Proof methods / preserver_image

Image under a real-rootedness preserver

8,704 sequences

• A144438 → (θ+1)²
  1 · 1, 4 · 1, 20, 9 · 1, 56, 126, 16 … Σ 1, 5, 30, 199, 1487, 12450, 115866, …
  (−∞, 0]nonnegative
• A125662 → basis A013610 → θ+1
  1 · 4, 6 · 15, 48, 27 · 56, 276, 324, 108 … Σ 1, 10, 90, 764, 6245, 49716, 388135, …
  (−∞, 0]nonnegative
• A038284 → x ↦ x/(x+1)
  64, 224, 196 · 512, 2688, 4704, 2744 … Σ 484, 10648, 234256, 5153632, 113379904, …
  [−1, 0]nonnegativerational roots
• A347056 → reverse → x ↦ x+1
  1 · 7, 3 · 32, 28, 6 · 120, 160, 70, 10 … Σ 1, 10, 66, 360, 1755, 7938, 34020, …
  (−∞, −1]nonnegativerational roots
• A008292 → γ (scale 1/4) → θ+1
  1 · 2 · 4, 4 · 8, 32 … Σ 1, 2, 8, 40, 240, 1680, 13440, 120960, …
  (−∞, 0]nonnegative
• A290319 → x ↦ x+1 → x ↦ x/(x+1)
  1 · 2, 3 · 12, 32, 21 · 120, 452, 562, 231 … Σ 1, 5, 65, 1365, 39585, 1464645, …
  [−1, 0]nonnegativerational roots
• A091042 → reverse → D
  1 · 10, 2 · 35, 42, 3 · 84, 252, 108, 4 … Σ 0, 1, 12, 80, 448, 2304, 11264, 53248, …
  (−∞, 0]nonnegative
• A091044 → basis A007318 → reverse
  1 · 2, 4 · 3, 16, 16 · 4, 40, 96, 64 … Σ 1, 6, 35, 204, 1189, 6930, 40391, …
  (−∞, 0]nonnegative
• A034807 → θ+1
  2 · 1 · 1, 4 · 1, 6 … Σ 2, 1, 5, 7, 15, 26, 48, 85, …
  (−∞, 0]nonnegative
• A008277 → θ+1 → D+1 → θ+1
  1 · 3, 4 · 7, 24, 9 · 15, 100, 90, 16 … Σ 1, 7, 40, 221, 1241, 7218, 43807, …
  (−∞, 0]nonnegative
• A099097 → basis A013609 → θ+1
  1 · 3, 12 · 10, 76, 108 · 33, 372, 1044, 864 … Σ 1, 15, 194, 2313, 26265, 288684, …
  (−∞, 0]nonnegative
• A144696 → θ+1
  1 · 1, 4 · 1, 14, 12 · 1, 36, 99, 32 … Σ 1, 5, 27, 168, 1200, 9720, 88200, …
  (−∞, 0]nonnegative
• A132440 → D+1
  1 · 2, 2 · 0, 6, 3 · 0, 0, 12, 4 … Σ 0, 1, 4, 9, 16, 25, 36, 49, …
  (−∞, 0]nonnegativerational roots
• A225469 → reverse
  1 · 1, 3 · 1, 10, 9 · 1, 21, 79, 27 … Σ 1, 4, 20, 128, 1008, 9280, 96704, …
  (−∞, 0]nonnegative
• A085880 → basis A013610 → reverse
  1 · 3, 2 · 18, 24, 8 · 135, 270, 180, 40 … Σ 1, 5, 50, 625, 8750, 131250, 2062500, …
  (−∞, 0]nonnegativerational roots
• A147716 → basis A013610 → x ↦ x+1
  1 · 18, 3 · 324, 108, 9 · 5832, 2916, 486, 27 … Σ 1, 21, 441, 9261, 194481, 4084101, …
  (−∞, −1]nonnegativerational roots
