Proof methods / preserver_image

Image under a real-rootedness preserver

8,704 sequences

• A132393 → basis A013609 → reverse
  1 · 2, 1 · 4, 6, 2 · 8, 24, 22, 6 … Σ 1, 3, 12, 60, 360, 2520, 20160, 181440, …
  (−∞, 0]nonnegativerational roots
• A059340: Triangle T(n,k) of numbers with e.g.f. exp((exp((1+x)*y)-1)/(1+x)), k=0..n-1.
  A008278 → x ↦ x+1 (shift +1)
  1 · 2, 1 · 5, 5, 1 · 15, 23, 10, 1 … Σ 1, 3, 11, 49, 257, 1539, 10299, 75905, …
  (−∞, −1]nonnegative
• A052553 → basis A013609 → x ↦ x+1
  1 · 1 · 4, 2 · 7, 4 … Σ 1, 1, 6, 11, 41, 96, 301, 781, …
  (−∞, −1]nonnegative
• A038226 → basis A007318 → D+1
  297, 304, 64 · 4235, 7128, 3648, 512 … Σ 665, 15523, 349809, 7688939, 165898633, …
  (−∞, 0]nonnegativerational roots
• A147716 → basis A013610 → D
  3 · 90, 18 · 2025, 810, 81 · 40500, 24300, 4860, 324 … Σ 0, 3, 108, 2916, 69984, 1574640, …
  (−∞, 0]nonnegativerational roots
• A139548 → x ↦ x+1 → D+1
  1 · 16, 12, 2 · 192, 320, 192, 48, 4 … Σ 1, 30, 756, 17496, 384912, 8188128, …
  (−∞, 0]nonnegativerational roots
• A286785 → x ↦ x/(x+1)
  14, 42, 30 · 42, 198, 297, 143 … Σ 86, 680, 5722, 50260, 455534, 4228752, …
  [−1, 0]nonnegative
• A137597 → D+1 → x ↦ x/(x+1)
  1 · 3, 4 · 10, 27, 18 · 37, 151, 203, 90 … Σ 1, 7, 55, 481, 4633, 48655, 552271, …
  [−1, 0]nonnegative
• A038325 → basis A007318
  1 · 22, 11 · 484, 484, 121 · 10648, 15972, 7986, 1331 … Σ 1, 33, 1089, 35937, 1185921, 39135393, …
  (−∞, −1]nonnegativerational roots
• A113953 → basis A007318 → θ+1
  1 · 1, 2 · 3, 8, 3 · 5, 22, 21, 4 … Σ 1, 3, 14, 52, 200, 736, 2688, 9664, …
  (−∞, 0]nonnegative
• A269945 → (θ+1)²
  1 · 0, 4 · 0, 4, 9 · 0, 4, 45, 16 … Σ 1, 4, 13, 65, 442, 3907, 43305, 583092, …
  (−∞, 0]nonnegative
• A109983 → D
  1, 4 · 0, 2, 18, 24 · 0, 0, 3, 48, 150, 120 … Σ 0, 5, 44, 321, 2184, 14325, 91860, …
  (−∞, 0]nonnegative
• A099040 → basis A007318 → θ+1
  1 · 2, 4 · 6, 20, 12 · 16, 80, 96, 32 … Σ 1, 6, 38, 224, 1280, 7136, 39072, …
  (−∞, 0]nonnegative
• A063007 → basis A013610 → D
  6 · 54, 108 · 396, 1620, 1620 … Σ 0, 6, 162, 3636, 76140, 1537290, …
  (−∞, 0]nonnegative
• A026374 → θ+1 → θ+1
  1 · 1, 4 · 1, 12, 9 · 1, 16, 36, 16 … Σ 1, 5, 22, 69, 245, 665, 2150, 5425, …
  (−∞, 0]nonnegative
• A001263 → D → D
  2 · 12, 6 · 40, 60, 12 · 100, 300, 180, 20 … Σ 0, 0, 2, 18, 112, 600, 2970, 14014, …
