Proof methods / preserver_image

Image under a real-rootedness preserver

8,704 sequences

• A120910 → basis A013609
  3 · 9, 6 · 27, 36, 12 · 81, 162, 108, 24 … Σ 3, 15, 75, 375, 1875, 9375, 46875, …
  (−∞, −1]nonnegativerational roots
• A038330 → basis A013611 → D+1
  768, 1024, 256 · 16384, 36864, 24576, 4096 … Σ 2048, 81920, 3145728, 117440512, …
  (−∞, 0]nonnegativerational roots
• A075498 → x ↦ x/(x+1)
  1 · 3, 4 · 9, 27, 19 · 27, 144, 225, 109 … Σ 1, 7, 55, 505, 5497, 69823, 1007407, …
  [−1, 0]nonnegative
• A391533 → Veronese 2 → x ↦ x+1
  5, 1 · 9, 5 · 18, 15, 1 · 36, 39, 7 … Σ 6, 14, 34, 82, 198, 478, 1154, 2786, …
  (−∞, −1]nonnegative
• A011973 → basis A013611 → D+1
  1 · 1 · 6, 4 · 11, 8 … Σ 1, 1, 10, 19, 93, 232, 861, 2405, …
  (−∞, 0]nonnegative
• A178821 → basis A013610 → D
  15 · 180, 270 · 1260, 3780, 2835 … Σ 0, 15, 450, 7875, 105000, 1181250, …
  (−∞, 0]nonnegativerational roots
• basis-map coefficients of A297191, shifted → (θ+1)²
  1 · 0, 0, 9 · 0, 0, 0, 0, 25 · 0, 0, 0, 0, 0, 0, 49 … Σ 1, 9, 25, 49, 81, 121, 169, 225, …
  [−1, 0]nonnegativerational roots
• A134346 → x ↦ x/(x+1)
  1 · 3, 6 · 7, 28, 28 · 15, 90, 180, 120 … Σ 1, 9, 63, 405, 2511, 15309, 92583, …
  [−1, 0]nonnegativerational roots
• A086645 → basis A013609 → (θ+1)²
  1 · 2, 8 · 8, 64, 36 · 32, 384, 648, 128 … Σ 1, 10, 108, 1192, 12432, 123424, …
  (−∞, 0]nonnegative
• A249250 → θ+1
  1 · 1, 6 · 1, 12, 9 · 1, 18, 45, 12 … Σ 1, 7, 22, 76, 244, 772, 2392, 7312, …
  (−∞, 0]nonnegative
• A059364 → basis A013610 → θ+1
  1 · 3, 6 · 15, 66, 54 · 105, 732, 1269, 648 … Σ 1, 9, 135, 2754, 70506, 2165796, …
  (−∞, 0]nonnegative
• A039756 → x ↦ x+1 → reverse
  1 · 1, 2 · 1, 6, 6 · 1, 16, 38, 24 … Σ 1, 3, 13, 79, 601, 5339, 53861, 607527, …
  (−∞, 0]nonnegative
• basis-map coefficients of A113214, shifted → D
  -1 · 2, 2 · -3, -6, -3 · 4, 12, 12, 4 … Σ 0, -1, 4, -12, 32, -80, 192, -448, …
  (−∞, −1]rational roots
• A371259 → x ↦ x+1
  1 · 37, 1 · 1865, 102, 1 · 122961, 10267, 203, 1 … Σ 1, 38, 1968, 133432, 11482192, …
  (−∞, −1]nonnegative
• A130123 → Veronese 2 → (θ+1)²
  1 · 0, 16 · 0, 0, 144 · 0, 0, 0, 1024 … Σ 1, 0, 16, 0, 144, 0, 1024, 0, …
  (−∞, 0]nonnegativerational roots
• A178822 → basis A013609 → x ↦ x+1
  1 · 24, 12 · 336, 336, 84 · 3584, 5376, 2688, 448 … Σ 1, 36, 756, 12096, 163296, 1959552, …
