Proof methods / preserver_image

Image under a real-rootedness preserver

8,704 sequences

• A091042 → basis A013609 → basis A007318
  1 · 10, 6 · 76, 80, 20 · 568, 840, 392, 56 … Σ 1, 16, 176, 1856, 19456, 203776, …
  (−∞, −1]nonnegative
• A114656 → basis A007318 → x ↦ x/(x+1)
  1 · 3, 4 · 11, 30, 20 · 45, 186, 252, 112 … Σ 1, 7, 61, 595, 6217, 68047, 770149, …
  [−1, 0]nonnegative
• A085841 → θ+1
  1 · 3, 8 · 5, 80, 48 · 7, 280, 1008, 256 … Σ 1, 11, 133, 1551, 17225, 184531, …
  (−∞, 0]nonnegative
• type_b_eulerian → x ↦ x/(x+1)
  1 · 1, 2 · 1, 8, 8 · 1, 26, 72, 48 … Σ 1, 3, 17, 147, 1697, 24483, 423857, …
  [−1, 0]nonnegative
• A033282 → basis A013610 → reverse
  1 · 6, 3 · 45, 45, 11 · 378, 567, 279, 45 … Σ 1, 9, 101, 1269, 17081, 240849, …
  (−∞, 0]nonnegative
• A060187 → γ → (θ+1)²
  1 · 1 · 1, 16 · 1, 80 … Σ 1, 1, 17, 81, 1009, 9713, 134305, …
  (−∞, 0]nonnegative
• A038314 → x ↦ x/(x+1)
  100, 440, 484 · 1000, 6600, 14520, 10648 … Σ 1024, 32768, 1048576, 33554432, …
  [−1, 0]nonnegativerational roots
• A038279 → basis A013610 → D+1
  1 · 12, 3 · 135, 72, 9 · 1458, 1215, 324, 27 … Σ 1, 15, 216, 3024, 41472, 559872, …
  (−∞, 0]nonnegativerational roots
• A099093 → x ↦ x+1 → θ+1
  1 · 3, 6 · 12, 42, 27 · 45, 234, 297, 108 … Σ 1, 9, 81, 684, 5580, 44388, 346572, …
  (−∞, 0]nonnegative
• A120910 → basis A007318 → basis A007318
  3 · 12, 3 · 48, 24, 3 · 192, 144, 36, 3 … Σ 3, 15, 75, 375, 1875, 9375, 46875, …
  (−∞, −1]nonnegativerational roots
• A063007 → x ↦ x+1 → reverse
  1 · 2, 3 · 6, 18, 13 · 20, 90, 132, 63 … Σ 1, 5, 37, 305, 2641, 23525, 213445, …
  (−1, 0]nonnegative
• A132393 → basis A013609 → D
  2 · 6, 8 · 22, 48, 24 · 100, 280, 240, 64 … Σ 0, 2, 14, 94, 684, 5508, 49104, 482256, …
  (−∞, 0]nonnegative
• A001263 → D
  1 · 3, 2 · 6, 12, 3 · 10, 40, 30, 4 … Σ 0, 1, 5, 21, 84, 330, 1287, 5005, …
  (−∞, 0]nonnegative
• A038335 → reverse
  1 · 9, 12 · 81, 216, 144 · 729, 2916, 3888, 1728 … Σ 1, 21, 441, 9261, 194481, 4084101, …
  (−∞, 0]nonnegativerational roots
• A062264 → x ↦ x+1
  1 · 6, 5 · 28, 42, 15 · 120, 252, 168, 35 … Σ 1, 11, 85, 575, 3649, 22363, 134245, …
  (−∞, −1]nonnegative
• A136124 → basis A008277 → x ↦ x/(x+1)
  1 · 3, 4 · 12, 32, 21 · 60, 240, 315, 136 … Σ 1, 7, 65, 751, 10369, 166391, 3040897, …
  [−1, 0]nonnegative
• A131431 → (θ+1)² → x ↦ x+1
  1 · 16, 16 · 63, 126, 63 · 160, 480, 480, 160 … Σ 1, 32, 252, 1280, 5200, 18432, 59584, …
  (−∞, −1]nonnegativerational roots
• A038320 → basis A013610 → x ↦ x/(x+1)
  289, 1190, 1225 · 4913, 30345, 62475, 42875 … Σ 2704, 140608, 7311616, 380204032, …
