Proof methods / preserver_image

Image under a real-rootedness preserver

8,704 sequences

• basis-map coefficients of A112227 → θ+1 → D
  0, 6 · 0, 0, 12 · 0, 0, 0, 20 · 0, 0, 0, 0, 30 … Σ 6, 12, 20, 30, 42, 56, 72, 90, …
  (−∞, 0]nonnegativerational roots
• A272866 → basis A007318 → D+1
  1 · 10, 7, 1 · 75, 120, 65, 14, 1 … Σ 1, 18, 275, 3872, 51909, 673486, …
  (−∞, 0]nonnegative
• basis-map coefficients of A371080, shifted → basis A013611 → reverse
  1 · 4, 1 · 16, 20, 4 · 64, 192, 156, 28 … Σ 1, 5, 40, 440, 6160, 104720, 2094400, …
  (−∞, 0]nonnegativerational roots
• A008955 → basis A007318 → reverse
  1 · 1, 2 · 4, 13, 10 · 36, 157, 220, 100 … Σ 1, 3, 27, 513, 16929, 863379, 63026667, …
  (−∞, 0]nonnegativerational roots
• A178822 → basis A013609 → θ+1
  1 · 12, 24 · 84, 336, 252 · 448, 2688, 4032, 1792 … Σ 1, 36, 672, 8960, 96768, 903168, …
  (−∞, 0]nonnegativerational roots
• A106800 → x ↦ x+1 → D+1
  1 · 1 · 3, 1 · 10, 7, 1 … Σ 1, 1, 4, 18, 95, 579, 3966, 29944, …
  (−∞, 0]nonnegative
• A059344 → basis A007318 → D+1
  1 · 1 · 5, 2 · 13, 6 … Σ 1, 1, 7, 19, 133, 541, 3931, 20287, …
  (−∞, 0]nonnegative
• A133214 → basis A013609 → D+1
  45, 64, 16 · 291, 708, 432, 64 … Σ 125, 1495, 18305, 225947, 2793997, …
  (−∞, 0]nonnegative
• A122542 → basis A013609 → reverse
  1 · 2, 1 · 4, 8, 3 · 8, 28, 26, 7 … Σ 1, 3, 15, 69, 321, 1491, 6927, 32181, …
  (−∞, 0]nonnegative
• A286718 → θ+1
  1 · 1, 2 · 4, 10, 3 · 28, 78, 36, 4 … Σ 1, 3, 17, 146, 1686, 24484, 428548, …
  (−∞, 0]nonnegative
• A133214 → basis A007318
  13, 16, 4 · 63, 114, 60, 8 · 321, 768, 624, 192, 16 … Σ 33, 245, 1921, 15525, 127905, 1067925, …
  (−∞, −1]nonnegative
• A143495 → θ+1 → D+1
  1 · 5, 2 · 23, 20, 3 · 101, 146, 48, 4 … Σ 1, 7, 46, 299, 1967, 13248, 91903, …
  (−∞, 0]nonnegative
• A078812 → reverse
  1 · 1, 2 · 1, 4, 3 · 1, 6, 10, 4 … Σ 1, 3, 8, 21, 55, 144, 377, 987, …
  (−∞, 0]nonnegative
• A169803 → x ↦ x+1 → (θ+1)²
  1 · 2, 4 · 3, 8 · 5, 20, 9 … Σ 1, 6, 11, 34, 75, 190, 435, 1026, …
  (−∞, 0]nonnegative
• A081579 → D
  1 · 6, 2 · 11, 22, 3 · 16, 92, 48, 4 … Σ 0, 1, 8, 36, 160, 640, 2496, 9408, …
  (−∞, 0]nonnegative
• A134082 → basis A007318
  1 · 3, 1 · 5, 6, 1 · 7, 15, 9, 1 … Σ 1, 4, 12, 32, 80, 192, 448, 1024, …
  (−∞, −1]nonnegativerational roots
• A038301 → basis A013611 → x ↦ x/(x+1)