  (−∞, −1]nonnegativerational roots
• A111125 → reverse → (θ+1)²
  1 · 1, 12 · 1, 20, 45 · 1, 28, 126, 112 … Σ 1, 13, 66, 267, 985, 3444, 11597, …
  (−∞, 0]nonnegative
• A143491 → D
  5, 2 · 26, 18, 3 · 154, 142, 42, 4 … Σ 7, 47, 342, 2754, 24552, 241128, …
  (−∞, 0]nonnegative
• A161198 → basis A007318 → x ↦ x/(x+1)
  1 · 3, 5 · 15, 46, 35 · 105, 457, 659, 315 … Σ 1, 8, 96, 1536, 30720, 737280, …
  [−1, 0]nonnegativerational roots
• A030528 → basis A013609 → D+1
  1 · 4, 2 · 11, 16, 4 · 25, 68, 48, 8 … Σ 1, 6, 31, 149, 684, 3045, 13257, 56754, …
  (−∞, 0]nonnegative
• A116412 → basis A013611 → x ↦ x+1
  1 · 8, 4 · 61, 64, 16 · 467, 744, 384, 64 … Σ 1, 12, 141, 1659, 19518, 229629, …
  (−∞, −1]nonnegative
• A272867 → x ↦ x+1 → θ+1
  1 · 6, 12, 3 · 36, 144, 144, 48, 5 … Σ 1, 21, 377, 6253, 98865, 1513733, …
  (−∞, 0]nonnegative
• A143685 → basis A007318 → D+1
  1 · 3, 1 · 26, 15, 1 · 110, 114, 27, 1 … Σ 1, 4, 42, 252, 1890, 12312, 84078, …
  (−∞, 0]nonnegative
• A272866 → Veronese 2 → x ↦ x+1
  1 · 2, 1 · 13, 13, 1 · 62, 93, 33, 1 … Σ 1, 3, 27, 189, 1377, 9963, 72171, …
  (−∞, −1]nonnegative
• A178820 → γ
  1 · 4 · 10 · 20 … Σ 1, 4, 10, 20, 35, 56, 84, 120, …
  (−∞, −1][−1, 0][−3−2√2, −3+2√2]+2
• A357613 → x ↦ x+1
  1 · 5, 2 · 41, 32, 6 · 377, 438, 165, 20 … Σ 1, 7, 79, 1000, 13327, 182887, 2557684, …
  (−∞, −1]nonnegative
• A286718 → basis A013609 → θ+1
  1 · 2, 4 · 10, 28, 12 · 80, 264, 180, 32 … Σ 1, 6, 50, 556, 7788, 131888, 2622352, …
  (−∞, 0]nonnegative
• A046716 → x ↦ x+1
  1 · 2, 1 · 5, 5, 1 · 16, 25, 11, 1 … Σ 1, 3, 11, 53, 345, 2947, 31411, 400437, …
  (−∞, −1]nonnegative
• A178821 → basis A013611 → x ↦ x/(x+1)
  1 · 10, 30 · 60, 360, 540 · 280, 2520, 7560, 7560 … Σ 1, 40, 960, 17920, 286720, 4128768, …
  [−1, 0]nonnegativerational roots
• A008459 → basis A013611 → x ↦ x+1
  1 · 6, 4 · 46, 56, 16 · 396, 696, 384, 64 … Σ 1, 10, 118, 1540, 21286, 304300, …
  (−∞, −1]nonnegative
• A229032 → (θ+1)²
  1 · 2 · 3, 16 · 4, 64 … Σ 1, 2, 19, 68, 309, 1190, 4615, 17160, …
  (−∞, 0]nonnegative
• basis-map coefficients of A030528, shifted → θ+1 → basis A007318
  1 · -2, -2 · 3, 6, 3 · -4, -12, -12, -4 … Σ 1, -4, 12, -32, 80, -192, 448, -1024, …
  (−∞, −1]rational roots
• A038226 → basis A013609 → D+1
  473, 864, 256 · 7139, 22704, 20736, 4096 … Σ 1593, 54675, 1791153, 56864187, …
