Proof methods / preserver_image

Image under a real-rootedness preserver

8,704 sequences

• A345013 → D
  3 · 20, 12 · 105, 120, 30 · 504, 840, 420, 60 … Σ 0, 3, 32, 255, 1824, 12355, 81024, …
  (−∞, −1]nonnegative
• A125092 → D+1 → D+1
  1 · 9, 4 · 35, 44, 9 · 79, 216, 123, 16 … Σ 1, 13, 88, 434, 1784, 6512, 21856, …
  (−∞, 0]nonnegative
• A060920: Bisection of Fibonacci triangle A037027: even-indexed members of column sequences of A037027 (not counting leading zeros).
  1 · 2, 1 · 5, 5, 1 · 13, 20, 9, 1 … Σ 1, 3, 11, 43, 171, 683, 2731, 10923, …
  (−∞, −1]nonnegative
• A131431 → (θ+1)² → D+1
  1 · 16, 16 · 0, 126, 63 · 0, 0, 480, 160 … Σ 1, 32, 189, 640, 1625, 3456, 6517, …
  (−∞, 0]nonnegativerational roots
• A241171 → x ↦ x+1
  1 · 7, 6 · 121, 210, 90 · 3907, 10206, 8820, 2520 … Σ 1, 13, 421, 25453, 2473141, 352444093, …
  (−∞, −1]nonnegative
• A099097 → x ↦ x−7
  1 · -21, 3 · 434, -125, 9 · -8967, 3885, -561, 27 … Σ 1, -18, 318, -5616, 99180, -1751544, …
  (59/9, 7]
• A027465 → (θ+1)²
  1 · 3, 4 · 9, 24, 9 · 27, 108, 81, 16 … Σ 1, 7, 42, 232, 1216, 6144, 30208, …
  (−∞, 0]nonnegative
• A053122 → x ↦ x+1 → D
  1 · -2, 2 · 1, -6, 3 · 2, 6, -12, 4 … Σ 0, 1, 0, -2, 0, 3, 0, -4, …
  (−∞, ∞)
• A038319 → x ↦ x+1 → θ+1
  256, 320, 75 · 4096, 7680, 3600, 500 … Σ 651, 15876, 379701, 8946126, 208289151, …
  (−∞, 0]nonnegativerational roots
• A197208 → D
  120, 60 · 600, 1200, 180 · 2100, 10500, 6300, 420 … Σ 180, 1980, 19320, 177240, 1567944, …
  (−∞, 0]nonnegative
• A114656 → D+1
  1 · 3, 1 · 10, 8, 1 · 32, 48, 15, 1 … Σ 1, 4, 19, 96, 501, 2668, 14407, 78592, …
  (−∞, 0]nonnegative
• A033282 → x ↦ x+1 → x ↦ x+1
  1 · 5, 2 · 31, 25, 5 · 215, 261, 105, 14 … Σ 1, 7, 61, 595, 6217, 68047, 770149, …
  (−3, −2)nonnegative
• A257618: Triangle read by rows: T(n,k) = t(n-k, k); t(n,m) = f(m)*t(n-1,m) + f(n)*t(n,m-1), where f(x) = 8*x + 2.
