Proof methods / preserver_image

Image under a real-rootedness preserver

8,704 sequences

• A123519 → basis A013611 → D+1
  67, 184, 64 · 345, 1712, 2240, 512 … Σ 315, 4809, 69881, 982571, 13494179, …
  (−∞, 0]nonnegative
• basis-map coefficients of A026729 → basis A013609 → (θ+1)²
  1 · 1, 8 · 1, 16, 36 · 1, 24, 108, 128 … Σ 1, 9, 53, 261, 1161, 4833, 19197, …
  (−∞, 0]nonnegative
• A142459 → x ↦ x/(x+1)
  1 · 1, 2 · 1, 12, 12 · 1, 62, 180, 120 … Σ 1, 3, 25, 363, 7345, 190803, 6056905, …
  [−1, 0]nonnegative
• A026374 → θ+1 → x ↦ x+1
  1 · 3, 2 · 10, 12, 3 · 25, 44, 24, 4 … Σ 1, 5, 25, 97, 429, 1529, 6413, 21901, …
  (−∞, −1]nonnegative
• A391533 → Veronese 2 → (θ+1)²
  4, 4 · 4, 20 · 4, 52, 9 · 4, 100, 63 … Σ 8, 24, 65, 167, 418, 1022, 2452, 5792, …
  (−∞, 0]nonnegative
• A038320 → basis A013609 → (θ+1)²
  289, 1632, 1296 · 4913, 41616, 66096, 27648 … Σ 3217, 140273, 5672545, 218062049, …
  (−∞, 0]nonnegative
• basis-map coefficients of A030528, shifted → basis A013611
  1 · -1, -4 · 1, 8, 16 · -1, -12, -48, -64 … Σ 1, -5, 25, -125, 625, -3125, 15625, …
  [−1, 0]rational roots
• A253284 → D+1
  1 · 4, 2 · 24, 42, 12 · 168, 624, 600, 120 … Σ 1, 6, 78, 1512, 38520, 1211760, …
  (−∞, 0]nonnegative
• A013610 → D+1
  1 · 4, 3 · 7, 24, 9 · 10, 63, 108, 27 … Σ 1, 7, 40, 208, 1024, 4864, 22528, …
  (−∞, 0]nonnegativerational roots
• A132812 → D
  2 · 9, 6 · 24, 48, 12 · 50, 200, 150, 20 … Σ 0, 2, 15, 84, 420, 1980, 9009, 40040, …
  (−∞, 0]nonnegative
• A038333 → reverse
  49, 168, 144 · 343, 1764, 3024, 1728 … Σ 361, 6859, 130321, 2476099, 47045881, …
  (−∞, 0]nonnegativerational roots
• A181543 → θ+1
  1 · 1, 2 · 1, 16, 3 · 1, 54, 81, 4 … Σ 1, 3, 20, 140, 1038, 7882, 60736, …
  (−∞, 0]nonnegative
• A111125 → basis A013610 → D+1
  1 · 7, 3 · 32, 39, 9 · 122, 273, 171, 27 … Σ 1, 10, 80, 593, 4195, 28756, 192698, …
  (−∞, 0]nonnegative
• A143495 → reverse → D
  3 · 7, 18 · 12, 74, 81 · 18, 194, 525, 324 … Σ 0, 3, 25, 167, 1061, 6754, 43996, …
  (−∞, 0]nonnegative
• A038303 → basis A013609 → θ+1
  1 · 11, 4 · 121, 88, 12 · 1331, 1452, 396, 32 … Σ 1, 15, 221, 3211, 46137, 656903, …
  (−∞, 0]nonnegativerational roots
• A109692 → basis A013609 → basis A007318
  1 · 4, 2 · 40, 44, 12 · 640, 1104, 632, 120 … Σ 1, 6, 96, 2496, 89856, 4133376, …
  (−∞, −1]nonnegativerational roots
