Proof methods / preserver_image

Image under a real-rootedness preserver

8,704 sequences

• A034839 → D
  1 · 3 · 6, 2 · 10, 10 … Σ 0, 0, 1, 3, 8, 20, 48, 112, …
  (−∞, 0]nonnegative
• A013622 → basis A007318 → basis A007318
  1 · 13, 5 · 169, 130, 25 · 2197, 2535, 975, 125 … Σ 1, 18, 324, 5832, 104976, 1889568, …
  (−∞, −1]nonnegativerational roots
• A008955 → basis A007318 → D+1
  1 · 3, 1 · 23, 21, 4 · 320, 534, 265, 36 … Σ 1, 4, 48, 1155, 46323, 2785698, …
  (−∞, 0]nonnegative
• A126351 → reverse → θ+1
  1 · 2, 2 · 4, 10, 3 · 8, 38, 27, 4 … Σ 1, 4, 17, 77, 372, 1915, 10481, 60814, …
  (−∞, 0]nonnegative
• A172431 → basis A007318 → θ+1
  1 · 3, 4 · 8, 20, 9 · 21, 76, 66, 16 … Σ 1, 7, 37, 179, 833, 3791, 16989, 75243, …
  (−∞, 0]nonnegative
• A228955 → basis A007318
  1 · 2, 1 · 8, 6 · 48, 48, 6 … Σ 1, 3, 14, 102, 984, 11880, 172080, …
  (−∞, −1]nonnegative
• A081580 → basis A007318 → (θ+1)²
  1 · 2, 4 · 9, 36, 9 · 28, 168, 144, 16 … Σ 1, 6, 54, 356, 2418, 15288, 95158, …
  (−∞, 0]nonnegative
• A085881 → basis A013611 → (θ+1)²
  1 · 2, 16 · 12, 192, 432 · 120, 2880, 12960, 15360 … Σ 1, 18, 636, 31320, 1950480, 146149920, …
  (−∞, 0]nonnegative
• A038327 → basis A013610 → D+1
  1 · 16, 3 · 247, 96, 9 · 3718, 2223, 432, 27 … Σ 1, 19, 352, 6400, 114688, 2031616, …
  (−∞, 0]nonnegativerational roots
• A075503 → D+1
  88, 26, 1 · 960, 544, 51, 1 … Σ 115, 1556, 24581, 442206, 8852215, …
  (−∞, 0]nonnegative
• A178820 → Veronese 2 → (θ+1)²
  1 · 4 · 10, 40 · 20, 240 … Σ 1, 4, 50, 260, 1190, 4816, 17808, …
  (−∞, 0]nonnegative
• A038319 → D+1
  231, 160, 25 · 3146, 3465, 1200, 125 … Σ 416, 7936, 147456, 2686976, 48234496, …
  (−∞, 0]nonnegativerational roots
• A133087: A133080 * A007318.
