Proof methods / preserver_image

Image under a real-rootedness preserver

8,704 sequences

• A123519 → reverse → x ↦ x/(x+1)
  4, 14, 11 · 8, 44, 76, 41 · 16, 120, 324, 372, 153 … Σ 29, 169, 985, 5741, 33461, 195025, …
  [−1, 0]nonnegative
• A103327 → reverse → D+1
  1 · 4, 3 · 11, 20, 5 · 22, 91, 56, 7 … Σ 1, 7, 36, 176, 832, 3840, 17408, 77824, …
  (−∞, 0]nonnegative
• A156289 → D
  3 · 15, 30 · 63, 420, 315 · 255, 4410, 9450, 3780 … Σ 0, 3, 45, 798, 17895, 500643, 17106180, …
  (−∞, 0]nonnegative
• A166343 → θ+1
  1, 24, 3 · 1, 54, 81, 4 · 1, 116, 486, 232, 5 … Σ 28, 140, 840, 5880, 47040, 423360, …
  (−∞, 0]nonnegative
• A225470 → basis A013609 → basis A007318
  1 · 5, 2 · 40, 26, 4 · 440, 366, 96, 8 … Σ 1, 7, 70, 910, 14560, 276640, 6086080, …
  (−∞, −1]nonnegativerational roots
• A038271 → basis A013610 → D
  15 · 360, 450 · 6480, 16200, 10125 … Σ 0, 15, 810, 32805, 1180980, 39858075, …
  (−∞, 0]nonnegativerational roots
• A081580 → γ → D
  5 · 10 · 15, 50 · 20, 150 … Σ 0, 0, 5, 10, 65, 170, 700, 2030, …
  (−∞, 0]nonnegative
• A161198 → basis A013610 → (θ+1)²
  1 · 3, 24 · 15, 192, 324 · 105, 1704, 4860, 3456 … Σ 1, 27, 531, 10125, 200889, 4242987, …
  (−∞, 0]nonnegative
• A093375 → D
  1 · 4, 2 · 9, 12, 3 · 16, 36, 24, 4 … Σ 0, 1, 6, 24, 80, 240, 672, 1792, …
  (−∞, −1]nonnegativerational roots
• A304330 → D
  1 · 1, 24 · 1, 120, 1080 · 1, 504, 15120, 80640 … Σ 0, 1, 25, 1201, 96265, 11652001, …
  (−∞, 0]nonnegative
• A178822 → θ+1
  1 · 6, 12 · 21, 84, 63 · 56, 336, 504, 224 … Σ 1, 18, 168, 1120, 6048, 28224, 118272, …
  (−∞, 0]nonnegativerational roots
• A135838 → θ+1
  1 · 2, 4 · 2, 8, 6 · 4, 24, 36, 16 … Σ 1, 6, 16, 80, 192, 896, 2048, 9216, …
  (−∞, 0]nonnegativerational roots
• A085841 → D+1
  1 · 7, 4 · 45, 72, 16 · 147, 812, 528, 64 … Σ 1, 11, 133, 1551, 17225, 184531, …
  (−∞, 0]nonnegative
• A084950 → (θ+1)²
  1 · 2, 4 · 6, 16 · 24, 72, 9 … Σ 1, 6, 22, 105, 585, 3784, 27976, …
  (−∞, 0]nonnegative
• A093375 → D → (θ+1)²
  1 · 4, 8 · 9, 48, 27 · 16, 144, 216, 64 … Σ 0, 1, 12, 84, 440, 1920, 7392, 25984, …
  (−∞, 0]nonnegative
• A052553 → basis A013609 → θ+1
  1 · 1 · 2, 4 · 3, 8 … Σ 1, 1, 6, 11, 37, 84, 233, 565, …
  (−∞, 0]nonnegative
• A008277 → θ+1 → reverse → x ↦ x+1
  1 · 3, 1 · 10, 8, 1 · 37, 49, 17, 1 … Σ 1, 4, 19, 104, 641, 4380, 32803, …
  (−∞, −1]nonnegative
• A229032 → D+1
  1 · 2 · 7, 4 · 20, 16 … Σ 1, 2, 11, 36, 133, 454, 1551, 5192, …
  (−∞, 0]nonnegative
• A038271 → basis A013611 → basis A007318
  1 · 32, 20 · 1024, 1280, 400 … Σ 1, 52, 2704, 140608, 7311616, …
  (−∞, −1]nonnegativerational roots
• A178822 → basis A013609 → D
  12 · 168, 168 · 1344, 2688, 1344 … Σ 0, 12, 336, 5376, 64512, 645120, …
  (−∞, 0]nonnegativerational roots
• A048854 → D+1
  1 · 3, 1 · 24, 14, 1 · 300, 240, 33, 1 … Σ 1, 4, 39, 574, 11149, 267576, 7625779, …
  (−∞, 0]nonnegative
• A111596: The matrix inverse of the unsigned Lah numbers A271703.
