Proof methods / preserver_image

Image under a real-rootedness preserver

8,704 sequences

• A038208 → basis A013611 → D+1
  1 · 12, 8 · 80, 192, 64 · 448, 1920, 2304, 512 … Σ 1, 20, 336, 5184, 76032, 1078272, …
  (−∞, 0]nonnegativerational roots
• A011973 → D → D
  2 · 6 · 12, 6 · 20, 24 … Σ 0, 0, 0, 0, 2, 6, 18, 44, …
  (−∞, 0]nonnegative
• chebyshev_t → x ↦ x+1 → θ+1
  1 · 1, 2 · 1, 8, 6 · 1, 18, 36, 16 … Σ 1, 3, 15, 71, 321, 1407, 6031, 25419, …
  (−∞, 0]nonnegative
• A229032 → x ↦ x+1 → D
  4 · 16 · 72, 32 · 272, 192 … Σ 0, 0, 4, 16, 104, 464, 2252, 9952, …
  (−∞, 0]nonnegative
• A028326 → basis A013609
  2 · 4, 4 · 8, 16, 8 · 16, 48, 48, 16 … Σ 2, 8, 32, 128, 512, 2048, 8192, 32768, …
  (−∞, 0]nonnegativerational roots
• A028326 → basis A013611 → x ↦ x+1
  2 · 12, 8 · 72, 96, 32 · 432, 864, 576, 128 … Σ 2, 20, 200, 2000, 20000, 200000, …
  (−∞, −1]nonnegativerational roots
• A103327 → basis A013609 → reverse
  1 · 2, 4 · 4, 24, 16 · 8, 96, 160, 64 … Σ 1, 6, 44, 328, 2448, 18272, 136384, …
  (−∞, 0]nonnegative
• A257609 → x ↦ x+1
  1 · 4, 2 · 24, 24, 4 · 192, 288, 112, 8 … Σ 1, 6, 52, 600, 8656, 149856, 3026752, …
  (−∞, −1]nonnegative
• A013610 → Veronese 2 → D+1
  1 · 1 · 10, 9 · 28, 27 … Σ 1, 1, 19, 55, 352, 1396, 6832, 29296, …
  (−∞, 0]nonnegative
• A207607 → basis A013610 → D+1
  1 · 9, 6 · 35, 63, 18 · 120, 369, 297, 54 … Σ 1, 15, 116, 840, 5851, 39669, 263654, …
  (−∞, 0]nonnegative
• A038281 → x ↦ x+1 → basis A007318
  196, 84, 9 · 2744, 1764, 378, 27 … Σ 289, 4913, 83521, 1419857, 24137569, …
  (−∞, −1]nonnegativerational roots
• A081581 → γ → D+1
  1 · 1 · 7, 6 · 13, 12 … Σ 1, 1, 13, 25, 145, 373, 1573, 4609, …
  (−∞, 0]nonnegative
• A038301 → x ↦ x+1 → (θ+1)²
  400, 1760, 1089 · 8000, 52800, 65340, 21296 … Σ 3249, 147436, 6251305, 253104336, …
  (−∞, 0]nonnegative
• A204420 → basis A013609 → D+1
  1 · 3, 2 · 33, 48, 12 · 915, 1770, 900, 120 … Σ 1, 5, 93, 3705, 255465, 27077085, …
  (−∞, 0]nonnegative
• A038208 → D → (θ+1)²
  2 · 8, 32 · 24, 192, 216 · 64, 768, 1728, 1024 … Σ 0, 2, 40, 432, 3584, 25600, 165888, …
  (−∞, 0]nonnegative
• A122542 → θ+1 → x ↦ x+1
  1 · 2, 2 · 7, 10, 3 · 20, 40, 24, 4 … Σ 1, 4, 20, 88, 376, 1560, 6344, 25400, …
  (−∞, −1]nonnegative
• A027467 → basis A013610 → (θ+1)²
  1 · 16, 12 · 256, 384, 81 · 4096, 9216, 3888, 432 … Σ 1, 28, 721, 17632, 416233, 9575164, …