  1 · 2, 2 · 4, 40, 4 · 8, 472, 472, 8 … Σ 1, 4, 48, 960, 26880, 967680, 42577920, …
  (−∞, 0)nonnegative
• A112007 → x ↦ x+1
  1 · 3, 1 · 15, 10, 1 · 105, 105, 25, 1 … Σ 1, 4, 26, 236, 2752, 39208, 660032, …
  (−∞, −1]nonnegative
• A088996 → basis A007318 → basis A007318
  1 · 2, 1 · 10, 9, 2 · 80, 102, 43, 6 … Σ 1, 3, 21, 231, 3465, 65835, 1514205, …
  (−∞, −1]nonnegativerational roots
• A225471 → basis A013611 → basis A007318
  1 · 8, 4 · 96, 80, 16 · 1536, 1664, 576, 64 … Σ 1, 12, 192, 3840, 92160, 2580480, …
  (−∞, −1]nonnegativerational roots
• A236076 → basis A007318
  1 · 2, 2 · 4, 7, 3 · 8, 21, 18, 5 … Σ 1, 4, 14, 52, 188, 688, 2504, 9136, …
  (−∞, −1]nonnegative
• A113214 → basis A007318
  1 · 3, 1 · 4, 5, 1 · 7, 13, 7, 1 … Σ 1, 4, 10, 28, 76, 208, 568, 1552, …
  (−∞, −1]nonnegative
• A088996 → basis A013609 → θ+1
  1 · 1, 4 · 3, 20, 24 · 15, 136, 300, 192 … Σ 1, 5, 47, 643, 11493, 253017, 6609411, …
  (−∞, 0]nonnegative
• A128099 → basis A013611 → D+1
  1 · 1 · 11, 8 · 21, 16 … Σ 1, 1, 19, 37, 315, 853, 5051, 16309, …
  (−∞, 0]nonnegative
• A130534 → D+1
  1 · 2, 1 · 5, 5, 1 · 17, 23, 9, 1 … Σ 1, 3, 11, 50, 274, 1764, 13068, 109584, …
  (−∞, −1]nonnegative
• A059364 → basis A007318 → reverse
  1 · 1, 3 · 2, 11, 15 · 6, 47, 122, 105 … Σ 1, 4, 28, 280, 3640, 58240, 1106560, …
  (−∞, 0]nonnegativerational roots
• A090452 → reverse
  1 · 2, 3, 1 · 5, 15, 16, 7, 1 … Σ 1, 6, 44, 360, 3152, 28896, 273856, …
  (−∞, 0]nonnegative
• A134059 → D
  3 · 6, 6 · 9, 18, 9 · 12, 36, 36, 12 … Σ 0, 3, 12, 36, 96, 240, 576, 1344, …
  (−∞, 0]nonnegativerational roots
• A249252 → x ↦ x/(x+1)
  1 · 1, 5 · 1, 10, 17 · 1, 15, 59, 61 … Σ 1, 6, 28, 136, 656, 3168, 15296, 73856, …
  [−1, 0]nonnegative
• A008288 → basis A007318 → θ+1
  1 · 2, 2 · 5, 10, 3 · 12, 36, 24, 4 … Σ 1, 4, 18, 76, 314, 1272, 5078, 20036, …
  (−∞, 0]nonnegative
• A038326 → x ↦ x+1 → basis A007318
  1 · 35, 12 · 1225, 840, 144 … Σ 1, 47, 2209, 103823, 4879681, …
  (−∞, −1]nonnegativerational roots
• A007318 → −D²+(−1+n)D+1+n → x ↦ x+1 → (θ+1)²
  1 · 4, 8 · 14, 56, 27 · 44, 264, 270, 64 … Σ 1, 12, 97, 642, 3729, 19728, 97281, …
  (−∞, 0]nonnegative
• A136124 → basis A013609
  1 · 3, 2 · 12, 14, 4 · 60, 94, 48, 8 … Σ 1, 5, 30, 210, 1680, 15120, 151200, …
  (−∞, −1]nonnegativerational roots
• A082985 → D
  3 · 5, 10 · 7, 28, 21 · 9, 54, 90, 36 … Σ 0, 3, 15, 56, 189, 605, 1872, 5655, …
  (−∞, 0]nonnegative
• A137320 → basis A013611 → reverse
  1 · 8, 2 · 64, 40, 6 · 512, 576, 208, 24 … Σ 1, 10, 110, 1320, 17160, 240240, …
  (−∞, 0]nonnegativerational roots
• A207824 → D+1
  1 · 6, 1 · 34, 12, 1 · 188, 103, 18, 1 … Σ 1, 7, 47, 310, 2017, 12981, 82799, …
  (−∞, 0]nonnegative
• A199881 → basis A007318
  2, 1 · 2, 3, 1 · 4, 8, 5, 1 · 6, 17, 17, 7, 1 … Σ 3, 6, 18, 48, 132, 360, 984, 2688, …
  (−∞, −1]nonnegative
• A136572: Triangle read by rows: row n consists of n zeros followed by n!.
