Proof methods / preserver_image

Image under a real-rootedness preserver

8,704 sequences

• A085880 → basis A013611 → x ↦ x/(x+1)
  1 · 2, 6 · 8, 48, 72 · 40, 360, 1080, 1080 … Σ 1, 8, 128, 2560, 57344, 1376256, …
  [−1, 0]nonnegativerational roots
• A232535 → basis A013610 → D
  6 · 42, 54 · 240, 666, 324 · 1248, 5328, 6156, 1620 … Σ 0, 6, 96, 1230, 14352, 158694, 1693968, …
  (−∞, 0]nonnegative
• A038279 → basis A013609 → D
  2 · 36, 8 · 486, 216, 24 · 5832, 3888, 864, 64 … Σ 0, 2, 44, 726, 10648, 146410, 1932612, …
  (−∞, 0]nonnegativerational roots
• A113953 → x ↦ x−7
  1 · -7, 1 · 35, -12, 1 · -147, 91, -17, 1 … Σ 1, -6, 24, -72, 144, 0, -1728, 10368, …
  (−1, 7]
• A179900 → D
  -1 · -10, 2 · -73, 30, -3 · -470, 294, -60, 4 … Σ 0, -1, -8, -46, -232, -1091, -4912, …
  (−∞, ∞)
• A059473 → x ↦ x+1 → D
  2 · 18, 8 · 120, 112, 24 · 712, 1016, 456, 64 … Σ 0, 2, 26, 256, 2248, 18528, 146688, …
  (−∞, 0]nonnegative
• A159854 → basis A013610 → D+1
  7, 24, 9 · 17, 87, 117, 27 · 40, 270, 603, 486, 81 … Σ 40, 248, 1480, 8600, 49000, 275000, …
  (−∞, 0]nonnegative
• A100862 → x ↦ x+1 → reverse
  1 · 1, 2 · 1, 5, 5 · 1, 9, 21, 14 … Σ 1, 3, 11, 45, 201, 963, 4899, 26253, …
  (−∞, 0]nonnegative
• A039755 → reverse → θ+1
  1 · 1, 2 · 1, 8, 3 · 1, 18, 39, 4 … Σ 1, 3, 12, 62, 372, 2492, 18384, 147800, …
  (−∞, 0]nonnegative
• A290319 → basis A013610 → D+1
  1 · 5, 3 · 36, 42, 9 · 396, 600, 243, 27 … Σ 1, 8, 87, 1266, 23277, 518652, …
  (−∞, 0]nonnegative
• A062196 → D → (θ+1)²
  3 · 8, 48 · 15, 240, 270 · 24, 720, 2160, 960 … Σ 0, 3, 56, 525, 3864, 24990, 148896, …
  (−∞, 0]nonnegative
• A028338 → basis A013611 → x ↦ x+1
  1 · 6, 4 · 48, 56, 16 · 480, 752, 384, 64 … Σ 1, 10, 120, 1680, 26880, 483840, …
  (−∞, −1]nonnegativerational roots
• A081578 → basis A013610 → D
  3 · 21, 18 · 90, 216, 81 · 366, 1404, 1377, 324 … Σ 0, 3, 39, 387, 3471, 29211, 236583, …
  (−∞, 0]nonnegative
• A030528 → basis A013610 → D
  3 · 12, 18 · 30, 108, 81 · 66, 378, 648, 324 … Σ 0, 3, 30, 219, 1416, 8568, 49728, …
  (−∞, 0]nonnegative
• A059473 → basis A013609 → basis A007318
  1 · 8, 4 · 70, 68, 16 · 608, 880, 416, 64 … Σ 1, 12, 154, 1968, 25156, 321552, …
  (−∞, −1]nonnegative
• A156992 → basis A013611 → x ↦ x/(x+1)
  1 · 4, 12 · 24, 144, 216 · 192, 1728, 5184, 5184 … Σ 1, 16, 384, 12288, 491520, 23592960, …