  [−1, 0]nonnegativerational roots
• A062264 → x ↦ x+1 → x ↦ x+1
  1 · 11, 5 · 85, 72, 15 · 575, 693, 273, 35 … Σ 1, 16, 172, 1576, 13327, 107704, …
  (−∞, −1]nonnegative
• A038305 → x ↦ x+1 → reverse
  9, 78, 169 · 27, 351, 1521, 2197 … Σ 256, 4096, 65536, 1048576, 16777216, …
  (−∞, 0]nonnegativerational roots
• A001263 → D → D+1
  1 · 5, 2 · 18, 18, 3 · 50, 100, 42, 4 … Σ 0, 1, 7, 39, 196, 930, 4257, 19019, …
  (−∞, 0]nonnegative
• A038337 → basis A007318 → D
  506, 242 · 17457, 16698, 3993 … Σ 748, 38148, 1729376, 73498480, …
  (−∞, 0]nonnegativerational roots
• A071951 → D
  1 · 8, 2 · 52, 40, 3 · 320, 584, 120, 4 … Σ 0, 1, 10, 95, 1028, 13145, 197622, …
  (−∞, 0]nonnegative
• A038319 → basis A013610 → reverse
  225, 480, 256 · 3375, 10800, 11520, 4096 … Σ 961, 29791, 923521, 28629151, …
  (−∞, 0]nonnegativerational roots
• A034870 → Veronese 2
  1 · 1, 1 · 1, 6, 1 · 1, 15, 15, 1 … Σ 1, 2, 8, 32, 128, 512, 2048, 8192, …
  (−∞, 0]nonnegative
• A082985 → D+1
  1 · 4, 3 · 6, 15, 5 · 8, 35, 35, 7 … Σ 1, 7, 26, 85, 265, 804, 2393, 7019, …
  (−∞, 0]nonnegative
• A113953 → x ↦ x−9
  1 · -9, 1 · 63, -16, 1 · -405, 171, -23, 1 … Σ 1, -8, 48, -256, 1280, -6144, 28672, …
  (1, 9]
• A272866 → basis A013610 → D
  15, 18 · 150, 630, 810, 324 … Σ 0, 33, 1914, 83259, 3219348, 116701365, …
  (−∞, 0]nonnegative
• A131689 → x ↦ x+1 → x ↦ x/(x+1)
  1 · 1, 2 · 3, 11, 10 · 13, 70, 125, 74 … Σ 1, 3, 24, 282, 4416, 86448, 2030784, …
  [−1, −1/2]nonnegative
• Veronese parent of A098172 → x ↦ x+1
  1, 1 · 2, 7, 9, 5, 1 · 4, 24, 61, 85, 70, 34, 9, 1 … Σ 2, 24, 288, 3456, 41472, 497664, …
  (−∞, −1]nonnegativerational roots
• A038323 → x ↦ x+1 → θ+1
  1 · 20, 18 · 400, 720, 243 · 8000, 21600, 14580, 2916 … Σ 1, 38, 1363, 47096, 1585285, 52338794, …
  (−∞, 0]nonnegativerational roots
• A049020 → reverse → D+1
  1 · 2, 1 · 4, 7, 2 · 7, 26, 25, 5 … Σ 1, 3, 13, 63, 337, 1963, 12333, 82967, …
  (−∞, 0]nonnegative
• A119808 → D
  1 · 5 · 17, 4 · 49, 32 … Σ 0, 1, 5, 21, 81, 297, 1053, 3645, …
  (−∞, 0]nonnegative
• A159854 → x ↦ x+1 → reverse
  1, 2, 1 · 1, 4, 5, 2 · 1, 6, 13, 12, 4 … Σ 4, 12, 36, 108, 324, 972, 2916, 8748, …
  (−∞, 0]nonnegativerational roots
• A390433 → x ↦ x+1
  1 · 1, 1 · 5, 6, 1 · 57, 79, 23, 1 … Σ 1, 2, 12, 160, 3760, 136480, 7042752, …
  (−∞, −1]nonnegative
• A391045 → reverse → x ↦ x/(x+1)
  1 · 1, 2 · 1, 6, 6 · 1, 13, 32, 21 … Σ 1, 3, 13, 67, 377, 2243, 13877, 88371, …
  [−1, 0]nonnegative
• A038303: Triangle whose (i,j)-th entry is binomial(i,j)*10^(i-j)*1^j.
