Proof methods / preserver_image

Image under a real-rootedness preserver

8,704 sequences

• A038284 → D
  96, 72 · 1152, 1728, 648 · 12288, 27648, 20736, 5184 … Σ 168, 3528, 65856, 1152480, 19361664, …
  (−∞, 0]nonnegativerational roots
• A135838 → D
  2 · 4, 4 · 12, 24, 12 · 16, 48, 48, 16 … Σ 0, 2, 8, 48, 128, 640, 1536, 7168, …
  (−∞, 0]nonnegativerational roots
• A257619 → x ↦ x/(x+1)
  1 · 2, 4 · 4, 52, 52 · 8, 588, 1716, 1144 … Σ 1, 6, 108, 3456, 154872, 8940456, …
  [−1, 0]nonnegative
• A173018 → x ↦ x+1 → θ+1
  1 · 1 · 2, 2 · 6, 12, 3 … Σ 1, 1, 4, 21, 142, 1175, 11476, 129073, …
  (−∞, 0]nonnegative
• A178820 → Veronese 2 (j=1) → θ+1
  4 · 20 · 60, 40 · 140, 280 … Σ 0, 4, 20, 100, 420, 1568, 5376, 17280, …
  (−∞, 0]nonnegative
• A028338 → basis A008277 → reverse
  1 · 1, 2 · 1, 7, 8 · 1, 15, 57, 48 … Σ 1, 3, 16, 121, 1179, 14026, 196783, …
  (−∞, 0]nonnegative
• A075501 → (θ+1)²
  36, 72, 9 · 216, 1008, 324, 16 … Σ 117, 1564, 23341, 383166, 6857257, …
  (−∞, 0]nonnegative
• A099097 → reverse → θ+1
  1 · 3 · 9, 2 · 27, 12 … Σ 1, 3, 11, 39, 138, 486, 1705, 5961, …
  (−∞, 0]nonnegative
• A081577 → D+1
  1 · 2, 1 · 5, 6, 1 · 8, 21, 10, 1 … Σ 1, 3, 12, 40, 132, 420, 1312, 4032, …
  (−∞, 0]nonnegative
• A257606 → x ↦ x+1
  1 · 8, 4 · 72, 72, 16 · 720, 1080, 488, 64 … Σ 1, 12, 160, 2352, 37840, 661872, …
  (−∞, −1]nonnegative
• A165253 → x ↦ x+1 → x ↦ x+1
  1 · 1 · 3, 1 · 11, 7, 1 … Σ 1, 1, 4, 19, 91, 436, 2089, 10009, …
  (−6, −2)nonnegative
• A038327 → x ↦ x+1 → (θ+1)²
  1 · 13, 4 · 169, 104, 9 · 2197, 2028, 351, 16 … Σ 1, 17, 282, 4592, 73696, 1168944, …
  (−∞, 0]nonnegative
• A196347 → basis A013611 → D
  4 · 32, 64 · 288, 1152, 1152 … Σ 0, 4, 96, 2592, 82944, 3110400, …
  (−∞, 0]nonnegativerational roots
• A163936 → D+1
  1 · 1 · 3, 1 · 14, 10, 1 … Σ 1, 1, 4, 25, 210, 2205, 27720, 405405, …
  (−∞, 0]nonnegative
• A103327 → reverse → x ↦ x/(x+1)
  1 · 1, 4 · 1, 12, 16 · 1, 24, 80, 64 … Σ 1, 5, 29, 169, 985, 5741, 33461, …
  [−1, 0]nonnegative