  (−∞, 0]nonnegative
• A269944 → D
  1 · 1, 2 · 4, 10, 3 · 36, 98, 42, 4 … Σ 0, 1, 3, 17, 180, 3160, 83860, 3147020, …
  (−∞, 0]nonnegative
• A133080 → D
  1 · 0, 2 · 0, 2, 3 · 0, 0, 0, 4 … Σ 0, 1, 2, 5, 4, 9, 6, 13, …
  (−∞, 0]nonnegativerational roots
• A109692 → basis A007318 → D
  1 · 10, 6 · 100, 136, 45 · 1136, 2488, 1788, 420 … Σ 0, 1, 16, 281, 5832, 141993, 3990024, …
  (−∞, 0]nonnegative
• A008955 → basis A013610 → reverse
  1 · 3, 2 · 36, 39, 10 · 972, 1413, 660, 100 … Σ 1, 5, 85, 3145, 204425, 20646925, …
  (−∞, 0]nonnegativerational roots
• A134346 → x ↦ x+1
  1 · 6, 3 · 28, 28, 7 · 120, 180, 90, 15 … Σ 1, 9, 63, 405, 2511, 15309, 92583, …
  (−∞, −1]nonnegativerational roots
• A060187 → γ → θ+1
  1 · 1 · 1, 8 · 1, 40 … Σ 1, 1, 9, 41, 385, 3393, 40041, 508233, …
  (−∞, 0]nonnegative
• A075504 → x ↦ x+1
  109, 29, 1 · 1351, 678, 57, 1 … Σ 139, 2087, 37267, 772583, 18099811, …
  (−∞, −1]nonnegative
• A272866 → basis A013611 → x ↦ x/(x+1)
  1 · 5, 30, 41 · 25, 300, 1310, 2460, 1681 … Σ 1, 76, 5776, 438976, 33362176, …
  [−1, 0]nonnegative
• A143495 → θ+1 → x ↦ x+1
  1 · 5, 2 · 26, 20, 3 · 141, 158, 48, 4 … Σ 1, 7, 49, 351, 2601, 20039, 160833, …
  (−∞, −1]nonnegative
• A008292 → x ↦ x+1 → D+1
  1 · 3, 1 · 12, 8, 1 · 60, 64, 17, 1 … Σ 1, 4, 21, 142, 1175, 11476, 129073, …
  (−∞, 0]nonnegative
• A207607 → basis A007318 → x ↦ x/(x+1)
  1 · 3, 5 · 8, 25, 19 · 21, 96, 144, 71 … Σ 1, 8, 52, 332, 2116, 13484, 85924, …
  [−1, −1/2)nonnegative
• A008277 → θ+2 (shift +1) → reverse → x ↦ x/(x+1)
  2 · 3, 5 · 4, 17, 15 · 5, 39, 84, 52 … Σ 2, 8, 36, 180, 988, 5892, 37852, …
  [−1, 0]nonnegative
• A038271 → basis A013609 → x ↦ x+1
  1 · 22, 10 · 484, 440, 100 · 10648, 14520, 6600, 1000 … Σ 1, 32, 1024, 32768, 1048576, 33554432, …
  (−∞, −1]nonnegativerational roots
• A344565 → θ+1
  3 · 15, 30 · 45, 180, 135 · 105, 630, 945, 420 … Σ 3, 45, 360, 2100, 10080, 42336, 161280, …
  (−∞, 0]nonnegativerational roots
• A075501 → D+1
  54, 20, 1 · 468, 324, 39, 1 · 4536, 5040, 1080, 64, 1 … Σ 75, 832, 10721, 156264, 2525083, …
  (−∞, 0]nonnegative
• A075505 → (θ+1)²
  100, 120, 9 · 1000, 2800, 540, 16 … Σ 229, 4356, 94125, 2257786, 59247609, …
  (−∞, 0]nonnegative
• A062264 → x ↦ x+1 → D+1
  1 · 11, 5 · 70, 72, 15 · 372, 588, 273, 35 … Σ 1, 16, 157, 1268, 9281, 64168, 427885, …
