Proof methods / preserver_image

Image under a real-rootedness preserver

8,704 sequences

• A257626 → D+1
  1 · 12, 6 · 144, 180, 36 · 1620, 4212, 2052, 216 … Σ 1, 18, 360, 8100, 204120, 5715360, …
  (−∞, 0]nonnegative
• A156992 → basis A008277 → x ↦ x+1
  1 · 6, 2 · 60, 42, 6 · 888, 960, 288, 24 … Σ 1, 8, 108, 2160, 59280, 2121120, …
  (−∞, −1]nonnegative
• A106246 → D+1 → reverse
  1 · 1, 3 · 1, 6, 5 · 1, 9, 15, 3 … Σ 1, 4, 12, 28, 55, 96, 154, 232, …
  (−∞, 0]nonnegative
• Veronese parent of A109446 → (θ+1)²
  0, 4 · 1, 4 · 0, 4, 18, 16 · 1, 12, 27, 16 … Σ 4, 5, 38, 56, 272, 432, 1696, 2816, …
  (−∞, 0]nonnegative
• A344565 → γ
  3 · 15 · 45 · 105 … Σ 3, 15, 45, 105, 210, 378, 630, 990, …
  (−∞, −1][−1, 0][−3−2√2, −3+2√2]+2
• A142075 → θ+1
  1 · 1, 4 · 1, 16, 12 · 1, 44, 132, 32 … Σ 1, 5, 29, 209, 1809, 18269, 210853, …
  (−∞, 0]nonnegative
• A046716 → basis A013610 → D+1
  1 · 5, 3 · 20, 33, 9 · 91, 273, 180, 27 … Σ 1, 8, 62, 571, 7247, 129266, 2994532, …
  (−∞, 0]nonnegative
• A103327 → θ+1
  1 · 3, 2 · 5, 20, 3 · 7, 70, 63, 4 … Σ 1, 5, 28, 144, 704, 3328, 15360, 69632, …
  (−∞, 0]nonnegative
• A094262 → θ+1
  1 · 1, 4, 3 · 1, 12, 36, 40, 15 … Σ 1, 8, 104, 1888, 44032, 1254656, …
  (−∞, 0]nonnegative
• A038301 → x ↦ x+1 → D
  440, 242 · 13200, 14520, 3993 … Σ 682, 31713, 1310804, 50793655, …
  (−∞, 0]nonnegativerational roots
• A075502 → x ↦ x/(x+1)
  49, 119, 71 · 343, 1372, 1757, 729 … Σ 239, 4201, 84617, 1988631, 53963799, …
  [−1, 0]nonnegative
• A207823 → basis A013610 → D+1
  1 · 8, 3 · 54, 48, 9 · 334, 489, 216, 27 … Σ 1, 11, 111, 1066, 9905, 89889, 801439, …
  (−∞, 0]nonnegative
• A105070 → (θ+1)²
  1 · 2 · 3, 8 · 4, 32 … Σ 1, 2, 11, 36, 121, 382, 1171, 3496, …
  (−∞, 0]nonnegative
• A249139 → basis A013609 → D
  2 · 4 · 18, 8 · 44, 24 … Σ 0, 2, 4, 26, 68, 280, 812, 2814, …
  (−∞, 0]nonnegative
• A114656 → reverse → D+1
  1 · 3, 2 · 7, 14, 4 · 13, 60, 48, 8 … Σ 1, 5, 25, 129, 681, 3653, 19825, …
  (−∞, 0]nonnegative
• type_b_eulerian → γ → D+1
  1 · 1 · 5, 4 · 21, 20 … Σ 1, 1, 9, 41, 385, 3393, 40041, 508233, …
  (−∞, 0]nonnegative
• A166341 → (θ+1)²