  A059110 → x ↦ −x−1
  1 · 0, 1 · 0, -2, 1 · 0, 6, -6, 1 … Σ 1, 1, -1, 1, 1, -19, 151, -1091, …
  [−1, ∞)
• A375853: Triangle read by rows: T(n, k) = k*(n - k)*binomial(2*n+2, 2*k+1)/(4*n + 2) for 1 <= k <= n-1.
  2 · 8, 8 · 20, 56, 20 · 40, 216, 216, 40 … Σ 2, 16, 96, 512, 2560, 12288, 57344, …
  (−∞, 0)nonnegative
• A172431 → basis A013610 → reverse
  1 · 6, 3 · 27, 30, 8 · 108, 198, 114, 21 … Σ 1, 9, 65, 441, 2929, 19305, 126881, …
  (−∞, 0]nonnegative
• A088996 → θ+1
  1 · 0, 2 · 0, 2, 6 · 0, 4, 21, 24 … Σ 1, 2, 8, 49, 403, 4152, 51342, 740211, …
  (−∞, 0]nonnegative
• A038329 → basis A013610 → basis A007318
  576, 432, 81 · 13824, 15552, 5832, 729 … Σ 1089, 35937, 1185921, 39135393, …
  (−∞, −1]nonnegativerational roots
• A038319 → basis A013611
  256, 640, 400 · 4096, 15360, 19200, 8000 … Σ 1296, 46656, 1679616, 60466176, …
  [−1, 0]nonnegativerational roots
• A159854 → basis A013609 → (θ+1)²
  1, 16, 36 · 2, 40, 144, 128 · 4, 96, 468, 768, 400 … Σ 53, 314, 1736, 9152, 46592, 230912, …
  (−∞, 0]nonnegative
• A013622 → basis A007318
  1 · 8, 5 · 64, 80, 25 · 512, 960, 600, 125 … Σ 1, 13, 169, 2197, 28561, 371293, …
  (−∞, −1]nonnegativerational roots
• A257621: Triangle read by rows: T(n, k) = t(n-k, k), where t(0,0) = 1, t(n,m) = 0 if n < 0 or m < 0, else t(n,m) = f(m)*t(n-1,m) + f(n)*t(n,m-1), and f(n) = 4*…
  1 · 3, 3 · 9, 42, 9 · 27, 393, 393, 27 … Σ 1, 6, 60, 840, 15120, 332640, 8648640, …
  (−∞, 0)nonnegative
• A290598 → D
  1 · 14, 2 · 210, 60, 3 · 3640, 1560, 156, 4 … Σ 0, 1, 16, 273, 5360, 120965, 3101376, …
  (−∞, 0]nonnegative
• A026729 → basis A013611 → D
  4 · 12, 32 · 28, 160, 192 · 60, 512, 1344, 1024 … Σ 0, 4, 44, 380, 2940, 21400, 149800, …
  (−∞, 0]nonnegative
• A159854 → basis A008277 → x ↦ x/(x+1)
  1, 5, 5 · 2, 16, 33, 20 · 4, 48, 158, 200, 87 … Σ 11, 71, 497, 3757, 30523, 265287, …
  [−1, 0]nonnegative
• basis-map coefficients of A371080, shifted → D+1
  1 · 1, 1 · 3, 5, 1 · 18, 36, 12, 1 … Σ 1, 2, 9, 67, 698, 9354, 153304, …
  (−∞, 0]nonnegative
• A086645 → Veronese 2 → x ↦ x+1
