Proof methods / preserver_image

Image under a real-rootedness preserver

8,704 sequences

• A038320 → basis A013610 → reverse
  324, 612, 289 · 5832, 16524, 15606, 4913 … Σ 1225, 42875, 1500625, 52521875, …
  (−∞, 0]nonnegativerational roots
• A133087 → x ↦ x+1 → D+1
  1 · 4, 1 · 8, 6, 1 · 28, 30, 10, 1 … Σ 1, 5, 15, 69, 189, 837, 2187, 9477, …
  (−∞, 0]nonnegative
• A091044 → basis A013611 → D
  8 · 64, 96 · 384, 1280, 768 … Σ 0, 8, 160, 2432, 33280, 430080, …
  (−∞, 0]nonnegative
• A178821 → Veronese 2 → D+1
  1 · 5 · 30, 15 · 140, 105 … Σ 1, 5, 45, 245, 1120, 4536, 16800, …
  (−∞, 0]nonnegative
• A166961 → x ↦ x/(x+1)
  1 · 1, 2 · 1, 11, 11 · 1, 62, 163, 103 … Σ 1, 3, 23, 329, 6913, 202811, 7861271, …
  [−1, 0]nonnegative
• A131431 → D+1
  1 · 4, 4 · 0, 14, 7 · 0, 0, 30, 10 … Σ 1, 8, 21, 40, 65, 96, 133, 176, …
  (−∞, 0]nonnegativerational roots
• A038335 → θ+1
  1 · 12, 18 · 144, 432, 243 · 1728, 7776, 8748, 2916 … Σ 1, 30, 819, 21168, 527877, 12835746, …
  (−∞, 0]nonnegativerational roots
• A152198 → basis A013610 → θ+1
  1 · 1 · 2, 6 · 2, 6 … Σ 1, 1, 8, 8, 55, 55, 350, 350, …
  (−∞, 0]nonnegativerational roots
• A062264 → (θ+1)²
  1 · 1, 20 · 1, 48, 135 · 1, 84, 567, 560 … Σ 1, 21, 184, 1212, 6975, 37147, 188188, …
  (−∞, 0]nonnegative
• A059364 → basis A013611 → x ↦ x/(x+1)
  1 · 3, 7 · 15, 74, 91 · 105, 803, 2043, 1729 … Σ 1, 10, 180, 4680, 159120, 6683040, …
  [−1, 0]nonnegativerational roots
• A122542 → x ↦ x+1 → x ↦ x/(x+1)
  1 · 1, 2 · 3, 10, 8 · 7, 34, 54, 28 … Σ 1, 3, 21, 123, 741, 4443, 26661, …
  [−1, 0]nonnegative
• A079510 → D+1
  1 · 2, 2 · 3, 15, 6 · 0, 40, 92, 24 … Σ 1, 4, 24, 156, 1165, 9780, 91448, …
  (−∞, 0]nonnegative
• A114687 → reverse → x ↦ x/(x+1)
  1 · 2, 3 · 4, 14, 11 · 8, 48, 84, 45 … Σ 1, 5, 29, 185, 1257, 8925, 65445, …
  [−1, 0]nonnegative
• A011973 → basis A013609 → D
  2 · 4 · 10, 8 · 20, 24 … Σ 0, 0, 2, 4, 18, 44, 136, 348, …
  (−∞, 0]nonnegative
• A049020 → x ↦ x+1 → reverse
  1 · 1, 2 · 1, 5, 6 · 1, 9, 25, 22 … Σ 1, 3, 12, 57, 309, 1866, 12351, 88563, …
  (−∞, 0]nonnegative
• A253283 → θ+1
  1 · 0, 2 · 0, 4, 9 · 0, 6, 36, 40 … Σ 1, 2, 13, 82, 513, 3186, 19661, 120674, …
  (−∞, 0]nonnegative
• A038259 → basis A007318 → x ↦ x+1
  1 · 16, 5 · 256, 160, 25 · 4096, 3840, 1200, 125 … Σ 1, 21, 441, 9261, 194481, 4084101, …
  (−∞, −1]nonnegativerational roots
• A103327 → basis A013610 → x ↦ x/(x+1)
  1 · 4, 7 · 16, 68, 61 · 64, 432, 888, 547 … Σ 1, 11, 145, 1931, 25729, 342827, …
  [−1, 0]nonnegative
• A038320 → basis A013609 → reverse
  144, 408, 289 · 1728, 7344, 10404, 4913 … Σ 841, 24389, 707281, 20511149, …
  (−∞, 0]nonnegativerational roots
• A028338 → basis A013610 → x ↦ x/(x+1)
  1 · 2, 5 · 8, 34, 35 · 48, 276, 516, 315 … Σ 1, 7, 77, 1155, 21945, 504735, …
  [−1, 0]nonnegativerational roots
• A137597: Triangle read by rows: A008277 * A007318.
