Proof methods / preserver_image

Image under a real-rootedness preserver

8,704 sequences

• A084534 → D+1
  1 · 3, 2 · 5, 8, 2 · 7, 24, 15, 2 … Σ 1, 5, 15, 48, 151, 463, 1390, 4105, …
  (−∞, 0]nonnegative
• A176230 → D
  1 · 6, 2 · 45, 30, 3 · 420, 420, 84, 4 … Σ 0, 1, 8, 78, 928, 13100, 214176, …
  (−∞, 0]nonnegative
• A269951 → D
  1 · 2, 2 · 5, 10, 3 · 16, 46, 27, 4 … Σ 0, 1, 4, 18, 93, 553, 3760, 28946, …
  (−∞, 0]nonnegative
• A225470 → x ↦ x+1 → x ↦ x/(x+1)
  1 · 3, 4 · 18, 45, 28 · 162, 585, 702, 280 … Σ 1, 7, 91, 1729, 43225, 1339975, …
  [−1, 0]nonnegativerational roots
• A249250 → basis A013609 → x ↦ x/(x+1)
  1 · 4, 10 · 10, 44, 46 · 28, 180, 372, 244 … Σ 1, 14, 100, 824, 6544, 52448, 419392, …
  [−1, 0]nonnegative
• A133087 → x ↦ x+1 → (θ+1)²
  1 · 3, 4 · 4, 16, 9 · 12, 64, 63, 16 … Σ 1, 7, 29, 155, 513, 2511, 7533, 35235, …
  (−∞, 0]nonnegative
• A038329 → reverse
  9, 72, 144 · 27, 324, 1296, 1728 … Σ 225, 3375, 50625, 759375, 11390625, …
  (−∞, 0]nonnegativerational roots
• A137597 → x ↦ x+1 → reverse
  1 · 1, 3 · 1, 7, 11 · 1, 12, 43, 47 … Σ 1, 4, 19, 103, 622, 4117, 29521, …
  (−∞, 0]nonnegative
• A038330 → basis A013609 → D+1
  512, 384, 64 · 10240, 12288, 4608, 512 … Σ 960, 27648, 774144, 21233664, …
  (−∞, 0]nonnegativerational roots
• A109692 → basis A013609 → (θ+1)²
  1 · 2, 8 · 8, 80, 108 · 48, 800, 2448, 1920 … Σ 1, 10, 196, 5216, 172544, 6788480, …
  (−∞, 0]nonnegative
• A207607 → reverse
  1 · 2, 1 · 2, 5, 1 · 2, 9, 9, 1 … Σ 1, 3, 8, 21, 55, 144, 377, 987, …
  (−∞, 0]nonnegative
• A048993 → reverse → x ↦ x+1
  1 · 1 · 2, 1 · 5, 5, 1 … Σ 1, 1, 3, 11, 49, 257, 1539, 10299, …
  (−∞, −1]nonnegative
• A269947 → D
  1 · 1, 2 · 8, 18, 3 · 216, 502, 108, 4 … Σ 0, 1, 3, 29, 830, 54454, 6893964, …
  (−∞, 0]nonnegative
• A038334 → x ↦ x+1 → reverse
  64, 320, 400 · 512, 3840, 9600, 8000 … Σ 784, 21952, 614656, 17210368, …
  (−∞, 0]nonnegativerational roots
• A257614 → x ↦ x+1
  1 · 4, 2 · 36, 36, 4 · 504, 756, 268, 8 … Σ 1, 6, 76, 1536, 42136, 1459176, …
  (−∞, −1]nonnegative
• A038327 → basis A013609
  1 · 13, 2 · 169, 52, 4 · 2197, 1014, 156, 8 … Σ 1, 15, 225, 3375, 50625, 759375, …
  (−∞, −1]nonnegativerational roots
• A249139 → basis A013609 → basis A013609
  1 · 6, 4 · 11, 8 · 41, 52, 16 … Σ 1, 10, 19, 109, 280, 1261, 3781, 15130, …