  1, 40, 9 · 1, 92, 207, 16 · 1, 200, 1242, 800, 25 … Σ 50, 316, 2268, 18432, 167760, 1692000, …
  (−∞, 0]nonnegative
• A257615 → x ↦ x/(x+1)
  1 · 5, 10 · 25, 120, 120 · 125, 1090, 2520, 1680 … Σ 1, 15, 265, 5415, 125905, 3285375, …
  [−1, 0]nonnegative
• A052553 → Veronese 2 → x ↦ x+1
  1 · 1 · 1 · 1 … Σ 1, 1, 1, 1, 3, 7, 13, 21, …
  (−∞, −1]nonnegative
• A209599 → θ+1
  1 · 2 · 3, 2 · 5, 6 … Σ 1, 2, 5, 11, 25, 55, 121, 263, …
  (−∞, 0]nonnegative
• A305540 → x ↦ x+1
  1 · 2, 1 · 3, 2 · 8, 10, 3 … Σ 1, 3, 5, 21, 37, 201, 365, 2433, …
  (−∞, −1]nonnegative
• A133087 → Veronese 2 (j=1) → x ↦ x+1
  1 · 2 · 6, 1 · 8, 4 … Σ 0, 1, 2, 7, 12, 41, 70, 239, …
  (−∞, −1]nonnegative
• A131689 → (θ+1)² → x ↦ x/(x+1)
  1 · 0, 4 · 0, 4, 22 · 0, 4, 62, 154 … Σ 1, 4, 26, 220, 2288, 28144, 399056, …
  [−1, 0]nonnegative
• A371081 → D
  1 · 52, 2 · 2948, 232, 3 · 203072, 24688, 648, 4 … Σ 0, 1, 54, 3183, 228412, 20146261, …
  (−∞, 0]nonnegative
• A136572 → (θ+1)² → θ+1
  1 · 0, 8 · 0, 0, 54 · 0, 0, 0, 384 … Σ 1, 8, 54, 384, 3000, 25920, 246960, …
  (−∞, 0]nonnegativerational roots
• A081579 → γ → (θ+1)²
  1 · 1 · 1, 16 · 1, 32 … Σ 1, 1, 17, 33, 193, 497, 1969, 5633, …
  (−∞, 0]nonnegative
• A122542 → θ+1 → θ+1
  1 · 0, 4 · 0, 8, 9 · 0, 8, 36, 16 … Σ 1, 4, 17, 60, 201, 640, 1969, 5896, …
  (−∞, 0]nonnegative
• A052553 → Veronese 2 (j=1) → x ↦ x+1
  1 · 2 · 3 · 4 … Σ 0, 0, 1, 2, 3, 4, 7, 14, …
  (−∞, −1]nonnegative
• A358735 → basis A007318
  1 · 2, 1 · 7, 8, 2 · 33, 60, 34, 6 … Σ 1, 3, 17, 133, 1313, 15623, 217409, …
  (−3, −1)nonnegative
• A059473 → γ → (θ+1)²
  1 · 2 · 4, 8 · 8, 32 … Σ 1, 2, 12, 40, 148, 504, 1696, 5568, …
  (−∞, 0]nonnegative
• A114655 → x ↦ x/(x+1)
  2 · 4, 6 · 8, 28, 22 · 16, 96, 168, 90 … Σ 2, 10, 58, 370, 2514, 17850, 130890, …
  [−1, 0]nonnegative
• A160562 → (θ+1)²
  1 · 1, 4 · 1, 40, 9 · 1, 364, 315, 16 … Σ 1, 5, 50, 696, 13344, 339728, 10805728, …
  (−∞, 0]nonnegative
• A122542 → x ↦ x/(x+1)
  1 · 0, 1 · 0, 2, 3 · 0, 2, 8, 7 … Σ 1, 1, 5, 17, 61, 217, 773, 2753, …
  [−1, 0]nonnegative
• A124860 → x ↦ x/(x+1)
  1 · 1, 2 · 3, 12, 12 · 5, 30, 60, 40 … Σ 1, 3, 27, 135, 891, 5103, 31347, …
  [−1, 0]nonnegativerational roots