  (−∞, 0]nonnegative
• A134991 → θ+1
  1 · 1, 6 · 1, 20, 45 · 1, 50, 315, 420 … Σ 1, 7, 66, 786, 11348, 192788, 3769328, …
  (−∞, 0]nonnegative
• A178820 → basis A013610 → (θ+1)²
  1 · 8, 48 · 40, 480, 810 · 160, 2880, 9720, 8640 … Σ 1, 56, 1330, 21400, 273875, 3010000, …
  (−∞, 0]nonnegative
• A145324 → basis A013611 → (θ+1)²
  1 · 3, 32 · 12, 272, 864 · 60, 2128, 14112, 24576 … Σ 1, 35, 1148, 40876, 1615576, 70878376, …
  (−∞, 0]nonnegative
• A091044 → basis A013609 → reverse
  1 · 4, 4 · 12, 32, 16 · 32, 160, 192, 64 … Σ 1, 8, 60, 448, 3344, 24960, 186304, …
  (−∞, 0]nonnegative
• A144698 → x ↦ x+1
  1 · 5, 4 · 30, 45, 16 · 210, 450, 305, 64 … Σ 1, 9, 91, 1029, 12931, 179349, 2726851, …
  (−∞, −1]nonnegative
• A143491 → basis A007318 → x ↦ x+1
  20, 9, 1 · 120, 74, 15, 1 · 840, 638, 179, 22, 1 … Σ 30, 210, 1680, 15120, 151200, 1663200, …
  (−∞, −1]nonnegativerational roots
• A038284 → basis A007318 → θ+1
  196, 336, 108 · 2744, 7056, 4536, 864 … Σ 640, 15200, 352000, 8000000, 179200000, …
  (−∞, 0]nonnegativerational roots
• Veronese parent of A098172 → θ+1
  0, 0, 3 · 0, 0, 0, 0, 5, 6 … Σ 3, 11, 32, 84, 208, 496, 1152, 2624, …
  (−∞, 0]nonnegativerational roots
• A013613 → D
  6 · 12, 72 · 18, 216, 648 · 24, 432, 2592, 5184 … Σ 0, 6, 84, 882, 8232, 72030, 605052, …
  (−∞, 0]nonnegativerational roots
• A081580 → γ → D+1
  1 · 1 · 6, 5 · 11, 10 … Σ 1, 1, 11, 21, 106, 266, 1001, 2811, …
  (−∞, 0]nonnegative
• A127773 → θ+1
  1 · 0, 6 · 0, 0, 18 · 0, 0, 0, 40 … Σ 1, 6, 18, 40, 75, 126, 196, 288, …
  [−1, 0]nonnegativerational roots
• A136572 → D
  1 · 0, 4 · 0, 0, 18 · 0, 0, 0, 96 … Σ 0, 1, 4, 18, 96, 600, 4320, 35280, …
  (−∞, 0]nonnegativerational roots
• A048993 → (θ+1)² → reverse
  1 · 4 · 9, 4 · 16, 27, 4 … Σ 1, 4, 13, 47, 188, 825, 3937, 20270, …
  (−∞, 0]nonnegative
• A099093 → basis A013609 → θ+1
  1 · 3, 12 · 12, 84, 108 · 45, 468, 1188, 864 … Σ 1, 15, 204, 2565, 30807, 358668, …
  (−∞, 0]nonnegative
• A038336 → x ↦ x/(x+1) → D+1
  672, 1496, 484 · 11232, 44352, 49368, 10648 … Σ 2652, 115600, 4795088, 192432384, …
  (−∞, 0]nonnegativerational roots
• A272866 → basis A013611 → D
  20, 32 · 200, 1120, 1920, 1024 … Σ 0, 52, 4264, 262236, 14335568, …
  (−∞, 0]nonnegative
• A156366 → θ+1
  1, 24, 27 · 1, 66, 297, 108 · 1, 156, 1782, 2808, 405 … Σ 52, 472, 5152, 65656, 956224, 15667072, …