  (−∞, −1]nonnegative
• A038271 → x ↦ x/(x+1) → θ+1
  1 · 7, 24 · 49, 336, 432 · 343, 3528, 9072, 6912 … Σ 1, 31, 817, 19855, 459553, 10295359, …
  (−∞, 0]nonnegativerational roots
• A086645 → basis A007318 → (θ+1)²
  1 · 2, 4 · 8, 32, 9 · 32, 192, 162, 16 … Σ 1, 6, 49, 402, 3129, 23398, 169817, …
  (−∞, 0]nonnegative
• A227450 → reverse → (θ+1)²
  2 · 4, 8 · 8, 48, 18 · 16, 192, 252, 32 … Σ 2, 12, 74, 492, 3482, 26036, 204794, …
  (−∞, 0]nonnegative
• A038333 → basis A013610 → D
  798, 882 · 22743, 50274, 27783 … Σ 1680, 100800, 5376000, 268800000, …
  (−∞, 0]nonnegativerational roots
• A038284 → basis A013610 → (θ+1)²
  196, 2016, 2916 · 2744, 42336, 122472, 93312 … Σ 5128, 260864, 12107776, 529006592, …
  (−∞, 0]nonnegative
• A135838 → x ↦ x/(x+1)
  1 · 2, 4 · 2, 8, 8 · 4, 24, 48, 32 … Σ 1, 6, 18, 108, 324, 1944, 5832, 34992, …
  [−1, 0]nonnegativerational roots
• A085841 → D
  4 · 40, 32 · 140, 672, 192 · 336, 4032, 6912, 1024 … Σ 0, 4, 72, 1004, 12304, 140244, 1527896, …
  (−∞, 0]nonnegative
• A122542 → D+1 → D+1
  1 · 2, 1 · 6, 6, 1 · 12, 24, 10, 1 … Σ 1, 3, 13, 47, 161, 523, 1637, 4975, …
  (−∞, 0]nonnegative
• A013610 → basis A007318
  1 · 4, 3 · 16, 24, 9 · 64, 144, 108, 27 … Σ 1, 7, 49, 343, 2401, 16807, 117649, …
  (−∞, −1]nonnegativerational roots
• A133080 → reverse
  1 · 1, 1 · 1 · 1, 1 … Σ 1, 2, 1, 2, 1, 2, 1, 2, …
  (−∞, 0]nonnegativerational roots
• A008292 → γ (shift +1) → x ↦ x+1
  1 · 1 · 3, 2 · 9, 8 … Σ 1, 1, 5, 17, 109, 649, 5285, 44513, …
  (−∞, −1]nonnegative
• image under θ+1 → θ+1 → reverse
  1 · 4 · 9 · 16 … Σ 1, 4, 9, 16, 25, 36, 49, 64, …
  (−∞, −1][−1, 0][−3−2√2, −3+2√2]+2
• image under θ+1 → θ+1 → D → θ+1
  4 · 0, 36 · 0, 0, 144 · 0, 0, 0, 400 … Σ 0, 4, 36, 144, 400, 900, 1764, 3136, …
  (−∞, 0]nonnegativerational roots
• A038220 → basis A013611 → basis A007318
  1 · 13, 8 · 169, 208, 64 · 2197, 4056, 2496, 512 … Σ 1, 21, 441, 9261, 194481, 4084101, …
  (−∞, −1]nonnegativerational roots
• A227450 → reverse → x ↦ x/(x+1)
  2 · 4, 6 · 8, 28, 22 · 16, 96, 172, 94 … Σ 2, 10, 58, 378, 2714, 21178, 177818, …
  [−1, 0]nonnegative
• A085880 → basis A013609
  1 · 2, 2 · 8, 16, 8 · 40, 120, 120, 40 … Σ 1, 4, 32, 320, 3584, 43008, 540672, …
  (−∞, 0]nonnegativerational roots