  1 · 10, 1 · 100, 20, 1 · 1000, 300, 30, 1 … Σ 1, 11, 121, 1331, 14641, 161051, …
  (−∞, −1]nonnegativerational roots
• A290319 → reverse
  1 · 1, 1 · 1, 6, 5 · 1, 15, 59, 45 … Σ 1, 2, 12, 120, 1680, 30240, 665280, …
  (−∞, 0]nonnegativerational roots
• A038328 → D
  48, 8 · 864, 288, 24 · 13824, 6912, 1152, 64 … Σ 56, 1176, 21952, 384160, 6453888, …
  (−∞, 0]nonnegativerational roots
• A099097 → basis A007318
  1 · 3, 3 · 10, 19, 9 · 33, 93, 87, 27 … Σ 1, 6, 38, 240, 1516, 9576, 60488, …
  (−∞, −1]nonnegative
• A134991 → x ↦ x/(x+1)
  1 · 1, 4 · 1, 12, 26 · 1, 28, 158, 236 … Σ 1, 5, 39, 423, 5889, 100125, 2010951, …
  [−1, 0)nonnegative
• A179900 → x ↦ x+1
  1 · 4, -1 · 15, -8, 1 · 56, -46, 12, -1 … Σ 1, 3, 8, 21, 55, 144, 377, 987, …
  (2, 6)
• A008277 → θ+2 (shift +1) → reverse
  2 · 3, 2 · 4, 9, 2 · 5, 24, 21, 2 … Σ 2, 5, 15, 52, 203, 877, 4140, 21147, …
  (−∞, 0]nonnegative
• A038277 → x ↦ x/(x+1) → D
  18 · 252, 648 · 2646, 13608, 17496 … Σ 0, 18, 900, 33750, 1125000, 35156250, …
  (−∞, 0]nonnegativerational roots
• A123519 → basis A013610 → reverse
  36, 42, 11 · 216, 396, 228, 41 … Σ 89, 881, 8721, 86329, 854569, 8459361, …
  (−∞, 0]nonnegative
• A113953 → basis A013609 → x ↦ x+1
  1 · 3, 2 · 15, 16, 4 · 63, 102, 52, 8 … Σ 1, 5, 35, 225, 1475, 9625, 62875, …
  (−∞, −1]nonnegative
• A274496 → Veronese 2 → x ↦ x+1
  1 · 2 · 2 · 4 … Σ 1, 2, 2, 4, 12, 24, 56, 112, …
  (−∞, −1]nonnegative
• A114656 → basis A013609 → reverse
  1 · 2, 3 · 4, 16, 11 · 8, 60, 102, 45 … Σ 1, 5, 31, 215, 1597, 12425, 99955, …
  (−∞, 0]nonnegative
• A207606 → x ↦ x/(x+1)
  4, 15, 13 · 5, 31, 58, 34 · 6, 54, 162, 201, 89 … Σ 32, 128, 512, 2048, 8192, 32768, …
  [−1, 0)nonnegative
• A134991 → D
  3 · 10, 30 · 25, 210, 315 · 56, 980, 3780, 3780 … Σ 0, 3, 40, 550, 8596, 153580, 3109296, …
  (−∞, 0]nonnegative