  (−∞, 0]nonnegative
• A327997 → (θ+1)²
  1 · 3, 4 · 9, 28, 9 · 27, 152, 108, 16 … Σ 1, 7, 46, 303, 2071, 15015, 117152, …
  (−∞, 0]nonnegative
• A122542 → basis A013610 → D
  3 · 12, 18 · 39, 126, 81 · 120, 576, 810, 324 … Σ 0, 3, 30, 246, 1830, 12870, 87270, …
  (−∞, 0]nonnegative
• A143491 → basis A013611 → D+1
  40, 60, 16 · 248, 572, 384, 64 … Σ 116, 1268, 14696, 181816, 2403552, …
  (−∞, 0]nonnegative
• A225470 → basis A013609 → D
  2 · 18, 8 · 198, 144, 24 · 2700, 2520, 720, 64 … Σ 0, 2, 26, 366, 6004, 114388, 2497200, …
  (−∞, 0]nonnegative
• A063967 → basis A007318 → reverse
  1 · 1, 2 · 1, 5, 6 · 1, 8, 20, 16 … Σ 1, 3, 12, 45, 171, 648, 2457, 9315, …
  (−∞, 0]nonnegative
• A030528 → basis A013609 → x ↦ x/(x+1)
  1 · 2, 4 · 3, 14, 15 · 5, 35, 79, 57 … Σ 1, 6, 32, 176, 960, 5248, 28672, …
  [−1, 0]nonnegative
• A038333 → x ↦ x+1 → basis A007318
  676, 364, 49 · 17576, 14196, 3822, 343 … Σ 1089, 35937, 1185921, 39135393, …
  (−∞, −1]nonnegativerational roots
• A081579 → basis A013610 → reverse
  1 · 3, 2 · 9, 24, 8 · 27, 126, 108, 24 … Σ 1, 5, 41, 285, 2081, 14965, 108121, …
  (−∞, 0]nonnegative
• A027467 → x ↦ x+1 → x ↦ x/(x+1)
  1 · 16, 17 · 256, 544, 289 · 4096, 13056, 13872, 4913 … Σ 1, 33, 1089, 35937, 1185921, 39135393, …
  [−1, 0]nonnegativerational roots
• A038279 → basis A013609 → (θ+1)²
  1 · 9, 8 · 81, 144, 36 · 729, 1944, 972, 128 … Σ 1, 17, 261, 3773, 52393, 706761, …
  (−∞, 0]nonnegative
• A249139 → basis A007318 → D
  1 · 2 · 9, 2 · 22, 6 … Σ 0, 1, 2, 11, 28, 101, 278, 863, …
  (−∞, 0]nonnegative
• A318772 → x ↦ (1/243)x → x ↦ x+1
  1 · 3 · 9 · 27 … Σ 1, 3, 9, 27, 83, 255, 783, 2403, …
  (−∞, −1]nonnegative
• A038328 → basis A013609 → (θ+1)²
  196, 448, 144 · 2744, 9408, 6048, 1024 … Σ 788, 19224, 447120, 10054368, …
  (−∞, 0]nonnegative
• A391403 → (θ+1)²
  1 · 1 · 1, 8 · 1, 24 … Σ 1, 1, 9, 25, 103, 351, 1251, 4299, …
  (−∞, 0]nonnegative
• A225472 → D
  3 · 21, 36 · 117, 540, 486 · 609, 5724, 12636, 7776 … Σ 0, 3, 57, 1143, 26745, 729303, …
  (−∞, 0]nonnegative
• A133080 → D+1
  1 · 2, 1 · 0, 2, 1 · 0, 2, 4, 1 … Σ 1, 3, 3, 7, 5, 11, 7, 15, …
  (−∞, 0]nonnegative
• A154986 → D+1 → reverse
  1 · 1, 2 · 1, 6, 5 · 1, 14, 33, 12 … Σ 1, 3, 12, 60, 360, 2520, 20160, 181440, …
  (−∞, 0]nonnegative