Proof methods / preserver_image

Image under a real-rootedness preserver

8,704 sequences

• A038335 → basis A013609 → D
  18 · 756, 648 · 23814, 40824, 17496 … Σ 0, 18, 1404, 82134, 4270968, 208209690, …
  (−∞, 0]nonnegativerational roots
• A152198 → basis A013610 → basis A007318
  1 · 1 · 5, 3 · 5, 3 … Σ 1, 1, 8, 8, 64, 64, 512, 512, …
  (−∞, −1]nonnegativerational roots
• A286718 → (θ+1)²
  1 · 1, 4 · 4, 20, 9 · 28, 156, 108, 16 … Σ 1, 5, 33, 308, 3760, 56892, 1028452, …
  (−∞, 0]nonnegative
• A144442 → (θ+1)²
  1 · 1, 4 · 1, 68, 9 · 1, 472, 1062, 16 … Σ 1, 5, 78, 1551, 38735, 1171262, …
  (−∞, 0]nonnegative
• A030528 → basis A013609 → reverse
  1 · 2, 2 · 4, 8, 3 · 8, 24, 20, 5 … Σ 1, 4, 15, 57, 216, 819, 3105, 11772, …
  (−∞, 0]nonnegative
• A088996 → basis A013611 → D
  4 · 20, 64 · 136, 800, 1152 … Σ 0, 4, 84, 2088, 62984, 2256636, …
  (−∞, 0]nonnegative
• A200536 → basis A013609 → basis A007318
  1 · 28, 30, 8 · 784, 1680, 1348, 480, 64 … Σ 1, 66, 4356, 287496, 18974736, …
  (−∞, −1]nonnegativerational roots
• A108299 → D
  -1 · -1, -2 · -1, -4, 3 · -1, -6, 6, 4 … Σ 0, -1, -3, -2, 3, 7, 4, -5, …
  (−∞, ∞)
• A391533 → reverse → x ↦ x+1
  9, 12, 4 · 18, 33, 20, 4 · 36, 84, 73, 28, 4 … Σ 25, 75, 225, 675, 2025, 6075, 18225, …
  (−∞, −1]nonnegativerational roots
• A116412 → basis A013609 → D
  2 · 16, 8 · 84, 96, 24 · 380, 696, 384, 64 … Σ 0, 2, 24, 204, 1524, 10626, 70968, …
  (−∞, 0]nonnegative
• A143494 → θ+1 → D+1
  1 · 4, 2 · 14, 16, 3 · 46, 92, 39, 4 … Σ 1, 6, 33, 181, 1020, 5977, 36589, …
  (−∞, 0]nonnegative
• A008292 → γ → θ+1
  1 · 1 · 1, 4 · 1, 16 … Σ 1, 1, 5, 17, 93, 513, 3477, 25569, …
  (−∞, 0]nonnegative
• A136124 → basis A013610 → D
  3 · 21, 18 · 141, 216, 81 · 1026, 2142, 1458, 324 … Σ 0, 3, 39, 438, 4950, 58572, 735012, …
  (−∞, 0]nonnegative
• A225473 → (θ+1)²
  1 · 3, 16 · 9, 160, 288 · 27, 1264, 6048, 6144 … Σ 1, 19, 457, 13483, 473425, 19309699, …
  (−∞, 0]nonnegative
• A121574 → basis A013610 → D
  3 · 21, 18 · 105, 198, 81 · 465, 1368, 1215, 324 … Σ 0, 3, 39, 384, 3372, 27792, 220032, …
  (−∞, 0]nonnegative
• A136572 → basis A013611
  1 · 1, 4 · 2, 16, 32 · 6, 72, 288, 384 … Σ 1, 5, 50, 750, 15000, 375000, 11250000, …
