Proof methods / preserver_image

Image under a real-rootedness preserver

8,704 sequences

• A038284 → basis A013610 → D
  504, 648 · 10584, 27216, 17496 … Σ 1152, 55296, 2359296, 94371840, …
  (−∞, 0]nonnegativerational roots
• A321434 → D+1
  1 · 1, 1 · 1, 1 · 1, 5, 2 … Σ 1, 2, 2, 8, 8, 44, 44, 308, …
  (−∞, 0]nonnegative
• A114687 → reverse → θ+1
  1 · 2, 2 · 4, 12, 3 · 8, 48, 36, 4 … Σ 1, 4, 19, 96, 501, 2668, 14407, 78592, …
  (−∞, 0]nonnegative
• A130123 → basis A013609 → D+1
  1 · 6, 4 · 20, 48, 16 · 56, 240, 288, 64 … Σ 1, 10, 84, 648, 4752, 33696, 233280, …
  (−∞, 0]nonnegativerational roots
• A039756 → x ↦ x/(x+1)
  1 · 1, 2 · 1, 6, 6 · 1, 12, 34, 24 … Σ 1, 3, 13, 71, 457, 3355, 27509, 248127, …
  [−1, 0]nonnegative
• A391533 → x ↦ x+1 → (θ+1)²
  9, 24, 9 · 18, 84, 72, 16 · 36, 240, 333, 160, 25 … Σ 42, 190, 794, 3150, 12042, 44766, …
  (−∞, 0]nonnegative
• A075497 → x ↦ x+1
  1 · 3, 1 · 11, 8, 1 · 49, 55, 15, 1 … Σ 1, 4, 20, 120, 832, 6496, 56128, …
  (−∞, −1]nonnegative
• A196347 → basis A013609 → θ+1
  1 · 2, 4 · 8, 32, 24 · 48, 288, 432, 192 … Σ 1, 6, 64, 960, 18432, 430080, 11796480, …
  (−∞, 0]nonnegativerational roots
• A178821 → Veronese 2 (j=1) → D
  35 · 280 · 1260, 252 · 4200, 2520 … Σ 0, 0, 0, 35, 280, 1512, 6720, 26400, …
  (−∞, 0]nonnegative
• A152828 → basis A007318 → D+1
  1 · 1 · 1 · 3, 1 … Σ 1, 1, 1, 4, 4, 4, 15, 15, …
  (−∞, 0]nonnegativerational roots
• A038314 → D+1
  340, 528, 144 · 4600, 12240, 9504, 1728 … Σ 1012, 28072, 745360, 19208992, …
  (−∞, 0]nonnegativerational roots
• A178821 → basis A013610 → D+1
  1 · 25, 15 · 240, 450, 135 · 1540, 5040, 4725, 945 … Σ 1, 40, 825, 12250, 148750, 1575000, …
  (−∞, 0]nonnegativerational roots
• A121574 → basis A013611 → x ↦ x+1
  1 · 7, 4 · 54, 60, 16 · 413, 684, 368, 64 … Σ 1, 11, 130, 1529, 17989, 211640, …
  (−∞, −1]nonnegative
• A196347 → basis A013610 → θ+1
  1 · 2, 6 · 8, 48, 54 · 48, 432, 972, 648 … Σ 1, 8, 110, 2100, 51000, 1500000, …
  (−∞, 0]nonnegativerational roots
• A305540 → D
  1 · 2 · 4, 6 · 6, 12 … Σ 0, 1, 2, 10, 18, 88, 158, 844, …
  (−∞, 0]nonnegative
• A225117 → (θ+1)²
  1 · 2, 4 · 4, 52, 9 · 8, 372, 540, 16 … Σ 1, 6, 65, 936, 16416, 338580, 8019000, …
  (−∞, 0]nonnegative
• A308737 → D+1
  1 · 4, 3 · 9, 22, 7 · 18, 79, 76, 15 … Σ 1, 7, 38, 188, 888, 4080, 18400, 81856, …
  (−∞, 0]nonnegative
• A144440 → (θ+1)²
  1 · 1, 4 · 1, 44, 9 · 1, 216, 486, 16 … Σ 1, 5, 54, 719, 11707, 226440, 5073154, …
  (−∞, 0]nonnegative
• A098158 → θ+1
  1 · 0, 2 · 0, 2, 3 · 0, 0, 9, 4 … Σ 1, 2, 5, 13, 32, 76, 176, 400, …
  (−∞, 0]nonnegative
• A130123 → (θ+1)²
  1 · 0, 8 · 0, 0, 36 · 0, 0, 0, 128 … Σ 1, 8, 36, 128, 400, 1152, 3136, 8192, …
  [−1, 0]nonnegativerational roots
• A038221 → x ↦ x+1
  1 · 6, 3 · 36, 36, 9 · 216, 324, 162, 27 … Σ 1, 9, 81, 729, 6561, 59049, 531441, …
  (−∞, −1]nonnegativerational roots
• A094305: Triangle read by rows: T(n,k) = ((n+1)(n+2)/2) * binomial(n,k) (0 <= k <= n).