• A128099 → D → θ+1
  2 · 4 · 6, 16 · 8, 48 … Σ 0, 0, 2, 4, 22, 56, 178, 460, …
  (−∞, 0]nonnegative
• A049020 → reverse → x ↦ x+1
  1 · 2, 1 · 6, 7, 2 · 22, 41, 25, 5 … Σ 1, 3, 15, 93, 681, 5691, 53079, 544053, …
  (−∞, −1]nonnegative
• A013612 → basis A013611 → D
  240, 800 · 2160, 14400, 24000 … Σ 1040, 40560, 1406080, 45697600, …
  (−∞, 0]nonnegativerational roots
• A013609 → Veronese 2 → D
  4 · 12 · 24, 32 · 40, 160 … Σ 0, 0, 4, 12, 56, 200, 732, 2548, …
  (−∞, 0]nonnegative
• A113214 → x ↦ x−12
  1 · -10, 1 · 108, -21, 1 · -1176, 338, -32, 1 … Σ 1, -9, 88, -869, 8591, -84942, 839861, …
  (8, 12]
• A038284 → θ+1
  64, 192, 108 · 512, 2304, 2592, 864 … Σ 364, 6272, 104272, 1690304, 26891200, …
  (−∞, 0]nonnegativerational roots
• A049029 → D
  1 · 15, 2 · 255, 60, 3 · 5175, 1650, 150, 4 … Σ 0, 1, 17, 318, 6979, 178475, 5239086, …
  (−∞, 0]nonnegative
• A113953 → D+1
  1 · 1, 1 · 2, 4, 1 · 0, 8, 7, 1 … Σ 1, 2, 7, 16, 41, 94, 219, 492, …
  (−∞, 0]nonnegative
• A063967 → x ↦ x−5
  1 · -4, 1 · 12, -7, 1 · -32, 32, -10, 1 … Σ 1, -3, 6, -9, 9, 0, -27, 81, …
  (0, 4]
• A290315 → x ↦ x+1
  1 · 3, 2 · 29, 40, 12 · 471, 994, 644, 120 … Σ 1, 5, 81, 2229, 86433, 4321125, …
  (−∞, −1]nonnegative
• A110441 → basis A007318 → θ+1
  1 · 4, 2 · 14, 16, 3 · 48, 88, 36, 4 … Σ 1, 6, 33, 176, 919, 4722, 23957, …
  (−∞, 0]nonnegative
• A110441 → reverse → D
  3 · 6, 14 · 9, 46, 45 · 12, 96, 216, 124 … Σ 0, 3, 20, 100, 448, 1892, 7696, 30496, …
  (−∞, 0]nonnegative
• A137320 → basis A013611 → θ+1
  1 · 2, 16 · 6, 80, 192 · 24, 416, 1728, 2048 … Σ 1, 18, 278, 4216, 65368, 1052432, …
  (−∞, 0]nonnegative
• A055151 → (θ+1)²
  1 · 1 · 1, 4 · 1, 12 … Σ 1, 1, 5, 13, 43, 131, 411, 1275, …
  (−∞, 0]nonnegative
• A013611 → basis A013611 → D
  16 · 160, 512 · 1200, 7680, 12288 … Σ 0, 16, 672, 21168, 592704, 15558480, …
  (−∞, 0]nonnegativerational roots
• A028338 → basis A013610 → D
  3 · 18, 18 · 132, 216, 81 · 1200, 2520, 1620, 324 … Σ 0, 3, 36, 429, 5664, 84027, 1395540, …
  (−∞, 0]nonnegative
• A038321 → basis A013611 → D+1
  1332, 2576, 784 · 33048, 111888, 108192, 21952 … Σ 4692, 275080, 15379088, 832806816, …
  (−∞, 0]nonnegativerational roots
• A086645 → basis A013611 → D