  [−1, 0]nonnegativerational roots
• A078812 → x ↦ x+1 → x ↦ x/(x+1)
  1 · 3, 4 · 8, 22, 15 · 21, 88, 122, 56 … Σ 1, 7, 45, 287, 1829, 11655, 74269, …
  [−1, −1/2)nonnegative
• A154986 → D+1
  1 · 2, 1 · 5, 6, 1 · 12, 33, 14, 1 … Σ 1, 3, 12, 60, 360, 2520, 20160, 181440, …
  (−∞, 0]nonnegative
• A008277 → θ+1 → D+1 → D
  2 · 12, 6 · 50, 60, 12 · 180, 390, 180, 20 … Σ 0, 2, 18, 122, 770, 4832, 30940, …
  (−∞, 0]nonnegative
• A154602 → x ↦ x/(x+1)
  1 · 1, 2 · 3, 10, 8 · 11, 52, 80, 40 … Σ 1, 3, 21, 183, 1929, 23691, 329565, …
  [−1, 0]nonnegative
• A038208 → basis A008277
  1 · 4, 2 · 16, 20, 4 · 64, 152, 72, 8 … Σ 1, 6, 40, 296, 2416, 21568, 208832, …
  (−∞, 0]nonnegative
• A225476 → reverse
  1 · 1, 1 · 2, 4, 1 · 6, 18, 13, 1 … Σ 1, 2, 7, 38, 277, 2522, 27547, 351038, …
  (−∞, 0]nonnegative
• A167884 → θ+1
  1 · 1, 2 · 1, 36, 3 · 1, 358, 537, 4 … Σ 1, 3, 40, 900, 28080, 1113840, …
  (−∞, 0]nonnegative
• A049374 → θ+1
  1 · 6, 2 · 42, 36, 3 · 336, 552, 108, 4 … Σ 1, 8, 81, 1000, 14549, 242784, 4554613, …
  (−∞, 0]nonnegative
• A111125 → reverse → θ+1
  1 · 1, 6 · 1, 10, 15 · 1, 14, 42, 28 … Σ 1, 7, 26, 85, 265, 804, 2393, 7019, …
  (−∞, 0]nonnegative
• A225470 → x ↦ x+1 → basis A008277
  1 · 4, 1 · 28, 12, 1 · 280, 160, 24, 1 … Σ 1, 5, 41, 465, 6721, 117941, 2433145, …
  (−∞, 0]nonnegative
• A094638 → basis A013609 → (θ+1)²
  1 · 2, 8 · 6, 56, 72 · 24, 368, 1044, 768 … Σ 1, 10, 134, 2204, 42860, 961440, …
  (−∞, 0]nonnegative
• A111577 → D
  1 · 5, 2 · 21, 24, 3 · 85, 210, 66, 4 … Σ 0, 1, 7, 48, 365, 3101, 29118, 298915, …
  (−∞, 0]nonnegative
• A003506 → Veronese 2 (j=1) → D
  4 · 20 · 60, 12 · 140, 84 … Σ 0, 0, 0, 0, 4, 20, 72, 224, …
  (−∞, 0]nonnegative
• A038314 → x ↦ x+1 → D
  528, 288 · 17424, 19008, 5184 … Σ 816, 41616, 1886592, 80180160, …
  (−∞, 0]nonnegativerational roots
• A172431 → basis A013609 → θ+1
  1 · 3, 8 · 8, 40, 36 · 21, 152, 264, 128 … Σ 1, 11, 84, 565, 3587, 22056, 132841, …
  (−∞, 0]nonnegative
• A011973 → Veronese 2 → x ↦ x+1
  1 · 1 · 1 · 1 … Σ 1, 1, 1, 1, 3, 7, 13, 21, …
  (−∞, −1]nonnegative
• A034870 → basis A013611 → (θ+1)²
  1 · 4, 64, 144 · 16, 512, 3456, 8192, 6400 … Σ 1, 212, 18576, 1228608, 70357248, …
  (−∞, 0]nonnegative
• A038323 → basis A013609 → θ+1