  [−1, 0]nonnegativerational roots
• A178821 → θ+1
  1 · 5, 10 · 15, 60, 45 · 35, 210, 315, 140 … Σ 1, 15, 120, 700, 3360, 14112, 53760, …
  (−∞, 0]nonnegativerational roots
• A038284 → basis A013610 → x ↦ x/(x+1)
  196, 896, 1024 · 2744, 18816, 43008, 32768 … Σ 2116, 97336, 4477456, 205962976, …
  [−1, 0]nonnegativerational roots
• A225468 → D
  1 · 7, 2 · 39, 30, 3 · 203, 318, 78, 4 … Σ 0, 1, 9, 72, 603, 5481, 54270, 582471, …
  (−∞, 0]nonnegative
• A034867 → x ↦ x+1
  1 · 2 · 4, 1 · 8, 4 … Σ 1, 2, 5, 12, 29, 70, 169, 408, …
  (−∞, −1]nonnegative
• A011973 → basis A013611 → θ+1
  1 · 1 · 2, 8 · 3, 16 … Σ 1, 1, 10, 19, 93, 232, 861, 2405, …
  (−∞, 0]nonnegative
• A038331 → basis A013609 → (θ+1)²
  289, 1360, 900 · 4913, 34680, 45900, 16000 … Σ 2549, 101493, 3768201, 133431057, …
  (−∞, 0]nonnegative
• A003506 → γ
  1 · 2 · 3 · 4 … Σ 1, 2, 3, 4, 5, 6, 7, 8, …
  (−∞, −1][−1, 0][−3−2√2, −3+2√2]+2
• A125662 → basis A013611 → reverse
  1 · 4, 4 · 16, 32, 15 · 64, 192, 184, 56 … Σ 1, 8, 63, 496, 3905, 30744, 242047, …
  (−∞, 0]nonnegative
• A269939 → θ+1
  1 · 0, 2 · 0, 2, 9 · 0, 2, 30, 60 … Σ 1, 2, 11, 92, 1022, 14100, 231996, …
  (−∞, 0]nonnegative
• A116666 → Veronese 2 → x ↦ x+1
  1 · 1 · 6, 5 · 16, 15 … Σ 1, 1, 11, 31, 97, 281, 795, 2199, …
  (−∞, −1]nonnegative
• basis-map coefficients of A297191, shifted → basis A013610 → reverse
  1 · 9, 6, 1 · 81, 108, 54, 12, 1 … Σ 1, 16, 256, 4096, 65536, 1048576, …
  (−∞, −1]nonnegativerational roots
• A103327 → (θ+1)²
  1 · 3, 4 · 5, 40, 9 · 7, 140, 189, 16 … Σ 1, 7, 54, 352, 2080, 11520, 60928, …
  (−∞, 0]nonnegative
• A062190 → D
  6 · 14, 42 · 24, 168, 168 · 36, 432, 1008, 504 … Σ 0, 6, 56, 360, 1980, 10010, 48048, …
  (−∞, 0]nonnegative
• A125092 → reverse → D
  1 · 8, 2 · 27, 24, 3 · 64, 108, 48, 4 … Σ 0, 1, 10, 54, 224, 800, 2592, 7840, …
  (−∞, 0]nonnegative
• A027465 → D → D+1
  1 · 8, 2 · 45, 24, 3 · 216, 180, 48, 4 … Σ 0, 1, 10, 72, 448, 2560, 13824, 71680, …
  (−∞, 0]nonnegativerational roots
• A052553 → D → x ↦ x+1
  1 · 2 · 5, 2 · 10, 6 … Σ 0, 0, 1, 2, 7, 16, 41, 94, …
  (−∞, −1]nonnegative
• A290319 → basis A013611 → D
  4 · 32, 32 · 368, 576, 192 · 5632, 11008, 6144, 1024 … Σ 0, 4, 64, 1136, 23808, 584256, …
  (−∞, 0]nonnegative
• A008288 → basis A013610 → D