  (−∞, 0]nonnegativerational roots
• A038303 → basis A013611 → D
  4 · 88, 32 · 1452, 1056, 192 … Σ 0, 4, 120, 2700, 54000, 1012500, …
  (−∞, 0]nonnegativerational roots
• A099097 → x ↦ x−3
  1 · -9, 3 · 78, -53, 9 · -675, 693, -237, 27 … Σ 1, -6, 34, -192, 1084, -6120, 34552, …
  (23/9, 3]
• A120910 → (θ+1)²
  3 · 6, 12 · 12, 48, 27 · 24, 144, 162, 48 … Σ 3, 18, 87, 378, 1539, 5994, 22599, …
  (−∞, 0]nonnegative
• A137320 → x ↦ x+1 → D
  2 · 10, 8 · 52, 72, 24 · 308, 568, 336, 64 … Σ 0, 2, 18, 148, 1276, 11888, 120432, …
  (−∞, 0]nonnegative
• A126216 → basis A007318 → D+1
  1 · 4, 1 · 18, 9, 1 · 87, 66, 15, 1 … Σ 1, 5, 28, 169, 1070, 6994, 46750, …
  (−∞, 0]nonnegative
• A104684 → basis A007318 → x ↦ x/(x+1)
  1 · 3, 4 · 13, 34, 22 · 63, 246, 318, 136 … Σ 1, 7, 69, 763, 8881, 106407, 1298949, …
  [−1, 0]nonnegative
• A103327 → basis A013611 → D+1
  1 · 8, 4 · 64, 80, 16 · 384, 1088, 576, 64 … Σ 1, 12, 160, 2112, 26880, 331776, …
  (−∞, 0]nonnegative
• A086645: Triangle read by rows: T(n, k) = binomial(2n, 2k).
  1 · 1, 1 · 1, 6, 1 · 1, 15, 15, 1 … Σ 1, 2, 8, 32, 128, 512, 2048, 8192, …
  (−∞, 0)nonnegative
• A286718 → reverse
  1 · 1, 1 · 1, 5, 4 · 1, 12, 39, 28 … Σ 1, 2, 10, 80, 880, 12320, 209440, …
  (−∞, 0]nonnegativerational roots
• A181371 → basis A007318
  1 · 3 · 9, 1 · 27, 6 … Σ 1, 3, 10, 33, 109, 360, 1189, 3927, …
  (−∞, −1]nonnegative
• basis-map coefficients of A026729 → D → D+1
  1 · 2, 2 · 0, 6, 3 · 0, 0, 12, 4 … Σ 0, 1, 4, 9, 16, 25, 36, 49, …
  (−∞, 0]nonnegativerational roots
• A038329 → (θ+1)²
  144, 288, 81 · 1728, 5184, 2916, 432 … Σ 513, 10260, 196425, 3645000, 66065625, …
  (−∞, 0]nonnegative
• A038330 → basis A007318 → reverse
  16, 128, 256 · 64, 768, 3072, 4096 … Σ 400, 8000, 160000, 3200000, 64000000, …
  (−∞, 0]nonnegativerational roots
• A091044 → D+1
  1 · 4, 2 · 13, 16, 3 · 32, 84, 40, 4 … Σ 1, 6, 32, 160, 768, 3584, 16384, 73728, …
  (−∞, 0]nonnegative
• A108838 → x ↦ x/(x+1)
  2 · 3, 5 · 4, 16, 14 · 5, 35, 70, 42 … Σ 2, 8, 34, 152, 706, 3376, 16514, 82256, …
  [−1, 0]nonnegative
• A144442 → D
  1 · 17, 2 · 118, 236, 3 · 729, 5362, 2187, 4 … Σ 0, 1, 19, 357, 8282, 230730, 7537767, …
  (−∞, 0]nonnegative
• A038284 → basis A013609 → (θ+1)²
  196, 1344, 1296 · 2744, 28224, 54432, 27648 … Σ 2836, 113048, 4156048, 144755936, …
  (−∞, 0]nonnegative