  400, 2560, 4096 · 8000, 76800, 245760, 262144 … Σ 7056, 592704, 49787136, 4182119424, …
  [−1, 0]nonnegativerational roots
• A038220 → basis A007318 → D
  2 · 20, 8 · 150, 120, 24 · 1000, 1200, 480, 64 … Σ 0, 2, 28, 294, 2744, 24010, 201684, …
  (−∞, 0]nonnegativerational roots
• A207824 → basis A013611 → D
  4 · 48, 32 · 424, 576, 192 · 3312, 6816, 4608, 1024 … Σ 0, 4, 80, 1192, 15760, 195212, 2320480, …
  (−∞, 0]nonnegative
• A113413 → D
  1 · 4, 2 · 8, 12, 3 · 12, 36, 24, 4 … Σ 0, 1, 6, 23, 76, 233, 682, 1935, …
  (−∞, 0]nonnegative
• A038331 → basis A013610 → reverse
  225, 510, 289 · 3375, 11475, 13005, 4913 … Σ 1024, 32768, 1048576, 33554432, …
  (−∞, 0]nonnegativerational roots
• A172431 → D
  2 · 4, 6 · 6, 20, 12 · 8, 42, 60, 20 … Σ 0, 2, 10, 38, 130, 420, 1308, 3970, …
  (−∞, 0]nonnegative
• A048993 → (θ+1)² → x ↦ x+1
  1 · 4, 4 · 13, 22, 9 · 47, 106, 75, 16 … Σ 1, 8, 44, 244, 1428, 8900, 59060, …
  (−∞, −1]nonnegative
• A013611 → basis A013611 → θ+1
  1 · 5, 32 · 25, 320, 768 · 125, 2400, 11520, 16384 … Σ 1, 37, 1113, 30429, 787185, 19642581, …
  (−∞, 0]nonnegativerational roots
• delannoy → basis A013610 → reverse
  1 · 3, 2 · 9, 15, 5 · 27, 72, 54, 12 … Σ 1, 5, 29, 165, 941, 5365, 30589, …
  (−∞, 0]nonnegative
• A102537 → D+1
  1 · 4, 3 · 9, 32, 12 · 16, 125, 220, 55 … Σ 1, 7, 53, 416, 3338, 27189, 223885, …
  (−∞, 0]nonnegative
• A227450 → reverse → D+1
  2 · 6, 2 · 20, 16, 2 · 64, 104, 34, 2 … Σ 2, 8, 38, 204, 1202, 7656, 52222, …
  (−∞, 0]nonnegative
• A038335 → basis A013609 → (θ+1)²
  1 · 21, 72 · 441, 3024, 2916 … Σ 1, 93, 6381, 381537, 21039993, …
  (−∞, 0]nonnegative
• A038324 → basis A007318 → basis A007318
  1 · 31, 10 · 961, 620, 100 · 29791, 28830, 9300, 1000 … Σ 1, 41, 1681, 68921, 2825761, 115856201, …
  (−∞, −1]nonnegativerational roots
• A114656 → θ+1 → reverse
  1 · 2, 2 · 3, 12, 4 · 4, 36, 48, 8 … Σ 1, 4, 19, 96, 501, 2668, 14407, 78592, …
  (−∞, 0]nonnegative
• A038328 → basis A013611 → reverse
  64, 224, 196 · 512, 2688, 4704, 2744 … Σ 484, 10648, 234256, 5153632, 113379904, …
  (−∞, 0]nonnegativerational roots
• A048993 → θ+1 → x ↦ x+1
  1 · 2, 2 · 5, 8, 3 · 15, 32, 21, 4 … Σ 1, 4, 16, 72, 360, 1976, 11784, 75704, …
  (−∞, −1]nonnegative
• A116666 → reverse → x ↦ x/(x+1)
  1 · 3, 4 · 5, 16, 12 · 7, 36, 60, 32 … Σ 1, 7, 33, 135, 513, 1863, 6561, 22599, …
  [−1, 0]nonnegativerational roots
• A038330 → basis A013609 → D