  3 · 15, 18 · 54, 144, 81 · 174, 720, 891, 324 … Σ 0, 3, 33, 279, 2109, 14979, 102249, …
  (−∞, 0]nonnegative
• A110441 → basis A013610 → reverse
  1 · 3, 4 · 9, 24, 14 · 27, 108, 132, 48 … Σ 1, 7, 47, 315, 2111, 14147, 94807, …
  (−∞, 0]nonnegative
• A008292 → γ (scale 1/4) (shift +1) → D
  2 · 16 · 88, 32 · 416, 544 … Σ 0, 0, 2, 16, 120, 960, 8400, 80640, …
  (−∞, 0]nonnegative
• A207824 → x ↦ x+1 → θ+1
  1 · 6, 2 · 35, 24, 3 · 204, 212, 54, 4 … Σ 1, 8, 62, 474, 3585, 26876, 200003, …
  (−∞, 0]nonnegative
• A120909 → basis A013610 → reverse
  3 · 18, 9 · 108, 108, 27 · 648, 972, 486, 81 … Σ 3, 27, 243, 2187, 19683, 177147, …
  (−∞, −1]nonnegativerational roots
• A257613 → θ+1
  1 · 4, 8 · 16, 96, 48 · 64, 832, 1248, 256 … Σ 1, 12, 160, 2400, 40320, 752640, …
  (−∞, 0]nonnegative
• A034870 → basis A013611 → x ↦ x/(x+1)
  1 · 4, 24, 36 · 16, 192, 864, 1728, 1296 … Σ 1, 64, 4096, 262144, 16777216, …
  [−1, 0]nonnegativerational roots
• A159854 → basis A013611 → D
  8, 32 · 20, 128, 192 · 48, 416, 1152, 1024 … Σ 40, 340, 2640, 19440, 138240, 959040, …
  (−∞, 0]nonnegativerational roots
• A165253 → θ+1
  1 · 1 · 1, 2 · 1, 6, 3 … Σ 1, 1, 3, 10, 32, 99, 299, 887, …
  (−∞, 0]nonnegative
• basis-map coefficients of A021012 → basis A008277 → D+1
  1 · -2, -1 · 8, 10, 2 · -48, -114, -54, -6 … Σ 1, -3, 20, -222, 3624, -80880, 2349360, …
  (−∞, 0]
• A225466 → θ+1
  1 · 2, 6 · 4, 42, 27 · 8, 234, 405, 108 … Σ 1, 8, 73, 755, 8740, 111761, 1560817, …
  (−∞, 0]nonnegative
• A201637 → reverse (shift +1) → reverse
  1 · 1 · 1, 2 · 1, 8, 6 … Σ 1, 1, 3, 15, 105, 945, 10395, 135135, …
  (−∞, 0]nonnegative
• A026729 → basis A013609 → θ+1
  1 · 1, 4 · 2, 12, 12 · 3, 28, 60, 32 … Σ 1, 5, 26, 123, 561, 2484, 10773, 45981, …
  (−∞, 0]nonnegative
• A166340 → D
  8, 2 · 19, 38, 3 · 42, 228, 126, 4 … Σ 10, 60, 400, 3000, 25200, 235200, …
  (−∞, 0]nonnegative
• A207607 → basis A007318 → D
  2 · 9, 4 · 33, 30, 6 · 111, 152, 63, 8 … Σ 0, 2, 13, 69, 334, 1532, 6783, 29291, …
  (−∞, 0]nonnegative
• A033282 → x ↦ x+1 → (θ+1)²
  1 · 3, 8 · 11, 60, 45 · 45, 372, 567, 224 … Σ 1, 11, 116, 1208, 12503, 128885, …
  (−∞, 0]nonnegative
• A172431 → basis A013609 → D
  4 · 20, 24 · 76, 176, 96 · 260, 888, 960, 320 … Σ 0, 4, 44, 348, 2428, 15896, 100152, …
  (−∞, 0]nonnegative