  1 · 2, 1 · 5, 5, 1 · 15, 22, 9, 1 … Σ 1, 3, 11, 47, 227, 1215, 7107, 44959, …
  (−∞, −1]nonnegative
• A290316 → x ↦ x+1
  1 · 7, 6 · 139, 228, 90 · 4609, 11142, 8694, 2160 … Σ 1, 13, 457, 26605, 2168905, 227515885, …
  (−∞, −1]nonnegative
• A098158 → D
  1 · 1, 2 · 0, 6, 3 · 0, 2, 18, 4 … Σ 0, 1, 3, 9, 24, 60, 144, 336, …
  (−∞, 0]nonnegative
• A100861 → D → θ+1
  1 · 3 · 6, 12 · 10, 60 … Σ 0, 0, 1, 3, 18, 70, 330, 1386, …
  (−∞, 0]nonnegative
• A027465 → basis A008277 → D
  1 · 9, 2 · 61, 30, 3 · 369, 302, 66, 4 … Σ 0, 1, 11, 94, 741, 5691, 43642, 338535, …
  (−∞, 0]nonnegative
• A124848 → reverse
  1 · 4, 1 · 10, 8, 1 · 20, 30, 12, 1 … Σ 1, 5, 19, 63, 192, 552, 1520, 4048, …
  (−∞, 0]nonnegative
• A132393 → θ+1
  1 · 0, 2 · 0, 2, 3 · 0, 4, 9, 4 … Σ 1, 2, 5, 17, 74, 394, 2484, 18108, …
  (−∞, 0]nonnegative
• A008288 → basis A013611 → reverse
  1 · 4, 2 · 16, 20, 5 · 64, 128, 72, 12 … Σ 1, 6, 41, 276, 1861, 12546, 84581, …
  (−∞, 0]nonnegative
• A048854 → x ↦ x/(x+1)
  1 · 2, 3 · 12, 36, 25 · 120, 540, 750, 331 … Σ 1, 5, 73, 1741, 57233, 2389141, …
  [−1, 0]nonnegative
• A122542 → θ+1
  1 · 0, 2 · 0, 4, 3 · 0, 4, 12, 4 … Σ 1, 2, 7, 20, 57, 158, 431, 1160, …
  (−∞, 0]nonnegative
• A038334 → basis A013610 → basis A007318
  1936, 2112, 576 · 85184, 139392, 76032, 13824 … Σ 4624, 314432, 21381376, 1453933568, …
  (−∞, −1]nonnegativerational roots
• A391403 → x ↦ x+1 → D
  2 · 6 · 24, 12 · 80, 60 … Σ 0, 0, 2, 6, 36, 140, 630, 2562, …
  (−∞, 0]nonnegative
• A048854 → θ+1
  1 · 2, 2 · 12, 24, 3 · 120, 360, 90, 4 … Σ 1, 4, 39, 574, 11149, 267576, 7625779, …
  (−∞, 0]nonnegative
• A026729 → θ+1 → (θ+1)²
  1 · 0, 8 · 0, 8, 27 · 0, 0, 54, 64 … Σ 1, 8, 35, 118, 344, 908, 2237, 5230, …
  (−∞, 0]nonnegative
• A225470 → basis A013610 → D
  3 · 27, 18 · 297, 324, 81 · 4050, 5670, 2430, 324 … Σ 0, 3, 45, 702, 12474, 253692, 5852412, …
  (−∞, 0]nonnegative