  256, 128 · 6144, 6144, 1536 … Σ 384, 13824, 442368, 13271040, …
  (−∞, 0]nonnegativerational roots
• A196347 → basis A013610 → D
  3 · 24, 36 · 216, 648, 486 · 2304, 10368, 15552, 7776 … Σ 0, 3, 60, 1350, 36000, 1125000, …
  (−∞, 0]nonnegativerational roots
• A038291 → basis A013609 → reverse
  1 · 2, 10 · 4, 40, 100 · 8, 120, 600, 1000 … Σ 1, 12, 144, 1728, 20736, 248832, …
  (−∞, 0]nonnegativerational roots
• A130534 → D²∘x (shift +1) → reverse
  1 · 3, 3 · 6, 18, 11 · 10, 60, 105, 50 … Σ 1, 6, 35, 225, 1624, 13132, 118124, …
  (−∞, 0]nonnegative
• A143494 → θ+1 → x ↦ x/(x+1)
  1 · 2, 4 · 4, 18, 17 · 8, 62, 127, 77 … Σ 1, 6, 39, 274, 2073, 16822, 145855, …
  [−1, 0]nonnegative
• A143491 → basis A013609 → D
  14, 8 · 94, 96, 24 · 684, 952, 432, 64 … Σ 22, 214, 2132, 22548, 255720, 3115320, …
  (−∞, 0]nonnegative
• A132393 → Veronese 2 → θ+1
  1 · 0, 2 · 0, 6 · 0, 22, 3 … Σ 1, 0, 2, 6, 25, 130, 807, 5817, …
  (−∞, 0]nonnegative
• A046716 → basis A013611 → reverse
  1 · 4, 2 · 16, 20, 5 · 64, 176, 100, 16 … Σ 1, 6, 41, 356, 4401, 78826, 1893481, …
  (−∞, 0]nonnegative
• A038301 → D
  198, 242 · 2673, 6534, 3993 … Σ 440, 13200, 352000, 8800000, 211200000, …
  (−∞, 0]nonnegativerational roots
• A121574 → reverse → D
  2 · 5, 8 · 8, 32, 24 · 11, 74, 132, 64 … Σ 0, 2, 13, 64, 281, 1158, 4584, 17648, …
  (−∞, 0]nonnegative
• A075497 → reverse → x ↦ x/(x+1)
  1 · 1, 3 · 1, 8, 11 · 1, 15, 55, 49 … Σ 1, 4, 20, 120, 832, 6496, 56128, …
  [−1, 0]nonnegative
• A128099 → basis A013610 → D
  6 · 12 · 42, 72 · 96, 216 … Σ 0, 0, 6, 12, 114, 312, 1758, 5604, …
  (−∞, 0]nonnegative
• A038326 → x ↦ x+1 → x ↦ x/(x+1)
  1 · 23, 35 · 529, 1610, 1225 … Σ 1, 58, 3364, 195112, 11316496, …
  [−1, 0]nonnegativerational roots
• A008955 → basis A007318
  1 · 2, 1 · 10, 13, 4 · 100, 220, 157, 36 … Σ 1, 3, 27, 513, 16929, 863379, 63026667, …
  (−∞, −1]nonnegativerational roots
• A161198 → basis A013611 → (θ+1)²
  1 · 3, 32 · 15, 256, 576 · 105, 2272, 8640, 8192 … Σ 1, 35, 847, 19209, 442417, 10650171, …
  (−∞, 0]nonnegative
• A207823 → basis A013611 → D
  4 · 40, 32 · 292, 480, 192 · 1880, 4704, 3840, 1024 … Σ 0, 4, 72, 964, 11448, 127344, 1359288, …
  (−∞, 0]nonnegative
• A038291 → basis A013611 → x ↦ x/(x+1)
  1 · 10, 14 · 100, 280, 196 · 1000, 4200, 5880, 2744 … Σ 1, 24, 576, 13824, 331776, 7962624, …
  [−1, 0]nonnegativerational roots