  1 · 2, 1 · 1, 2, 1 · 2, 5, 4, 1 … Σ 1, 3, 4, 12, 16, 48, 64, 192, …
  (−∞, −1]nonnegativerational roots
• A204420 → basis A007318 → x ↦ x/(x+1)
  1 · 1, 2 · 9, 30, 24 · 225, 1020, 1500, 720 … Σ 1, 3, 63, 3465, 363825, 62214075, …
  [−1, 0]nonnegativerational roots
• A038255 → basis A013611 → D
  4 · 56, 32 · 588, 672, 192 · 5488, 9408, 5376, 1024 … Σ 0, 4, 88, 1452, 21296, 292820, 3865224, …
  (−∞, 0]nonnegativerational roots
• A390433 → reverse
  1 · 1 · 1, 4 · 1, 20, 36 … Σ 1, 1, 5, 57, 1169, 37673, 1749541, …
  (−∞, 0]nonnegative
• A038226 → basis A013610 → reverse
  576, 528, 121 · 13824, 19008, 8712, 1331 … Σ 1225, 42875, 1500625, 52521875, …
  (−∞, 0]nonnegativerational roots
• A038259 → basis A013611 → reverse
  1 · 20, 11 · 400, 440, 121 · 8000, 13200, 7260, 1331 … Σ 1, 31, 961, 29791, 923521, 28629151, …
  (−∞, 0]nonnegativerational roots
• A137320 → basis A013610 → (θ+1)²
  1 · 2, 24 · 6, 120, 324 · 24, 624, 2916, 3456 … Σ 1, 26, 450, 7020, 107604, 1677312, …
  (−∞, 0]nonnegative
• A038326 → D
  12 · 264, 288 · 4356, 9504, 5184 … Σ 0, 12, 552, 19044, 584016, 16790460, …
  (−∞, 0]nonnegativerational roots
• A094638 → D+1 → x ↦ x/(x+1)
  1 · 2, 3 · 4, 15, 13 · 7, 49, 106, 70 … Σ 1, 5, 32, 232, 1872, 16704, 163872, …
  [−1, 0]nonnegative
• A274496 → basis A013610 → x ↦ x+1
  1 · 2 · 10, 6 · 20, 12 … Σ 1, 2, 16, 32, 256, 512, 4096, 8192, …
  (−∞, −1]nonnegativerational roots
• narayana → basis A013609 → basis A007318
  1 · 4, 2 · 19, 18, 4 · 100, 138, 60, 8 … Σ 1, 6, 41, 306, 2426, 20076, 171481, …
  (−∞, −1]nonnegative
• A134346 → (θ+1)²
  1 · 3, 12 · 7, 56, 63 · 15, 180, 405, 240 … Σ 1, 15, 126, 840, 4960, 27216, 142240, …
  (−∞, 0]nonnegative
• A145324 → basis A013609 → D+1
  1 · 7, 4 · 46, 82, 24 · 326, 1050, 968, 192 … Σ 1, 11, 152, 2536, 49676, 1118564, …
  (−∞, 0]nonnegative
• A144440 → x ↦ x+1
  1 · 2, 1 · 13, 13, 1 · 110, 165, 57, 1 … Σ 1, 3, 27, 333, 5463, 112509, 2794959, …
  (−∞, −1]nonnegative
• A108838 → reverse → x ↦ x/(x+1)
  2 · 2, 5 · 2, 12, 14 · 2, 21, 56, 42 … Σ 2, 7, 28, 121, 550, 2591, 12536, 61921, …
  [−1, 0]nonnegative
• A390433 → (θ+1)²
  1 · 0, 4 · 0, 16, 9 · 0, 144, 180, 16 … Σ 1, 4, 25, 340, 8049, 291964, 14976393, …
  (−∞, 0]nonnegative
• A008957 → x ↦ x+1
  1 · 2, 1 · 7, 7, 1 · 37, 59, 24, 1 … Σ 1, 3, 15, 121, 1345, 19371, 351663, …
  (−∞, −1]nonnegative
• A055151 → D
  1 · 3 · 6, 4 · 10, 20 … Σ 0, 0, 1, 3, 10, 30, 90, 266, …
  (−∞, 0]nonnegative
• A085478 → basis A013609 → θ+1
  1 · 1 · 2, 4 · 5, 20, 12 … Σ 1, 1, 6, 37, 217, 1230, 6805, 36973, …
  (−∞, 0]nonnegative
