Proof methods / preserver_image

Image under a real-rootedness preserver

8,704 sequences

• A038208 → D+1
  1 · 4, 2 · 12, 16, 4 · 32, 72, 48, 8 … Σ 1, 6, 32, 160, 768, 3584, 16384, 73728, …
  (−∞, 0]nonnegativerational roots
• A086915 → reverse
  2 · 4, 4 · 8, 24, 12 · 16, 96, 144, 48 … Σ 2, 8, 44, 304, 2512, 24064, 261536, …
  (−∞, 0]nonnegative
• A125662 → reverse
  1 · 1, 3 · 1, 6, 8 · 1, 9, 25, 21 … Σ 1, 4, 15, 56, 209, 780, 2911, 10864, …
  (−1, 0]nonnegative
• A136572 → basis A013610 → θ+1
  1 · 1, 6 · 2, 24, 54 · 6, 108, 486, 648 … Σ 1, 7, 80, 1248, 24576, 583680, …
  (−∞, 0]nonnegativerational roots
• A200536 → basis A013610 → θ+1
  1 · 6, 42, 54 · 36, 504, 1971, 3024, 1620 … Σ 1, 102, 7155, 437400, 24877125, …
  (−∞, 0]nonnegative
• A143491 → reverse
  1, 5, 6 · 1, 9, 26, 24 · 1, 14, 71, 154, 120 … Σ 12, 60, 360, 2520, 20160, 181440, …
  (−∞, 0]nonnegativerational roots
• A136572 → basis A013610 → D+1
  1 · 4, 3 · 14, 48, 18 · 60, 378, 648, 162 … Σ 1, 7, 80, 1248, 24576, 583680, …
  (−∞, 0]nonnegativerational roots
• A126351 → reverse
  1 · 2, 1 · 4, 5, 1 · 8, 19, 9, 1 … Σ 1, 3, 10, 37, 151, 674, 3263, 17007, …
  (−∞, 0]nonnegative
• A128813 → basis A013610 → basis A007318
  1 · 5, 3 · 65, 84, 27 · 1625, 3270, 2187, 486 … Σ 1, 8, 176, 7568, 537328, 56956768, …
  (−∞, −1]nonnegativerational roots
• A030528 → basis A013611 → basis A007318
  1 · 6, 4 · 35, 48, 16 · 205, 424, 288, 64 … Σ 1, 10, 99, 981, 9720, 96309, 954261, …
  (−∞, −1]nonnegative
• A102365 → x ↦ x+1 → D
  1 · 7, 2 · 51, 36, 3 · 431, 492, 123, 4 … Σ 0, 0, 1, 9, 90, 1050, 14175, 218295, …
  (−∞, 0]nonnegative
• A063967 → basis A013610 → x ↦ x+1
  1 · 5, 3 · 30, 33, 9 · 175, 285, 153, 27 … Σ 1, 8, 72, 640, 5696, 50688, 451072, …
  (−∞, −1]nonnegative
• image under θ+1 → (θ+1)² → D
  8 · 0, 54 · 0, 0, 192 · 0, 0, 0, 500 … Σ 0, 8, 54, 192, 500, 1080, 2058, 3584, …
  (−∞, 0]nonnegativerational roots
• A139548 → x ↦ x+1 → D
  8, 4 · 128, 192, 96, 16 … Σ 0, 12, 432, 11664, 279936, 6298560, …
  (−∞, 0]nonnegativerational roots
• A094816 → basis A013611 → (θ+1)²
  1 · 2, 16 · 5, 80, 144 · 16, 368, 1296, 1024 … Σ 1, 18, 229, 2704, 32017, 392054, …
  (−∞, 0]nonnegative
• Veronese parent of A098172 → Veronese 3 (j=1) → reverse
  1 · 1 · 1 · 1, 1 … Σ 1, 1, 1, 2, 5, 11, 22, 43, …