• A156992 → basis A008277 → θ+1
  1 · 4, 4 · 24, 60, 18 · 192, 912, 648, 96 … Σ 1, 8, 102, 1848, 44640, 1378800, …
  (−∞, 0]nonnegative
• A120910 → basis A013611
  3 · 9, 12 · 27, 72, 48 · 81, 324, 432, 192 … Σ 3, 21, 147, 1029, 7203, 50421, 352947, …
  [−1, 0]nonnegativerational roots
• A038321 → basis A013609 → (θ+1)²
  324, 2016, 1764 · 5832, 54432, 95256, 43904 … Σ 4104, 199424, 8962048, 382205952, …
  (−∞, 0]nonnegative
• A062145 → D → θ+1
  4 · 10, 40 · 18, 180, 180 · 28, 504, 1260, 560 … Σ 0, 4, 50, 378, 2352, 13200, 69498, …
  (−∞, 0]nonnegative
• A207606 → x ↦ x+1 → reverse
  2, 11, 13 · 2, 17, 44, 34 · 2, 23, 93, 155, 89 … Σ 26, 97, 362, 1351, 5042, 18817, 70226, …
  (−1, 0]nonnegative
• A104684 → basis A013611 → D
  4 · 32, 32 · 228, 480, 192 · 1536, 4992, 4608, 1024 … Σ 0, 4, 64, 900, 12160, 160420, 2081088, …
  (−∞, 0]nonnegative
• A059344 → basis A013610 → x ↦ x+1
  1 · 1 · 9, 6 · 25, 18 … Σ 1, 1, 15, 43, 673, 3081, 50191, 308995, …
  (−∞, −1]nonnegative
• A144443 → (θ+1)²
  1 · 1, 4 · 1, 80, 9 · 1, 636, 1431, 16 … Σ 1, 5, 90, 2084, 61072, 2178900, …
  (−∞, 0]nonnegative
• A013610 → basis A013611 → θ+1
  1 · 4, 24 · 16, 192, 432 · 64, 1152, 5184, 6912 … Σ 1, 28, 640, 13312, 262144, 4980736, …
  (−∞, 0]nonnegativerational roots
• A144439 → (θ+1)²
  1 · 1, 4 · 1, 32, 9 · 1, 124, 279, 16 … Σ 1, 5, 42, 420, 5000, 69380, 1100944, …
  (−∞, 0]nonnegative
• A094638 → basis A013609 → x ↦ x/(x+1)
  1 · 2, 4 · 6, 26, 28 · 24, 164, 372, 280 … Σ 1, 6, 60, 840, 15120, 332640, 8648640, …
  [−1, 0]nonnegativerational roots
• A086645 → basis A007318 → D+1
  1 · 3, 1 · 16, 10, 1 · 80, 84, 21, 1 … Σ 1, 4, 27, 186, 1253, 8288, 54047, …
  (−∞, 0]nonnegative
• A199478 → θ+1
  1, 2 · 1, 6 · 1, 10, 6 · 1, 14, 24 … Σ 3, 7, 17, 39, 89, 199, 441, 967, …
  (−∞, 0]nonnegative
• A003506 → Veronese 2 → θ+1
  1 · 2 · 3, 6 · 4, 24 … Σ 0, 1, 2, 9, 28, 80, 216, 560, …
  (−∞, 0]nonnegative
• A038331 → x ↦ x+1
  289, 170, 25 · 4913, 4335, 1275, 125 … Σ 484, 10648, 234256, 5153632, 113379904, …
  (−∞, −1]nonnegativerational roots
• A055151 → basis A007318 → θ+1
  1 · 1 · 2, 2 · 4, 6 … Σ 1, 1, 4, 10, 35, 111, 386, 1324, …
  (−∞, 0]nonnegative