• A139548 → basis A013609 → D+1
  1 · 24, 32, 8 · 320, 1024, 1152, 512, 64 … Σ 1, 64, 3072, 131072, 5242880, …
  (−∞, 0]nonnegativerational roots
• A007318 → Veronese 2 (j=1) → (θ+1)²
  1 · 2 · 3, 4 · 4, 16 … Σ 0, 1, 2, 7, 20, 54, 140, 352, …
  (−∞, 0]nonnegative
• chebyshev_u → x ↦ x+1 → reverse
  1 · 2, 2 · 4, 8, 3 · 8, 24, 20, 4 … Σ 1, 4, 15, 56, 209, 780, 2911, 10864, …
  (−∞, 0]nonnegative
• A127648 → Veronese 2 (j=1) → θ+1
  2 · 0, 8 · 0, 0, 18 · 0, 0, 0, 32 … Σ 0, 0, 2, 0, 8, 0, 18, 0, …
  (−∞, 0]nonnegativerational roots
• A008288 → basis A007318
  1 · 2, 1 · 5, 5, 1 · 12, 18, 8, 1 … Σ 1, 3, 11, 39, 139, 495, 1763, 6279, …
  (−∞, −1]nonnegative
• A257618 → θ+1
  1 · 2, 4 · 4, 80, 12 · 8, 944, 1416, 32 … Σ 1, 6, 96, 2400, 80640, 3386880, …
  (−∞, 0]nonnegative
• basis-map coefficients of A030528, shifted → D → (θ+1)²
  -1 · 0, 8 · 0, 0, -27 · 0, 0, 0, 64 … Σ 0, -1, 8, -27, 64, -125, 216, -343, …
  (−∞, 0]rational roots
• A038331 → reverse
  25, 120, 144 · 125, 900, 2160, 1728 … Σ 289, 4913, 83521, 1419857, 24137569, …
  (−∞, 0]nonnegativerational roots
• A038321 → basis A013610 → x ↦ x/(x+1)
  324, 1404, 1521 · 5832, 37908, 82134, 59319 … Σ 3249, 185193, 10556001, 601692057, …
  [−1, 0]nonnegativerational roots
• A088996 → basis A013611 → reverse
  1 · 4, 1 · 32, 20, 3 · 384, 400, 136, 15 … Σ 1, 5, 55, 935, 21505, 623645, 21827575, …
  (−∞, 0]nonnegativerational roots
• A114687 → basis A013610 → D
  6 · 42, 72 · 252, 864, 648 · 1452, 7488, 11664, 5184 … Σ 0, 6, 114, 1764, 25788, 369690, …
  (−∞, 0]nonnegative
• A008292 → γ (scale 1/2) (shift +1) → D → x ↦ x+1
  1 · 4 · 19, 8 · 94, 68 … Σ 0, 0, 1, 4, 27, 162, 1185, 9144, …
  (−∞, −1]nonnegative
• A030528 → D
  1 · 2, 2 · 1, 6, 3 · 0, 6, 12, 4 … Σ 0, 1, 4, 10, 22, 45, 88, 167, …
  (−∞, 0]nonnegative
• A013622 → basis A013611 → D+1
  1 · 28, 20 · 384, 1120, 400 … Σ 1, 48, 1904, 68992, 2370816, 78675968, …
  (−∞, 0]nonnegativerational roots
• A008278 → x ↦ x+1 (shift +1) → reverse → x ↦ x+1
  1 · 3, 2 · 11, 15, 5 · 49, 101, 68, 15 … Σ 1, 5, 31, 233, 2047, 20417, 226711, …
  (−∞, −1]nonnegative
• A038337 → basis A007318 → D+1
  1035, 748, 121 · 29624, 34155, 12342, 1331 … Σ 1904, 77452, 3065712, 118933904, …
  (−∞, 0]nonnegativerational roots
• A142963 → (θ+1)²