• A156992 → (θ+1)²
  1 · 2, 8 · 6, 48, 54 · 24, 288, 648, 384 … Σ 1, 10, 108, 1344, 19200, 311040, …
  (−∞, 0]nonnegative
• A028326 → basis A007318 → reverse
  2 · 2, 4 · 2, 8, 8 · 2, 12, 24, 16 … Σ 2, 6, 18, 54, 162, 486, 1458, 4374, …
  (−∞, 0]nonnegativerational roots
• A108426: Triangle read by rows: T(n,k) is number of paths from (0,0) to (3n,0) that stay in the first quadrant (but may touch the horizontal axis), consisting …
  1 · 1, 1 · 3, 5, 2 · 12, 28, 21, 5 … Σ 1, 2, 10, 66, 498, 4066, 34970, 312066, …
  (−∞, 0)nonnegative
• A178822 → basis A013610
  1 · 12, 18 · 84, 252, 189 · 448, 2016, 3024, 1512 … Σ 1, 30, 525, 7000, 78750, 787500, …
  [−1, 0]nonnegativerational roots
• A013610 → Veronese 2 (j=1) → D
  27 · 108 · 270, 486 · 540, 2916 … Σ 0, 0, 0, 27, 108, 756, 3456, 17712, …
  (−∞, 0]nonnegative
• A038325 → D+1
  1 · 22, 11 · 363, 484, 121 · 5324, 11979, 7986, 1331 … Σ 1, 33, 968, 26620, 702768, 18037712, …
  (−∞, 0]nonnegativerational roots
• A144439 → θ+1
  1 · 1, 2 · 1, 16, 3 · 1, 62, 93, 4 … Σ 1, 3, 20, 160, 1596, 19068, 265760, …
  (−∞, 0]nonnegative
• A272866 → θ+1
  1 · 1, 6, 3 · 1, 12, 33, 24, 5 … Σ 1, 10, 75, 500, 3125, 18750, 109375, …
  (−∞, 0]nonnegative
• A201637 → θ+1
  1 · 1 · 1, 4 · 1, 16, 18 … Σ 1, 1, 5, 35, 315, 3465, 45045, 675675, …
  (−∞, 0]nonnegative
• A128100 → basis A013610 → θ+1
  1 · 1 · 3, 6 · 5, 12 … Σ 1, 1, 9, 17, 80, 198, 721, 1999, …
  (−∞, 0]nonnegative
• A225471 → basis A007318 → x ↦ x+1
  1 · 5, 1 · 45, 14, 1 · 585, 227, 27, 1 … Σ 1, 6, 60, 840, 15120, 332640, 8648640, …
  (−∞, −1]nonnegativerational roots
• A178820 → basis A013611 → D+1
  1 · 24, 16 · 200, 480, 160 · 1120, 4800, 5760, 1280 … Σ 1, 40, 840, 12960, 166320, 1886976, …
  (−∞, 0]nonnegativerational roots
• A132393 → D → D
  2 · 6, 6 · 22, 36, 12 · 100, 210, 120, 20 … Σ 0, 0, 2, 12, 70, 450, 3248, 26264, …
  (−∞, 0]nonnegative
• Triangle read by rows: T(n,k) number of tilings of a 2n X 3 grid by dominoes, 2k of which are in a vertical position (0<=k<=n).