  (−∞, 0]nonnegative
• A269944 → x ↦ x+1
  1 · 1, 1 · 2, 3, 1 · 10, 17, 8, 1 … Σ 1, 2, 6, 36, 396, 7128, 192456, …
  (−∞, −1]nonnegativerational roots
• A115951 → θ+1
  1 · 0, 4 · 0, 4, 18 · 0, 0, 36, 80 … Σ 1, 4, 22, 116, 608, 3152, 16208, 82784, …
  (−∞, 0]nonnegative
• narayana → basis A013610 → x ↦ x/(x+1)
  1 · 2, 5 · 5, 25, 29 · 14, 105, 249, 185 … Σ 1, 7, 59, 553, 5541, 58107, 629799, …
  [−1, 0]nonnegative
• A038324 → basis A013609 → D
  20 · 840, 800 · 26460, 50400, 24000 … Σ 0, 20, 1640, 100860, 5513680, …
  (−∞, 0]nonnegativerational roots
• A094816 → D → D+1
  1 · 5, 2 · 20, 18, 3 · 82, 118, 42, 4 … Σ 0, 1, 7, 41, 246, 1609, 11697, 94737, …
  (−∞, 0]nonnegative
• A062196 → reverse → θ+1
  1 · 3, 2 · 6, 16, 3 · 10, 60, 45, 4 … Σ 1, 5, 25, 119, 546, 2442, 10725, 46475, …
  (−∞, 0]nonnegative
• A062264 → D
  5 · 12, 30 · 21, 126, 105 · 32, 336, 672, 280 … Σ 0, 5, 42, 252, 1320, 6435, 30030, …
  (−∞, 0]nonnegative
• A282629 → θ+1
  1 · 1, 6 · 1, 30, 27 · 1, 126, 324, 108 … Σ 1, 7, 58, 559, 6127, 74920, 1007299, …
  (−∞, 0]nonnegative
• basis-map coefficients of A021012 → θ+1 → D+1
  1 · -2, -2 · 0, 12, 6 · 0, 0, -72, -24 … Σ 1, -4, 18, -96, 600, -4320, 35280, …
  (−∞, 0]rational roots
• A094638 → basis A013610 → D
  3 · 21, 36 · 138, 522, 486 · 978, 5922, 11826, 7776 … Σ 0, 3, 57, 1146, 26502, 705717, …
  (−∞, 0]nonnegative
• A139548 → basis A013610 → D+1
  1 · 32, 60, 18 · 448, 2112, 3456, 2160, 324 … Σ 1, 110, 8500, 575000, 36250000, …
  (−∞, 0]nonnegativerational roots
• A172431 → basis A013610 → basis A007318
  1 · 9, 6 · 65, 84, 27 · 441, 834, 522, 108 … Σ 1, 15, 176, 1905, 19951, 205920, …
  (−∞, −1]nonnegative
• A038330 → basis A013609 → θ+1
  256, 512, 192 · 4096, 12288, 9216, 2048 … Σ 960, 27648, 774144, 21233664, …
  (−∞, 0]nonnegativerational roots
• A114687 → D+1
  1 · 3, 2 · 7, 14, 4 · 13, 60, 48, 8 … Σ 1, 5, 25, 129, 681, 3653, 19825, …
  (−∞, 0]nonnegative
• A304236 → basis A013609 → D
  6 · 12 · 54, 72 · 132, 216 … Σ 0, 0, 6, 12, 126, 348, 2136, 6948, …
  (−∞, 0]nonnegative
• basis-map coefficients of A113214, shifted → Veronese 2 → D+1
  1 · -1 · 2, 1 · -4, -3 … Σ 1, -1, 3, -7, 16, -36, 80, -176, …
  (−∞, 0]
• A094816 → basis A013611 → reverse
  1 · 4, 2 · 16, 20, 5 · 64, 144, 92, 16 … Σ 1, 6, 41, 316, 2721, 25946, 271801, …