  1 · 3, 3 · 6, 12, 6 · 10, 30, 30, 10 … Σ 1, 6, 24, 80, 240, 672, 1792, 4608, …
  (−∞, −1]nonnegativerational roots
• A104978 → D+1
  1 · 2, 1 · 7, 11, 3 · 26, 77, 64, 12 … Σ 1, 3, 21, 179, 1657, 16035, 159485, …
  (−∞, 0]nonnegative
• A114655 → D+1
  2 · 6, 2 · 20, 16, 2 · 64, 96, 30, 2 … Σ 2, 8, 38, 192, 1002, 5336, 28814, …
  (−∞, 0]nonnegative
• A225470 → basis A013609 → D+1
  1 · 5, 2 · 36, 26, 4 · 360, 342, 96, 8 … Σ 1, 7, 66, 806, 12164, 219108, 4591600, …
  (−∞, 0]nonnegative
• A249248 → reverse → x ↦ x/(x+1)
  1 · 3, 4 · 3, 13, 11 · 3, 31, 65, 38 … Σ 1, 7, 27, 137, 681, 3687, 20595, …
  [−1, 0]nonnegative
• A114655 → θ+1
  2 · 4, 4 · 8, 24, 6 · 16, 96, 72, 8 … Σ 2, 8, 38, 192, 1002, 5336, 28814, …
  (−∞, 0]nonnegative
• A181543 → x ↦ x/(x+1)
  1 · 1, 2 · 1, 10, 10 · 1, 30, 84, 56 … Σ 1, 3, 21, 171, 1521, 14283, 138909, …
  [−1, 0]nonnegative
• A130123 → (θ+1)² → θ+1
  1 · 0, 16 · 0, 0, 108 · 0, 0, 0, 512 … Σ 1, 16, 108, 512, 2000, 6912, 21952, …
  (−∞, 0]nonnegativerational roots
• A013609 → basis A013610 → D+1
  1 · 9, 6 · 45, 108, 36 · 189, 810, 972, 216 … Σ 1, 15, 189, 2187, 24057, 255879, …
  (−∞, 0]nonnegativerational roots
• A147716 → D+1
  1 · 15, 1 · 224, 30, 1 · 3332, 672, 45, 1 … Σ 1, 16, 255, 4050, 64125, 1012500, …
  (−∞, 0]nonnegativerational roots
• A075500 → reverse
  1, 15, 25 · 1, 30, 175, 125 · 1, 50, 625, 1875, 625 … Σ 41, 331, 3176, 35451, 447981, 6282416, …
  (−∞, 0]nonnegative
• A053122 → x ↦ x+1 → D+1
  1 · 0, 1 · -2, 0, 1 · 2, -5, 0, 1 … Σ 1, 1, -1, -2, 1, 3, -1, -4, …
  (−∞, ∞)
• A099097 → x ↦ x−12
  1 · -36, 3 · 1284, -215, 9 · -45792, 11520, -966, 27 … Σ 1, -33, 1078, -35211, 1150105, …
  (104/9, 12]
• A107131 → D
  1 · 1, 2 · 0, 6, 3 · 0, 4, 18, 4 … Σ 0, 1, 3, 9, 26, 75, 216, 623, …
  (−∞, 0]nonnegative
• A120910 → Veronese 2 → D+1
  3 · 6 · 15, 3 · 42, 18 … Σ 3, 6, 18, 60, 201, 666, 2184, 7104, …
  (−∞, 0]nonnegative
• A122431 → x ↦ x/(x+1)