  4 · 32, 32 · 192, 576, 192 · 1024, 5120, 6144, 1024 … Σ 0, 4, 64, 960, 13312, 174080, 2187264, …
  (−∞, 0]nonnegative
• A122542 → basis A013610 → x ↦ x+1
  1 · 4, 3 · 24, 30, 9 · 136, 246, 144, 27 … Σ 1, 7, 63, 553, 4865, 42791, 376383, …
  (−∞, −1]nonnegative
• A027467 → θ+1
  1 · 15, 2 · 225, 60, 3 · 3375, 1350, 135, 4 … Σ 1, 17, 288, 4864, 81920, 1376256, …
  (−∞, 0]nonnegativerational roots
• A249252 → basis A007318 → D
  4 · 24, 16 · 124, 160, 48 · 576, 1104, 672, 128 … Σ 0, 4, 40, 332, 2480, 17492, 118840, …
  (−∞, 0]nonnegative
• A099040 → basis A013610 → D+1
  1 · 8, 6 · 36, 102, 36 · 136, 696, 936, 216 … Σ 1, 14, 174, 1984, 21536, 226176, …
  (−∞, 0]nonnegative
• A055151 → D → (θ+1)²
  1 · 3 · 6, 16 · 10, 80 … Σ 0, 0, 1, 3, 22, 90, 390, 1526, …
  (−∞, 0]nonnegative
• A059344 → basis A013610 → D
  6 · 18 · 108, 216 · 420, 1080 … Σ 0, 0, 6, 18, 324, 1500, 21690, 131166, …
  (−∞, 0]nonnegative
• A046716 → basis A013611 → x ↦ x/(x+1)
  1 · 2, 6 · 5, 30, 41 · 16, 148, 424, 356 … Σ 1, 8, 76, 944, 16336, 386816, 11758528, …
  [−1, 0]nonnegative
• A249252 → D+1
  1 · 5, 4 · 9, 24, 8 · 13, 76, 80, 16 … Σ 1, 9, 41, 185, 793, 3305, 13481, 54105, …
  (−∞, 0]nonnegative
• A038305 → basis A013611 → x ↦ x+1
  625, 600, 144 · 15625, 22500, 10800, 1728 … Σ 1369, 50653, 1874161, 69343957, …
  (−∞, −1]nonnegativerational roots
• A038208: Triangle whose (i,j)-th entry is binomial(i,j)*2^i.
  1 · 2, 2 · 4, 8, 4 · 8, 24, 24, 8 … Σ 1, 4, 16, 64, 256, 1024, 4096, 16384, …
  (−∞, −1]nonnegativerational roots
• A039756 → θ+1
  1 · 1, 2 · 1, 8, 3 · 1, 18, 39, 4 … Σ 1, 3, 12, 62, 372, 2492, 18384, 147800, …
  (−∞, 0]nonnegative
• A126216 → (θ+1)²
  1 · 2, 4 · 5, 20, 9 · 14, 84, 81, 16 … Σ 1, 6, 34, 195, 1131, 6608, 38788, …
  (−∞, 0]nonnegative
• A113214 → x ↦ x−1
  1 · 1, 1 · -2, 1, 1 · 1, -3, 1, 1 … Σ 1, 2, 0, 0, 0, 0, 0, 0, …
  (−3, 1]
• A345013 → x ↦ x+1
  1 · 7, 3 · 41, 32, 6 · 231, 255, 90, 10 … Σ 1, 10, 79, 586, 4258, 30724, 221275, …
  (−∞, −1]nonnegative
• A114655 → x ↦ x+1 → D+1
  2 · 8, 2 · 38, 20, 2 · 192, 162, 36, 2 … Σ 2, 10, 60, 392, 2688, 19008, 137280, …
  (−∞, 0]nonnegative
• A038323 → x ↦ x+1
  1 · 20, 9 · 400, 360, 81 · 8000, 10800, 4860, 729 … Σ 1, 29, 841, 24389, 707281, 20511149, …
  (−∞, −1]nonnegativerational roots