  1 · 20, 36 · 400, 1440, 972 … Σ 1, 56, 2812, 132848, 6035920, …
  (−∞, 0]nonnegativerational roots
• A147716 → basis A013611 → θ+1
  1 · 15, 8 · 225, 240, 48 · 3375, 5400, 2160, 256 … Σ 1, 23, 513, 11191, 240065, 5082519, …
  (−∞, 0]nonnegativerational roots
• A038207 → D+1
  1 · 3, 1 · 8, 6, 1 · 20, 24, 9, 1 … Σ 1, 4, 15, 54, 189, 648, 2187, 7290, …
  (−∞, 0]nonnegativerational roots
• A102365 → D
  1 · 5, 2 · 18, 30, 3 · 58, 258, 111, 4 … Σ 0, 0, 1, 7, 51, 431, 4208, 46824, …
  (−∞, 0]nonnegative
• A038301 → reverse → basis A007318
  400, 360, 81 · 8000, 10800, 4860, 729 … Σ 841, 24389, 707281, 20511149, …
  (−∞, −1]nonnegativerational roots
• A128099 → basis A013609 → D+1
  1 · 1 · 7, 4 · 13, 8 … Σ 1, 1, 11, 21, 115, 293, 1203, 3493, …
  (−∞, 0]nonnegative
• A142462 → D+1
  1 · 2, 1 · 17, 18, 1 · 144, 429, 146, 1 … Σ 1, 3, 36, 720, 19872, 695520, 29410560, …
  (−∞, 0]nonnegative
• A008277 → θ+2 (shift +1) → reverse → x ↦ x+1
  2 · 5, 2 · 15, 13, 2 · 52, 72, 27, 2 … Σ 2, 7, 30, 153, 898, 5919, 43102, …
  (−∞, −1]nonnegative
• A038208 → basis A007318 → (θ+1)²
  1 · 4, 8 · 16, 64, 36 · 64, 384, 432, 128 … Σ 1, 12, 116, 1008, 8208, 63936, 482112, …
  (−∞, 0]nonnegative
• A139548 → basis A013610
  1 · 8, 24, 18 · 64, 384, 864, 864, 324 … Σ 1, 50, 2500, 125000, 6250000, …
  [−1, 0]nonnegativerational roots
• A008278 → θ+1 → reverse
  1 · 2, 1 · 3, 6, 1 · 4, 21, 12, 1 … Σ 1, 3, 10, 38, 161, 747, 3753, 20253, …
  (−∞, 0]nonnegative
• reversal of Riordan array (1+2x,x(1+x)).
  1 · 1, 2 · 1, 3 · 1, 4, 2 … Σ 1, 3, 4, 7, 11, 18, 29, 47, …
  (−∞, 0)nonnegative
• A113214 → x ↦ x−3
  1 · -1, 1 · 0, -3, 1 · 3, 5, -5, 1 … Σ 1, 0, -2, 4, -4, 0, 8, -16, …
  (−1, 3]
• A103327 → x ↦ x+1
  1 · 4, 1 · 16, 12, 1 · 64, 80, 24, 1 … Σ 1, 5, 29, 169, 985, 5741, 33461, …
  (−∞, −1]nonnegative
• A059344 → basis A007318
  1 · 1 · 3, 2 · 7, 6 … Σ 1, 1, 5, 13, 73, 281, 1741, 8485, …
  (−∞, −1]nonnegative
• basis-map coefficients of A026729, shifted → D → D+1
  -1 · 2, 2 · 0, -6, -3 · 0, 0, 12, 4 … Σ 0, -1, 4, -9, 16, -25, 36, -49, …
  (−∞, 0]rational roots
• A028338 → x ↦ x+1 → θ+1
  1 · 2, 2 · 8, 12, 3 · 48, 88, 36, 4 … Σ 1, 4, 23, 176, 1689, 19524, 264207, …
  (−∞, 0]nonnegative