  (−∞, 0]nonnegative
• A108838 → reverse → D
  3 · 8, 8 · 15, 40, 15 · 24, 120, 120, 24 … Σ 0, 3, 16, 70, 288, 1155, 4576, 18018, …
  (−∞, 0]nonnegative
• A225473 → D
  4 · 40, 64 · 316, 1344, 1152 … Σ 0, 4, 104, 2812, 88208, 3217204, …
  (−∞, 0]nonnegative
• A114655 → reverse → D
  4 · 12, 16 · 24, 96, 48 · 40, 320, 480, 128 … Σ 0, 4, 28, 168, 968, 5500, 31092, …
  (−∞, 0]nonnegative
• A111125 → (θ+1)²
  1 · 3, 4 · 5, 20, 9 · 7, 56, 63, 16 … Σ 1, 7, 34, 142, 541, 1939, 6653, 22091, …
  (−∞, 0]nonnegative
• A133214 → basis A007318 → x ↦ x/(x+1)
  13, 42, 33 · 63, 303, 477, 245 … Σ 88, 1088, 14176, 190208, 2600704, …
  [−1, 0]nonnegative
• A038338 → x ↦ x+1 → (θ+1)²
  576, 2304, 1296 · 13824, 82944, 93312, 27648 … Σ 4176, 217728, 10637568, 497166336, …
  (−∞, 0]nonnegative
• A166973 → θ+1
  1 · 1, 2 · 1, 14, 3 · 1, 86, 54, 4 … Σ 1, 3, 18, 145, 1383, 15262, 191431, …
  (−∞, 0]nonnegative
• A038221 → basis A013610 → basis A007318
  1 · 15, 9 · 225, 270, 81 · 3375, 6075, 3645, 729 … Σ 1, 24, 576, 13824, 331776, 7962624, …
  (−∞, −1]nonnegativerational roots
• A013610 → Veronese 2 → x ↦ x+1
  1 · 1 · 10, 9 · 28, 27 … Σ 1, 1, 19, 55, 433, 1801, 10963, 52543, …
  (−∞, −1]nonnegative
• A085478 → basis A013611 → D+1
  1 · 1 · 6, 4 · 25, 52, 16 … Σ 1, 1, 10, 93, 805, 6666, 53561, 421065, …
  (−∞, 0]nonnegative
• A094816 → basis A013609 → (θ+1)²
  1 · 2, 8 · 5, 40, 36 · 16, 184, 324, 128 … Σ 1, 10, 81, 652, 5525, 50310, 495573, …
  (−∞, 0]nonnegative
• A013609 → Veronese 2 (j=1) → (θ+1)²
  2 · 4 · 6, 32 · 8, 128 … Σ 0, 2, 4, 38, 136, 618, 2380, 9230, …
  (−∞, 0]nonnegative
• basis-map coefficients of A026729 → basis A013609 → D
  2 · 4, 8 · 6, 24, 24 · 8, 48, 96, 64 … Σ 0, 2, 12, 54, 216, 810, 2916, 10206, …
  (−∞, 0]nonnegativerational roots
• A114687 → basis A013609 → reverse
  1 · 4, 3 · 16, 28, 11 · 64, 192, 168, 45 … Σ 1, 7, 55, 469, 4237, 39907, 387739, …
  (−∞, 0]nonnegative
• A063967 → basis A007318
  1 · 2, 1 · 6, 5, 1 · 16, 20, 8, 1 … Σ 1, 3, 12, 45, 171, 648, 2457, 9315, …
  (−∞, −1]nonnegative
• A257625 → D+1
  1 · 6, 3 · 63, 72, 9 · 648, 1863, 702, 27 … Σ 1, 9, 144, 3240, 93312, 3265920, …
  (−∞, 0]nonnegative
• A132393 → basis A013609 → D+1
  1 · 3, 2 · 8, 14, 4 · 28, 70, 48, 8 … Σ 1, 5, 26, 154, 1044, 8028, 69264, …
  (−∞, 0]nonnegative