• A046716 → x ↦ x+1 → θ+1
  1 · 2, 2 · 5, 10, 3 · 16, 50, 33, 4 … Σ 1, 4, 18, 103, 791, 7930, 98052, …
  (−∞, 0]nonnegative
• A130123 → (θ+1)² → D+1
  1 · 8, 8 · 0, 72, 36 · 0, 0, 384, 128 … Σ 1, 16, 108, 512, 2000, 6912, 21952, …
  (−∞, 0]nonnegativerational roots
• A081577 → basis A013611 → reverse
  1 · 4, 2 · 16, 24, 6 · 64, 160, 96, 16 … Σ 1, 6, 46, 336, 2476, 18216, 134056, …
  (−∞, 0]nonnegative
• A269944 → x ↦ x+1 → (θ+1)²
  1 · 1, 4 · 2, 12, 9 · 10, 68, 72, 16 … Σ 1, 5, 23, 166, 2006, 38160, 1068048, …
  (−∞, 0]nonnegative
• A114687 → basis A013611 → basis A007318
  1 · 11, 8 · 131, 184, 64 · 1661, 3408, 2304, 512 … Σ 1, 19, 379, 7885, 169957, 3772279, …
  (−∞, −1]nonnegative
• A257618 → D
  2 · 40, 8 · 472, 944, 24 · 4928, 33984, 14784, 64 … Σ 0, 2, 48, 1440, 53760, 2419200, …
  (−∞, 0]nonnegative
• A160562 → reverse
  1 · 1, 1 · 1, 10, 1 · 1, 35, 91, 1 … Σ 1, 2, 12, 128, 1872, 37600, 990784, …
  (−∞, 0]nonnegative
• delannoy → basis A013611 → reverse
  1 · 4, 2 · 16, 20, 5 · 64, 128, 72, 12 … Σ 1, 6, 41, 276, 1861, 12546, 84581, …
  (−∞, 0]nonnegative
• type_b_eulerian
  1 · 1, 1 · 1, 6, 1 · 1, 23, 23, 1 … Σ 1, 2, 8, 48, 384, 3840, 46080, 645120, …
  (−∞, 0)nonnegative
• A038334 → basis A013609 → (θ+1)²
  400, 2560, 2304 · 8000, 76800, 138240, 65536 … Σ 5264, 288576, 14618880, 702452736, …
  (−∞, 0]nonnegative
• A122848 → basis A013609 → D
  2 · 6, 8 · 18, 48, 24 · 56, 216, 240, 64 … Σ 0, 2, 14, 90, 576, 3780, 25596, 179172, …
  (−∞, 0]nonnegative
• A112493 → θ+1
  1 · 1, 2 · 1, 8, 9 · 1, 22, 75, 60 … Σ 1, 3, 18, 158, 1808, 25448, 424784, …
  (−∞, 0]nonnegative
• A038231 → (θ+1)²
  1 · 4, 4 · 16, 32, 9 · 64, 192, 108, 16 … Σ 1, 8, 57, 380, 2425, 15000, 90625, …
  (−∞, 0]nonnegative
• basis-map coefficients of A113214, shifted → (θ+1)²
  1 · -1, -4 · 1, 8, 9 · -1, -12, -27, -16 … Σ 1, -5, 18, -56, 160, -432, 1120, -2816, …
  (−∞, 0]
• A216973 → θ+1
  1 · 2, 4 · 3, 12, 9 · 4, 24, 36, 16 … Σ 0, 1, 6, 24, 80, 240, 672, 1792, …
  (−∞, 0]nonnegativerational roots
• A035607 → basis A007318 → x ↦ x+1
  1 · 1 · 5, 2 · 17, 12, 2 … Σ 1, 1, 7, 31, 145, 673, 3127, 14527, …
  (−∞, −1]nonnegative
• A008278 → x ↦ x+1 (shift +1) → x ↦ x/(x+1)
  1 · 2, 3 · 5, 15, 11 · 15, 68, 101, 49 … Σ 1, 5, 31, 233, 2047, 20417, 226711, …
  [−1, 0]nonnegative
• A102662 → reverse → D+1
  1 · 4, 1 · 8, 7, 1 · 14, 25, 10, 1 … Σ 1, 5, 16, 50, 147, 419, 1166, 3188, …
  (−∞, 0]nonnegative
• A056242 → reverse → D+1
  1 · 3, 1 · 9, 7, 1 · 24, 34, 12, 1 … Σ 1, 4, 17, 71, 288, 1140, 4428, 16948, …
  (−∞, 0]nonnegative