Proof methods / preserver_image

Image under a real-rootedness preserver

8,704 sequences

• A008292 → θ+1 (shift +2) → reverse
  3, 8, 1 · 4, 33, 22, 1 · 5, 104, 198, 52, 1 … Σ 12, 60, 360, 2520, 20160, 181440, …
  (−∞, 0]nonnegative
• A166962 → D
  1 · 12, 2 · 103, 138, 3 · 834, 4340, 948, 4 … Σ 0, 1, 14, 244, 6126, 203316, 8600272, …
  (−∞, 0]nonnegative
• A143491 → basis A008277 → x ↦ x+1
  21, 10, 1 · 136, 93, 18, 1 · 1045, 916, 258, 28, 1 … Σ 32, 248, 2248, 23272, 270400, 3479744, …
  (−∞, −1]nonnegative
• A063967 → basis A013609 → D+1
  1 · 4, 2 · 16, 18, 4 · 56, 104, 56, 8 … Σ 1, 6, 38, 224, 1280, 7136, 39072, …
  (−∞, 0]nonnegative
• A133087 → x ↦ x+1 → θ+1
  1 · 3, 2 · 4, 8, 3 · 12, 32, 21, 4 … Σ 1, 5, 15, 69, 189, 837, 2187, 9477, …
  (−∞, 0]nonnegative
• A159854 → basis A013610 → (θ+1)²
  1, 24, 81 · 2, 60, 324, 432 … Σ 106, 818, 5818, 39170, 253450, 1591250, …
  (−∞, 0]nonnegative
• A013622 → basis A013611 → θ+1
  1 · 8, 40 · 64, 640, 1200 · 512, 7680, 28800, 32000 … Σ 1, 48, 1904, 68992, 2370816, 78675968, …
  (−∞, 0]nonnegativerational roots
• basis-map coefficients of A026729 → D → θ+1
  1 · 0, 4 · 0, 0, 9 · 0, 0, 0, 16 … Σ 0, 1, 4, 9, 16, 25, 36, 49, …
  (−∞, 0]nonnegativerational roots
• A225473 → x ↦ x/(x+1)
  1 · 3, 7 · 9, 58, 81 · 27, 397, 1385, 1399 … Σ 1, 10, 148, 3208, 93328, 3398560, …
  [−1, 0)nonnegative
• A038271 → basis A007318
  1 · 12, 5 · 144, 120, 25 · 1728, 2160, 900, 125 … Σ 1, 17, 289, 4913, 83521, 1419857, …
  (−∞, −1]nonnegativerational roots
• A166972 → θ+1
  1 · 1, 2 · 1, 20, 3 · 1, 166, 123, 4 … Σ 1, 3, 24, 294, 5160, 123036, 3759876, …
  (−∞, 0]nonnegative
• A103633 → Veronese 2 (j=1) → D+1
  1 · 1 · 1, 1 · 2, 2 … Σ 0, 1, 1, 2, 4, 5, 11, 13, …
  (−∞, 0]nonnegative
• A038301 → basis A013609
  400, 880, 484 · 8000, 26400, 29040, 10648 … Σ 1764, 74088, 3111696, 130691232, …
  (−∞, 0]nonnegativerational roots
• A128100: Triangle read by rows: T(n,k) is the number of ways to tile a 2 X n rectangle with k pieces of 2 X 2 tiles and n-2k pieces of 1 X 2 tiles (0 <= k <= f…
  1 · 1 · 2, 1 · 3, 2 … Σ 1, 1, 3, 5, 11, 21, 43, 85, …
  (−∞, −1]nonnegative
• A358735 → basis A007318 → x ↦ x+1
  1 · 3, 1 · 17, 12, 2 · 133, 146, 52, 6 … Σ 1, 4, 31, 337, 4687, 79342, 1582153, …
  (−4, −2)nonnegative
• A173018 → reverse (shift +1) → reverse
