, 280 … Σ 29, 171, 1245, 10827, 109629, 1267371, …
  [−1, 0]nonnegative
• A367270 → basis A013610 → D+1
  1 · 1 · 9, 6 · 46, 90, 27 … Σ 1, 1, 15, 163, 1637, 15981, 153795, …
  (−∞, 0]nonnegative
• A038334 → basis A013610 → D
  960, 1152 · 28800, 69120, 41472 … Σ 2112, 139392, 8177664, 449771520, …
  (−∞, 0]nonnegativerational roots
• basis-map coefficients of A112227 → θ+1 → D+1
  0, 6, 3 · 0, 0, 12, 4 · 0, 0, 0, 20, 5 … Σ 9, 16, 25, 36, 49, 64, 81, 100, …
  (−∞, 0]nonnegativerational roots
• A035469 → x ↦ x+1
  1 · 5, 1 · 41, 14, 1 · 465, 211, 27, 1 … Σ 1, 6, 56, 704, 11096, 209952, 4631712, …
  (−∞, −1]nonnegative
• A081579 → basis A013609 → D+1
  1 · 4, 2 · 24, 24, 4 · 96, 184, 80, 8 … Σ 1, 6, 52, 368, 2640, 18208, 123968, …
  (−∞, 0]nonnegative
• A038329 → basis A013611 → reverse
  144, 360, 225 · 1728, 6480, 8100, 3375 … Σ 729, 19683, 531441, 14348907, …
  (−∞, 0]nonnegativerational roots
• A207607 → reverse → x ↦ x/(x+1)
  1 · 2, 3 · 2, 9, 8 · 2, 15, 33, 21 … Σ 1, 5, 19, 71, 265, 989, 3691, 13775, …
  [−1, 0]nonnegative
• A178820 → basis A013609 → (θ+1)²
  1 · 8, 32 · 40, 320, 360 · 160, 1920, 4320, 2560 … Σ 1, 40, 720, 8960, 89600, 774144, …
  (−∞, 0]nonnegative
• A225470 → basis A008277 → θ+1
  1 · 3, 2 · 18, 20, 3 · 162, 236, 63, 4 … Σ 1, 5, 41, 465, 6721, 117941, 2433145, …
  (−∞, 0]nonnegative
• A099040 → D
  2 · 2, 8 · 0, 16, 24 · 0, 8, 72, 64 … Σ 0, 2, 10, 40, 144, 488, 1592, 5056, …
  (−∞, 0]nonnegative
• A034870 → Veronese 2 (j=1) → x ↦ x+1
  2 · 8, 4 · 32, 32, 6 · 128, 192, 80, 8 … Σ 0, 2, 12, 70, 408, 2378, 13860, 80782, …
  (−∞, −1]nonnegative
• A142462 → (θ+1)²
  1 · 1, 4 · 1, 64, 9 · 1, 572, 1287, 16 … Σ 1, 5, 74, 1876, 61956, 2521440, …
  (−∞, 0]nonnegative
• A257626 → θ+1
  1 · 6, 12 · 36, 216, 108 · 216, 2808, 4212, 864 … Σ 1, 18, 360, 8100, 204120, 5715360, …
  (−∞, 0]nonnegative
• A003506 → D → (θ+1)²
  2 · 6, 24 · 12, 96, 108 · 20, 240, 540, 320 … Σ 0, 0, 2, 30, 216, 1120, 4800, 18144, …
  (−∞, 0]nonnegative
• A026374 → θ+1 → D+1
  1 · 3, 2 · 7, 12, 3 · 9, 32, 24, 4 … Σ 1, 5, 22, 69, 245, 665, 2150, 5425, …
  (−∞, 0]nonnegative
• A204420 → basis A007318 → D
  1 · 12, 6 · 345, 270, 45 · 18480, 18060, 5040, 420 … Σ 0, 1, 18, 660, 42000, 4142880, …
  (−∞, 0]nonnegative
• A033282 → θ+1 → D+1
  1 · 5, 4 · 11, 40, 15 · 19, 144, 231, 56 … Σ 1, 9, 66, 450, 2955, 18963, 119812, …
  (−∞, 0]nonnegative
• A137320 → basis A013609 → reverse
  1 · 4, 2 · 16, 20, 6 · 64, 144, 104, 24 … Σ 1, 6, 42, 336, 3024, 30240, 332640, …
  (−∞, 0]nonnegativerational roots
• A257180 → D+1
  33, 42, 9 · 168, 423, 222, 27 … Σ 84, 840, 9072, 105840, 1330560, …
  (−∞, 0]nonnegative
• A290315 → D+1
  1 · 3, 2 · 17, 40, 12 · 67, 634, 644, 120 … Σ 1, 5, 69, 1465, 41273, 1441757, …
  (−∞, 0]nonnegative
• A257626 → D
  6 · 108, 72 · 1404, 2808, 648 … Σ 0, 6, 180, 4860, 136080, 4082400, …
  (−∞, 0]nonnegative
• A013613 → basis A013611 → reverse
  1 · 24, 7 · 576, 336, 49 · 13824, 12096, 3528, 343 … Σ 1, 31, 961, 29791, 923521, 28629151, …
  (−∞, 0]nonnegativerational roots