  1, 6, 12, 8 · 0, 1, 6, 12, 8 · 0, 0, 1, 6, 12, 8 … Σ 27, 27, 27, 27, 27, 27, 27, 27, …
  [−1, 0]nonnegativerational roots
• A110608 → θ+1
  6, 16, 3 · 20, 90, 54, 4 · 70, 448, 504, 128, 5 … Σ 25, 168, 1155, 8008, 55692, 387600, …
  (−∞, 0]nonnegative
• A152842 → D+1
  1 · 4, 3 · 5, 10, 3 · 8, 37, 42, 9 … Σ 1, 7, 18, 96, 224, 1088, 2432, 11264, …
  (−∞, 0]nonnegative
• A038208 → D → θ+1
  2 · 8, 16 · 24, 96, 72 · 64, 384, 576, 256 … Σ 0, 2, 24, 192, 1280, 7680, 43008, …
  (−∞, 0]nonnegativerational roots
• A357613 → θ+1
  1 · 3, 4 · 15, 40, 18 · 84, 336, 315, 80 … Σ 1, 7, 73, 815, 9281, 106375, 1221305, …
  (−∞, 0]nonnegative
• A086645 → basis A013609 → θ+1
  1 · 2, 4 · 8, 32, 12 · 32, 192, 216, 32 … Σ 1, 6, 52, 472, 4176, 36064, 305728, …
  (−∞, 0]nonnegative
• A104684 → basis A007318 → x ↦ x+1
  1 · 4, 1 · 22, 10, 1 · 136, 90, 18, 1 … Σ 1, 5, 33, 245, 1921, 15525, 127905, …
  (−∞, −1]nonnegative
• A130534 → basis A013610 → x ↦ x/(x+1)
  1 · 2, 5 · 6, 27, 30 · 24, 150, 309, 210 … Σ 1, 7, 63, 693, 9009, 135135, 2297295, …
  [−1, 0]nonnegativerational roots
• A166973 → x ↦ x+1
  1 · 2, 1 · 9, 9, 1 · 63, 82, 21, 1 … Σ 1, 3, 19, 167, 1771, 21943, 310379, …
  (−∞, −1]nonnegative
• A137320 → basis A013609 → D
  4 · 20, 32 · 104, 288, 192 · 616, 2272, 2688, 1024 … Σ 0, 4, 52, 584, 6600, 78096, 980016, …
  (−∞, 0]nonnegative
• A059364: Triangle T(n,k)=Sum_{i=0..n} |stirling1(n,n-i)|*binomial(i,k), k=0..n-1.
  1 · 2, 1 · 6, 7, 2 · 24, 46, 29, 6 … Σ 1, 3, 15, 105, 945, 10395, 135135, …
  (−∞, −1]nonnegativerational roots
• A093375 → Veronese 2 → x ↦ x+1
  1 · 2 · 4, 1 · 10, 6 … Σ 1, 2, 5, 16, 45, 126, 345, 932, …
  (−∞, −1]nonnegative
• A280580 → x ↦ x/(x+1)
  1 · 1, 2 · 2, 10, 9 · 5, 45, 90, 51 … Σ 1, 3, 21, 191, 1961, 21595, 249085, …
  [−1, 0]nonnegative
• A099093 → x ↦ x+1 → x ↦ x/(x+1)
  1 · 3, 6 · 12, 45, 42 · 45, 252, 468, 288 … Σ 1, 9, 99, 1053, 11259, 120285, 1285227, …
  [−1, 0]nonnegative