  1 · 1 · 1, 1 · 1, 4, 1 … Σ 1, 1, 2, 6, 24, 120, 720, 5040, …
  (−∞, 0]nonnegative
• A299989 → D+1
  1, 1 · 3, 11, 7, 1 · 9, 57, 90, 54, 13, 1 … Σ 2, 22, 224, 2176, 20480, 188416, …
  (−∞, 0]nonnegative
• A207823 → reverse → D
  4 · 8, 30 · 12, 92, 168 · 16, 186, 696, 836 … Σ 0, 4, 38, 272, 1734, 10372, 59584, …
  (−∞, 0]nonnegative
• A130534 → D → D
  2 · 12, 6 · 70, 60, 12 · 450, 510, 180, 20 … Σ 0, 0, 2, 18, 142, 1160, 10208, 97720, …
  (−∞, 0]nonnegative
• A114656 → reverse → D
  2 · 6, 8 · 12, 48, 24 · 20, 160, 240, 64 … Σ 0, 2, 14, 84, 484, 2750, 15546, 87752, …
  (−∞, 0]nonnegative
• A028338 → basis A013609 → x ↦ x/(x+1)
  1 · 2, 4 · 8, 28, 24 · 48, 232, 368, 192 … Σ 1, 6, 60, 840, 15120, 332640, 8648640, …
  [−1, 0]nonnegativerational roots
• A207606 → basis A013609 → θ+1
  13, 44, 24 · 34, 176, 204, 64 … Σ 81, 478, 2721, 15101, 82242, 441425, …
  (−∞, 0]nonnegative
• A007318 → ×(−(1/2)n+(1/2)n²) → D
  2, 2 · 9, 18, 9 · 24, 72, 72, 24 … Σ 0, 0, 4, 36, 192, 800, 2880, 9408, …
  (−∞, 0]nonnegativerational roots
• reversed rows → (θ+1)²
  1 · 1, 8 · 1, 12 · 1, 16, 18 … Σ 1, 9, 13, 35, 66, 138, 267, 519, …
  (−∞, 0]nonnegative
• A039755 → x ↦ x+1 → x ↦ x+1
  1 · 3, 1 · 13, 8, 1 · 71, 61, 15, 1 … Σ 1, 4, 22, 148, 1156, 10192, 99544, …
  (−∞, −1]nonnegative
• A207824 → x ↦ x+1 → x ↦ x/(x+1)
  1 · 6, 7 · 35, 82, 48 · 204, 718, 842, 329 … Σ 1, 13, 165, 2093, 26549, 336765, …
  [−1, −4/5)nonnegative
• A281260 → θ+1
  1 · 0, 4 · 0, 4, 9 · 0, 4, 24, 16 … Σ 1, 4, 13, 44, 154, 552, 2013, 7436, …
  (−∞, 0]nonnegative
• A125662 → basis A013609
  1 · 4, 2 · 15, 16, 4 · 56, 92, 48, 8 … Σ 1, 6, 35, 204, 1189, 6930, 40391, …
  (−3, −1)nonnegative
• A088729 → reverse
  1, 9, 13 · 1, 18, 79, 75 · 1, 30, 265, 765, 541 … Σ 23, 173, 1602, 17575, 222497, 3188806, …
  (−∞, 0]nonnegative
• A038322 → basis A007318 → reverse
  1 · 8, 19 · 64, 304, 361 · 512, 3648, 8664, 6859 … Σ 1, 27, 729, 19683, 531441, 14348907, …
  (−∞, 0]nonnegativerational roots
• A143491 → basis A013609 → reverse
  4, 14, 12 · 8, 48, 94, 60 · 16, 144, 476, 684, 360 … Σ 30, 210, 1680, 15120, 151200, 1663200, …
  (−∞, 0]nonnegativerational roots
• A038324 → basis A013609 → D+1
  1 · 41, 20 · 1281, 1640, 400 … Σ 1, 61, 3321, 169781, 8339441, …
  (−∞, 0]nonnegativerational roots
• A132774 → x ↦ x/(x+1)
  1 · 2, 5 · 0, 4, 9 · 0, 0, 6, 13 … Σ 1, 7, 13, 19, 25, 31, 37, 43, …