• A013610 → basis A013611 → (θ+1)²
  1 · 4, 48 · 16, 384, 1296 · 64, 2304, 15552, 27648 … Σ 1, 52, 1696, 45568, 1097728, 24641536, …
  (−∞, 0]nonnegative
• A131431 → reverse
  1 · 4 · 7 · 10 … Σ 1, 4, 7, 10, 13, 16, 19, 22, …
  (−∞, −1][−1, 0][−3−2√2, −3+2√2]+2
• A201701 → (θ+1)²
  1 · 1 · 2, 4 · 4, 12 … Σ 1, 1, 6, 16, 49, 141, 402, 1128, …
  (−∞, 0]nonnegative
• A161198 → basis A007318
  1 · 3, 2 · 15, 16, 4 · 105, 142, 60, 8 … Σ 1, 5, 35, 315, 3465, 45045, 675675, …
  (−∞, −1]nonnegativerational roots
• basis-map coefficients of A371080, shifted → D
  1 · 3, 2 · 18, 18, 3 · 162, 198, 54, 4 … Σ 0, 1, 5, 39, 418, 5714, 95064, 1864456, …
  (−∞, 0]nonnegative
• A100861 → basis A013609 → D
  2 · 6 · 24, 24 · 80, 120 … Σ 0, 0, 2, 6, 48, 200, 1380, 6972, …
  (−∞, 0]nonnegative
• A122542 → reverse → D+1
  1 · 1 · 3, 2 · 5, 8, 2 … Σ 1, 1, 5, 15, 45, 129, 361, 991, …
  (−∞, 0]nonnegative
• A049020 → x ↦ x/(x+1)
  1 · 1, 2 · 2, 7, 6 · 5, 25, 41, 22 … Σ 1, 3, 15, 93, 681, 5691, 53079, 544053, …
  [−1, 0]nonnegative
• A038303 → basis A007318 → basis A013610
  1 · 12, 3 · 144, 72, 9 · 1728, 1296, 324, 27 … Σ 1, 15, 225, 3375, 50625, 759375, …
  (−∞, −1]nonnegativerational roots
• A094262 → reverse
  1 · 1, 2, 1 · 3, 10, 12, 6, 1 … Σ 1, 4, 32, 416, 7552, 176128, 5018624, …
  (−∞, 0]nonnegative
• A059473 → γ → D+1
  1 · 2 · 6, 2 · 16, 8 … Σ 1, 2, 8, 24, 76, 232, 704, 2112, …
  (−∞, 0]nonnegative
• A269945 → reverse
  1 · 1 · 1, 1 · 1, 5, 1 … Σ 1, 1, 2, 7, 37, 264, 2433, 27913, …
  (−∞, 0]nonnegative
• A019538 → (θ+1)²
  1 · 1, 8 · 1, 24, 54 · 1, 56, 324, 384 … Σ 1, 9, 79, 765, 8311, 100989, 1362439, …
  (−∞, 0]nonnegative
• A131689 → (θ+1)²
  1 · 0, 4 · 0, 4, 18 · 0, 4, 54, 96 … Σ 1, 4, 22, 154, 1306, 12994, 148282, …
  (−∞, 0]nonnegative
• A120986 → (θ+1)²
  1 · 2, 4 · 5, 24, 9 · 14, 112, 108, 16 … Σ 1, 6, 38, 250, 1677, 11368, 77520, …
  (−∞, 0]nonnegative