  1, 6, 4 · 1, 12, 20, 8 · 1, 20, 60, 56, 16 … Σ 11, 41, 153, 571, 2131, 7953, 29681, …
  (−2, 0)nonnegative
• A001263 → basis A013611 → basis A007318
  1 · 6, 4 · 41, 52, 16 · 306, 564, 336, 64 … Σ 1, 10, 109, 1270, 15562, 198100, …
  (−∞, −1]nonnegative
• A274496 → basis A013611 → (θ+1)²
  1 · 2 · 4, 32 · 8, 64 … Σ 1, 2, 36, 72, 848, 1696, 16704, 33408, …
  (−∞, 0]nonnegative
• A038328 → θ+1
  144, 96, 12 · 1728, 1728, 432, 32 … Σ 252, 3920, 60368, 921984, 13983424, …
  (−∞, 0]nonnegativerational roots
• A104684 → θ+1
  1 · 2, 2 · 6, 12, 3 · 20, 60, 36, 4 … Σ 1, 4, 21, 120, 705, 4188, 24997, …
  (−∞, 0]nonnegative
• A225117 → D
  1 · 13, 2 · 93, 120, 3 · 545, 2262, 753, 4 … Σ 0, 1, 15, 216, 3564, 68040, 1487160, …
  (−∞, 0]nonnegative
• A357367 → reverse
  1 · 2 · 12, 6 · 120, 120, 24 … Σ 1, 2, 18, 264, 5400, 141840, 4551120, …
  (−∞, 0]nonnegative
• A028338 → basis A013610 → basis A007318
  1 · 5, 3 · 35, 36, 9 · 315, 429, 189, 27 … Σ 1, 8, 80, 960, 13440, 215040, 3870720, …
  (−∞, −1]nonnegativerational roots
• A049020 → D
  1 · 3, 2 · 10, 12, 3 · 37, 62, 30, 4 … Σ 0, 1, 5, 25, 133, 761, 4677, 30745, …
  (−∞, −1]nonnegative
• A142075 → (θ+1)²
  1 · 1, 8 · 1, 32, 36 · 1, 88, 396, 128 … Σ 1, 9, 69, 613, 6313, 73937, 970861, …
  (−∞, 0]nonnegative
• Veronese parent of A109447 → D
  1, 2 · 2, 2 · 1, 6, 9, 4 · 4, 12, 12, 4 … Σ 3, 4, 20, 32, 112, 192, 576, 1024, …
  (−∞, 0]nonnegativerational roots
• A097806 → (θ+1)²
  1 · 1, 4 · 0, 4, 9 · 0, 0, 9, 16 … Σ 1, 5, 13, 25, 41, 61, 85, 113, …
  (−∞, 0]nonnegativerational roots
• A356546 → D
  2 · 12, 12 · 60, 120, 60 · 280, 840, 840, 280 … Σ 0, 2, 24, 240, 2240, 20160, 177408, …
  (−∞, 0]nonnegativerational roots
• A069466 → x ↦ x/(x+1)
  1 · 2, 4 · 6, 36, 36 · 20, 240, 600, 400 … Σ 1, 6, 78, 1260, 22470, 424116, 8305836, …
  [−1, 0]nonnegative
• A145597 → γ → (θ+1)²
  1 · 3 · 6, 12 · 10, 60 … Σ 1, 3, 18, 70, 276, 1008, 3584, 12384, …
  (−∞, 0]nonnegative
• A052553 → x ↦ x+1 → x ↦ x+1
  1 · 1 · 3, 1 · 5, 2 … Σ 1, 1, 4, 7, 19, 40, 97, 217, …
  (−∞, −1]nonnegative
• A038208 → x ↦ x/(x+1)
  1 · 2, 4 · 4, 16, 16 · 8, 48, 96, 64 … Σ 1, 6, 36, 216, 1296, 7776, 46656, …
  [−1, 0]nonnegativerational roots
• A123519 → basis A007318 → θ+1
  11, 28, 12 · 41, 152, 132, 32 … Σ 51, 357, 2429, 16187, 106175, 687785, …
  (−∞, 0]nonnegative
• A120986 → x ↦ x/(x+1)
  1 · 2, 3 · 5, 16, 12 · 14, 70, 110, 55 … Σ 1, 5, 33, 249, 2033, 17485, 156033, …
  [−1, 0]nonnegative
• A232535 → basis A013610 → reverse
  1 · 6, 3 · 27, 42, 12 · 108, 333, 240, 48 … Σ 1, 9, 81, 729, 6561, 59049, 531441, …
  (−∞, 0]nonnegative
• A161198 → basis A013611 → x ↦ x/(x+1)
  1 · 3, 11 · 15, 94, 143 · 105, 883, 2411, 2145 … Σ 1, 14, 252, 5544, 144144, 4324320, …
  [−1, 0]nonnegativerational roots
• A204420 → θ+1
  1 · 0, 2 · 0, 12, 9 · 0, 240, 270, 60 … Σ 1, 2, 21, 570, 29505, 2489130, …
  (−∞, 0]nonnegative