  1 · 0, 1 · 0, 0, 2 · 0, 0, 0, 6 … Σ 1, 1, 2, 6, 24, 120, 720, 5040, …
  [−1, 0]nonnegativerational roots
• A134082 → θ+1
  1 · 2, 2 · 0, 8, 3 · 0, 0, 18, 4 … Σ 1, 4, 11, 22, 37, 56, 79, 106, …
  (−∞, 0]nonnegativerational roots
• A038226 → basis A013611 → x ↦ x/(x+1)
  121, 946, 1849 · 1331, 15609, 61017, 79507 … Σ 2916, 157464, 8503056, 459165024, …
  [−1, 0]nonnegativerational roots
• A207824 → D
  1 · 10, 2 · 73, 30, 3 · 470, 294, 60, 4 … Σ 0, 1, 12, 106, 828, 6051, 42408, …
  (−∞, 0]nonnegative
• A034807 → D
  2 · 3 · 4, 4 · 5, 10 … Σ 0, 0, 2, 3, 8, 15, 30, 56, …
  (−∞, 0]nonnegative
• A178821 → x ↦ x/(x+1)
  1 · 5, 10 · 15, 60, 60 · 35, 210, 420, 280 … Σ 1, 15, 135, 945, 5670, 30618, 153090, …
  [−1, 0]nonnegativerational roots
• A013612 → basis A013610 → (θ+1)²
  36, 720, 2025 · 216, 6480, 36450, 54000 … Σ 2781, 97146, 3052161, 89516826, …
  (−∞, 0]nonnegative
• A086645 → D → (θ+1)²
  1 · 6, 8 · 15, 120, 27 · 28, 560, 756, 64 … Σ 0, 1, 14, 162, 1408, 10400, 69120, …
  (−∞, 0]nonnegative
• A143495 → x ↦ x+1 → x ↦ x+1
  1 · 5, 1 · 27, 11, 1 · 157, 97, 18, 1 … Σ 1, 6, 39, 273, 2046, 16329, 138117, …
  (−∞, −1]nonnegative
• A128813 → basis A013610 → reverse
  1 · 3, 2 · 27, 30, 8 · 486, 729, 354, 56 … Σ 1, 5, 65, 1625, 66625, 4064125, …
  (−∞, 0]nonnegativerational roots
• A094305 → x ↦ x+1 → θ+1
  1 · 6, 6 · 24, 48, 18 · 80, 240, 180, 40 … Σ 1, 12, 90, 540, 2835, 13608, 61236, …
  (−∞, 0]nonnegativerational roots
• A136124 → basis A013609 → D
  2 · 14, 8 · 94, 96, 24 · 684, 952, 432, 64 … Σ 0, 2, 22, 214, 2132, 22548, 255720, …
  (−∞, 0]nonnegative
• A081577 → x ↦ x+1 → x ↦ x+1
  1 · 3, 1 · 13, 8, 1 · 51, 47, 13, 1 … Σ 1, 4, 22, 112, 580, 2992, 15448, 79744, …
  (−∞, −1]nonnegative
• A028326 → basis A013609 → θ+1
  2 · 4, 8 · 8, 32, 24 · 16, 96, 144, 64 … Σ 2, 12, 64, 320, 1536, 7168, 32768, …
  (−∞, 0]nonnegativerational roots
• A008292 → γ → (θ+1)²
  1 · 1 · 1, 8 · 1, 32 … Σ 1, 1, 9, 33, 233, 1433, 11289, 92097, …
  (−∞, 0]nonnegative
• A053117 → x ↦ x+1 → reverse
  1 · 2, 2 · 4, 8, 3 · 8, 24, 20, 4 … Σ 1, 4, 15, 56, 209, 780, 2911, 10864, …
  (−∞, 0]nonnegative
• A106246 → D → D+1
  1 · 6, 2 · 15, 18, 3 · 12, 60, 36, 4 … Σ 0, 1, 8, 36, 112, 275, 576, 1078, …
  (−∞, 0]nonnegative