  [−1, 0]nonnegativerational roots
• A038338 → basis A013609 → D+1
  1728, 2304, 576 · 55296, 124416, 82944, 13824 … Σ 4608, 276480, 15925248, 891813888, …
  (−∞, 0]nonnegativerational roots
• A038284 → D+1
  160, 168, 36 · 1664, 2880, 1512, 216 … Σ 364, 6272, 104272, 1690304, 26891200, …
  (−∞, 0]nonnegativerational roots
• A124324 → θ+1
  1 · 1 · 1, 2 · 1, 8 … Σ 1, 1, 3, 9, 32, 128, 565, 2719, …
  (−∞, 0]nonnegative
• A049020 → x ↦ x+1 → x ↦ x/(x+1)
  1 · 2, 3 · 6, 17, 12 · 22, 91, 125, 57 … Σ 1, 5, 35, 295, 2865, 31205, 374435, …
  [−1, 0]nonnegative
• narayana → basis A013610 → (θ+1)²
  1 · 2, 12 · 5, 60, 81 · 14, 252, 729, 432 … Σ 1, 14, 146, 1427, 13659, 129480, …
  (−∞, 0]nonnegative
• A178821 → basis A013609 → D+1
  1 · 20, 10 · 180, 240, 60 · 1120, 2520, 1680, 280 … Σ 1, 30, 480, 5600, 53760, 451584, …
  (−∞, 0]nonnegativerational roots
• A204420 → (θ+1)²
  1 · 0, 4 · 0, 24, 27 · 0, 480, 810, 240 … Σ 1, 4, 51, 1530, 84525, 7476840, …
  (−∞, 0]nonnegative
• A038334 → basis A013609
  400, 640, 256 · 8000, 19200, 15360, 4096 … Σ 1296, 46656, 1679616, 60466176, …
  (−∞, 0]nonnegativerational roots
• A113413 → x ↦ x/(x+1)
  1 · 2, 3 · 2, 8, 7 · 2, 14, 28, 17 … Σ 1, 5, 17, 61, 217, 773, 2753, 9805, …
  [−1, 0]nonnegative
• A075497 → reverse
  1 · 1, 2 · 1, 6, 4 · 1, 12, 28, 8 … Σ 1, 3, 11, 49, 257, 1539, 10299, 75905, …
  (−∞, 0]nonnegative
• A038255 → D+1
  1 · 7, 1 · 48, 14, 1 · 324, 144, 21, 1 … Σ 1, 8, 63, 490, 3773, 28812, 218491, …
  (−∞, 0]nonnegativerational roots
• A142458 → x ↦ x/(x+1)
  1 · 1, 2 · 1, 10, 10 · 1, 42, 120, 80 … Σ 1, 3, 21, 243, 3861, 78003, 1913301, …
  [−1, 0]nonnegative
• A128099 → basis A013609 → D
  4 · 8 · 28, 32 · 64, 96 … Σ 0, 0, 4, 8, 60, 160, 740, 2232, …
  (−∞, 0]nonnegative
• A028326 → D → (θ+1)²
  2 · 4, 16 · 6, 48, 54 · 8, 96, 216, 128 … Σ 0, 2, 20, 108, 448, 1600, 5184, 15680, …
  (−∞, 0]nonnegative
• A109983 → (θ+1)²
  1 · 0, 4, 18 · 0, 0, 9, 96, 150 … Σ 1, 22, 255, 2376, 19785, 153798, …
  (−∞, 0]nonnegative
• A038325 → basis A007318 → reverse
  1 · 11, 22 · 121, 484, 484 · 1331, 7986, 15972, 10648 … Σ 1, 33, 1089, 35937, 1185921, 39135393, …
  (−∞, 0]nonnegativerational roots
• A102662 → reverse → (θ+1)²
  1 · 3, 4 · 3, 20, 9 · 3, 44, 63, 16 … Σ 1, 7, 32, 126, 447, 1489, 4738, 14572, …
  (−∞, 0]nonnegative