• A059364 → basis A013609 → x ↦ x/(x+1)
  1 · 3, 5 · 15, 52, 45 · 105, 559, 991, 585 … Σ 1, 8, 112, 2240, 58240, 1863680, …
  [−1, 0]nonnegativerational roots
• A145324 → basis A007318 → x ↦ x+1
  1 · 5, 2 · 35, 29, 6 · 315, 401, 170, 24 … Σ 1, 7, 70, 910, 14560, 276640, 6086080, …
  (−∞, −1]nonnegativerational roots
• A147716 → basis A013609
  1 · 15, 2 · 225, 60, 4 · 3375, 1350, 180, 8 … Σ 1, 17, 289, 4913, 83521, 1419857, …
  (−∞, −1]nonnegativerational roots
• A122848 → x ↦ x/(x+1)
  1 · 0, 1 · 0, 1, 2 · 0, 0, 3, 4 … Σ 1, 1, 3, 7, 25, 81, 331, 1303, …
  [−1, 0]nonnegative
• A093375 → D → basis A007318
  1 · 6, 2 · 24, 18, 3 · 80, 96, 36, 4 … Σ 0, 1, 8, 45, 216, 945, 3888, 15309, …
  (−∞, −1]nonnegativerational roots
• A253283 → x ↦ x/(x+1)
  1 · 0, 1 · 0, 2, 5 · 0, 3, 18, 25 … Σ 1, 1, 7, 46, 307, 2086, 14374, 100108, …
  [−1, 0]nonnegative
• A094638 → basis A013611 → D+1
  1 · 6, 4 · 34, 92, 32 · 208, 1112, 1616, 384 … Σ 1, 10, 158, 3320, 86616, 2695536, …
  (−∞, 0]nonnegative
• A344565 → basis A007318
  3 · 30, 15 · 180, 180, 45 · 840, 1260, 630, 105 … Σ 3, 45, 405, 2835, 17010, 91854, 459270, …
  (−∞, −1]nonnegativerational roots
• A008292 → γ (scale 1/4) → x ↦ x+1 → θ+1
  1 · 2 · 6, 4 · 24, 32 … Σ 1, 2, 10, 56, 408, 3456, 34016, 378496, …
  (−∞, 0]nonnegative
• A127648 → D → D+1
  2 · 6, 6 · 0, 24, 12 · 0, 0, 60, 20 … Σ 0, 0, 2, 12, 36, 80, 150, 252, …
  (−∞, 0]nonnegativerational roots
• A159854 → x ↦ x+1 → D
  2, 2 · 5, 8, 3 · 12, 26, 18, 4 · 28, 76, 75, 32, 5 … Σ 4, 16, 60, 216, 756, 2592, 8748, 29160, …
  (−∞, 0]nonnegativerational roots
• A059364 → D
  1 · 7, 4 · 46, 58, 18 · 326, 658, 438, 96 … Σ 0, 1, 11, 122, 1518, 21423, 340869, …
  (−∞, −1]nonnegative
• A112007 → x ↦ x/(x+1)
  1 · 2, 3 · 6, 20, 15 · 24, 130, 210, 105 … Σ 1, 5, 41, 469, 6889, 123605, 2620169, …
  [−1, 0]nonnegative
• A060920 → Veronese 2 → θ+1
  1 · 2 · 5, 2 · 13, 18 … Σ 1, 2, 7, 31, 139, 615, 2691, 11679, …
  (−∞, 0]nonnegative
• A225468 → θ+1
  1 · 2, 2 · 4, 14, 3 · 8, 78, 45, 4 … Σ 1, 4, 21, 135, 1008, 8505, 79785, …
  (−∞, 0]nonnegative
• A128908 → D
  1 · 2, 2 · 3, 8, 3 · 4, 20, 18, 4 … Σ 0, 1, 4, 14, 46, 145, 444, 1331, …
  (−∞, 0]nonnegative
• A166341 → θ+1
  1, 20, 3 · 1, 46, 69, 4 · 1, 100, 414, 200, 5 … Σ 24, 120, 720, 5040, 40320, 362880, …
  (−∞, 0]nonnegative