  (−∞, 0]nonnegative
• A038327 → reverse
  1 · 1, 12 · 1, 24, 144 · 1, 36, 432, 1728 … Σ 1, 13, 169, 2197, 28561, 371293, …
  (−∞, 0]nonnegativerational roots
• A121574 → basis A013610 → reverse
  1 · 3, 3 · 9, 21, 10 · 27, 99, 105, 33 … Σ 1, 6, 40, 264, 1744, 11520, 76096, …
  (−∞, 0]nonnegative
• A048993 → reverse → θ+1
  1 · 1 · 1, 2 · 1, 6, 3 … Σ 1, 1, 3, 10, 38, 161, 747, 3753, …
  (−∞, 0]nonnegative
• A193685 → θ+1
  1 · 5, 2 · 25, 22, 3 · 125, 182, 54, 4 … Σ 1, 7, 50, 365, 2727, 20878, 163967, …
  (−∞, 0]nonnegative
• A139548 → basis A013610 → (θ+1)²
  1 · 8, 96, 162 · 64, 1536, 7776, 13824, 8100 … Σ 1, 266, 31300, 2825000, 222250000, …
  (−∞, 0]nonnegative
• A286785 → x ↦ x+1
  30, 18, 2 · 143, 132, 33, 2 · 728, 910, 364, 52, 2 … Σ 50, 310, 2056, 14273, 102410, 753390, …
  (−∞, −1]nonnegative
• A196347 → γ
  1 · 1 · 2 · 6 … Σ 1, 1, 2, 6, 24, 120, 720, 5040, …
  (−∞, −1][−1, 0][−3−2√2, −3+2√2]+2
• A038291 → basis A013611 → D+1
  1 · 14, 4 · 180, 112, 16 · 2200, 2160, 672, 64 … Σ 1, 18, 308, 5096, 82320, 1306144, …
  (−∞, 0]nonnegativerational roots
• A038323 → θ+1
  1 · 11, 18 · 121, 396, 243 · 1331, 6534, 8019, 2916 … Σ 1, 29, 760, 18800, 448000, 10400000, …
  (−∞, 0]nonnegativerational roots
• A100861 → D → (θ+1)²
  1 · 3 · 6, 24 · 10, 120 … Σ 0, 0, 1, 3, 30, 130, 780, 3696, …
  (−∞, 0]nonnegative
• A038335 → basis A013610 → D
  27 · 1134, 1458 · 35721, 91854, 59049 … Σ 0, 27, 2592, 186624, 11943936, …
  (−∞, 0]nonnegativerational roots
• A038259 → basis A013610 → D+1
  1 · 26, 15 · 451, 780, 225 · 6776, 20295, 17550, 3375 … Σ 1, 41, 1456, 47996, 1511536, 46154576, …
  (−∞, 0]nonnegativerational roots
• A038338 → basis A013610 → x ↦ x/(x+1)
  576, 2880, 3600 · 13824, 103680, 259200, 216000 … Σ 7056, 592704, 49787136, 4182119424, …
  [−1, 0]nonnegativerational roots
• basis-map coefficients of A371080, shifted → basis A013609 → θ+1
  1 · 1, 4 · 4, 20, 12 · 28, 156, 144, 32 … Σ 1, 5, 36, 360, 4644, 73548, 1382184, …
  (−∞, 0]nonnegative
• A104684 → basis A013611 → basis A007318
  1 · 7, 4 · 61, 64, 16 · 595, 900, 432, 64 … Σ 1, 11, 141, 1991, 29761, 460251, …
  (−∞, −1]nonnegative
• A094638 → basis A013609 → θ+1
  1 · 2, 4 · 6, 28, 24 · 24, 184, 348, 192 … Σ 1, 6, 58, 748, 11964, 227824, 5027536, …
  (−∞, 0]nonnegative