  1 · 1 · 2, 1 · 16, 15 … Σ 1, 1, 3, 31, 145, 601, 2979, 14743, …
  (−∞, −1]nonnegative
• A038324 → basis A007318 → (θ+1)²
  1 · 21, 40 · 441, 1680, 900 … Σ 1, 61, 3021, 134881, 5651641, …
  (−∞, 0]nonnegative
• A038320 → x ↦ x+1 → x ↦ x+1
  529, 276, 36 · 12167, 9522, 2484, 216 … Σ 841, 24389, 707281, 20511149, …
  (−∞, −1]nonnegativerational roots
• A075501 → reverse
  1, 18, 36 · 1, 36, 252, 216 · 1, 60, 900, 3240, 1296 … Σ 55, 505, 5497, 69823, 1007407, …
  (−∞, 0]nonnegative
• A225467 → reverse
  1 · 4, 3 · 16, 40, 9 · 64, 336, 316, 27 … Σ 1, 7, 65, 743, 9921, 150151, 2526593, …
  (−∞, 0]nonnegative
• A391045 → θ+1 → x ↦ x/(x+1)
  1 · 1, 3 · 1, 10, 12 · 1, 21, 69, 53 … Σ 1, 4, 23, 144, 941, 6308, 43007, …
  [−1, 0]nonnegative
• A124932 → basis A007318 → D+1
  1 · 8, 3 · 39, 33, 6 · 152, 204, 84, 10 … Σ 1, 11, 78, 450, 2295, 10773, 47628, …
  (−∞, 0]nonnegative
• A038303 → basis A013609 → D+1
  1 · 13, 2 · 165, 52, 4 · 2057, 990, 156, 8 … Σ 1, 15, 221, 3211, 46137, 656903, …
  (−∞, 0]nonnegativerational roots
• A054142 → D
  1 · 3, 2 · 5, 12, 3 · 7, 30, 30, 4 … Σ 0, 1, 5, 20, 71, 235, 744, 2285, …
  (−∞, 0]nonnegative
• A114655 → D
  2 · 12, 4 · 48, 48, 6 · 160, 320, 120, 8 … Σ 0, 2, 16, 102, 608, 3530, 20256, …
  (−∞, 0]nonnegative
• A099097 → x ↦ x−5
  1 · -15, 3 · 220, -89, 9 · -3225, 1965, -399, 27 … Σ 1, -12, 140, -1632, 19024, -221760, …
  (41/9, 5]
• A086915 → x ↦ x/(x+1)
  2 · 4, 8 · 12, 48, 44 · 48, 288, 528, 304 … Σ 2, 12, 104, 1168, 16032, 259264, …
  [−1, 0]nonnegative
• A130534 → D → D+1
  1 · 5, 2 · 23, 18, 3 · 120, 130, 42, 4 … Σ 0, 1, 7, 44, 296, 2204, 18236, 166984, …
  (−∞, 0]nonnegative
• A257619 → D+1
  1 · 4, 2 · 48, 52, 4 · 572, 1692, 588, 8 … Σ 1, 6, 104, 2860, 106392, 4964960, …
  (−∞, 0]nonnegative
• A063007 → x ↦ x/(x+1)
  1 · 1, 3 · 1, 8, 13 · 1, 15, 57, 63 … Σ 1, 4, 22, 136, 886, 5944, 40636, …
  [−1, 0)nonnegative
• A069466 → D
  2 · 24, 12 · 180, 360, 60 · 1120, 5040, 3360, 280 … Σ 0, 2, 36, 600, 9800, 158760, 2561328, …
  (−∞, 0]nonnegative