  1 · 1, 8 · 1, 40, 36 · 1, 120, 648, 128 … Σ 1, 9, 77, 897, 12765, 208929, 3866589, …
  (−∞, 0]nonnegative
• A347056 → x ↦ x/(x+1)
  1 · 3, 7 · 6, 28, 32 · 10, 70, 160, 120 … Σ 1, 10, 66, 360, 1755, 7938, 34020, …
  [−1, 0]nonnegativerational roots
• A207824 → reverse
  1 · 1, 5 · 1, 10, 24 · 1, 15, 73, 115 … Σ 1, 6, 35, 204, 1189, 6930, 40391, …
  (−1/3, 0]nonnegative
• A142460 → x ↦ x/(x+1)
  1 · 1, 2 · 1, 14, 14 · 1, 86, 252, 168 … Σ 1, 3, 29, 507, 12461, 395643, 15414029, …
  [−1, 0]nonnegative
• A100861 → basis A007318 → (θ+1)²
  1 · 1 · 2, 4 · 4, 12 … Σ 1, 1, 6, 16, 85, 321, 1726, 7876, …
  (−∞, 0]nonnegative
• A115951 → (θ+1)²
  1 · 0, 8 · 0, 8, 54 · 0, 0, 108, 320 … Σ 1, 8, 62, 428, 2764, 17032, 101456, …
  (−∞, 0]nonnegative
• A038334 → D
  192, 128 · 3456, 4608, 1536 … Σ 320, 9600, 256000, 6400000, 153600000, …
  (−∞, 0]nonnegativerational roots
• A386789 → x ↦ x+1
  1 · 2, 2 · 9, 15, 6 · 44, 104, 80, 20 … Σ 1, 4, 30, 248, 2150, 19164, 173950, …
  (−∞, −1]nonnegative
• A102365 → x ↦ x+1
  1 · 1 · 2, 1 · 7, 7, 1 … Σ 1, 1, 3, 15, 105, 945, 10395, 135135, …
  (−∞, −1]nonnegative
• A207607 → basis A013609 → D+1
  1 · 7, 4 · 26, 34, 8 · 87, 186, 108, 16 … Σ 1, 11, 68, 397, 2243, 12380, 67141, …
  (−∞, 0]nonnegative
• A327997 → x ↦ x+1 → reverse
  1 · 1, 4 · 1, 9, 17 · 1, 15, 65, 78 … Σ 1, 5, 27, 159, 1029, 7353, 58095, …
  (−∞, 0]nonnegative
• A130123 → basis A008277 → x ↦ x+1
  1 · 4, 2 · 20, 20, 4 · 120, 176, 72, 8 … Σ 1, 6, 44, 376, 3632, 38880, 454848, …
  (−∞, −1]nonnegative
• A130534 → basis A013610 → D+1
  1 · 5, 3 · 21, 33, 9 · 102, 240, 162, 27 … Σ 1, 8, 63, 531, 4878, 48942, 534780, …
  (−∞, 0]nonnegative
• A075499 → x ↦ x+1
  29, 14, 1 · 201, 163, 27, 1 · 1657, 1884, 526, 44, 1 … Σ 44, 392, 4112, 49248, 659136, 9715840, …
  (−∞, −1]nonnegative
• A232535 → reverse → x ↦ x/(x+1)
  1 · 2, 3 · 3, 14, 12 · 4, 37, 80, 48 … Σ 1, 5, 29, 169, 985, 5741, 33461, …
  [−1, 0]nonnegative
• A178822 → x ↦ x+1 → D
  6 · 84, 42 · 672, 672, 168 · 4032, 6048, 3024, 504 … Σ 0, 6, 126, 1512, 13608, 102060, 673596, …
  (−∞, 0]nonnegativerational roots
• A120910 → basis A013610 → (θ+1)²
  3 · 9, 36 · 27, 216, 243 · 81, 972, 2187, 1296 … Σ 3, 45, 486, 4536, 38880, 314928, …
  (−∞, 0]nonnegative
• A113953 → x ↦ x−1
  1 · -1, 1 · -1, 0, 1 · 3, -5, 1, 1 … Σ 1, 0, 0, 0, 0, 0, 0, 0, …
  (−7, 1]