Sequences

• basis-map coefficients of A127647 → D+1
  1 · 2, 1 · 6, 8, 2 · 12, 27, 18, 3 … Σ 1, 3, 16, 60, 240, 896, 3328, 12096, …
  (−∞, 0]nonnegativerational roots
• A103327 → basis A013609 → basis A013610
  1 · 6, 6 · 44, 96, 36 · 328, 1128, 1080, 216 … Σ 1, 12, 176, 2752, 43776, 699392, …
  (−∞, 0]nonnegative
• A046716 → basis A013609 → basis A013611
  1 · 4, 8 · 19, 72, 64 · 118, 648, 1088, 512 … Σ 1, 12, 155, 2366, 50205, 1666336, …
  (−∞, 0]nonnegative
• A200536 → basis A013609 → basis A008277
  1 · 28, 38, 8 · 784, 3572, 3236, 864, 64 … Σ 1, 74, 8520, 1426040, 323596656, …
  (−∞, 0]nonnegative
• A172431 → basis A007318 → x ↦ x+1
  1 · 5, 2 · 21, 16, 3 · 85, 94, 34, 4 … Σ 1, 7, 40, 217, 1159, 6160, 32689, …
  (−∞, −1]nonnegative
• A063007 → basis A013610 → θ+1
  1 · 3, 12 · 13, 108, 162 · 63, 792, 2430, 2160 … Σ 1, 15, 283, 5445, 104541, 1995939, …
  (−∞, 0]nonnegative
• A059364 → basis A007318 → basis A007318
  1 · 4, 1 · 28, 15, 2 · 280, 234, 65, 6 … Σ 1, 5, 45, 585, 9945, 208845, 5221125, …
  (−∞, −1]nonnegativerational roots
• A144441 → x ↦ x/(x+1)
  1 · 1, 2 · 1, 16, 16 · 1, 86, 252, 168 … Σ 1, 3, 33, 507, 10537, 278067, 8917809, …
  [−1, 0]nonnegative
• A269944 → basis A013610
  1 · 1, 3 · 2, 9, 9 · 10, 51, 72, 27 … Σ 1, 4, 20, 160, 2080, 41600, 1206400, …
  (−∞, 0]nonnegativerational roots
• A038335 → x ↦ x+1 → θ+1
  1 · 21, 18 · 441, 756, 243 · 9261, 23814, 15309, 2916 … Σ 1, 39, 1440, 51300, 1782000, 60750000, …
  (−∞, 0]nonnegativerational roots
• A391533 → basis A013609 → D+1
  21, 20, 4 · 60, 106, 56, 8 · 156, 416, 388, 144, 16 … Σ 45, 230, 1120, 5280, 24320, 110080, …
  (−∞, 0]nonnegative
• A113953 → θ+1 → D
  2 · 4, 6 · 0, 24, 12 · 0, 24, 72, 20 … Σ 0, 2, 10, 36, 116, 334, 918, 2400, …
  (−∞, 0]nonnegative
• A144699 → (θ+1)²
  1 · 1, 20 · 1, 64, 225 · 1, 156, 1539, 2000 … Σ 1, 21, 290, 3696, 47460, 633360, …
  (−∞, 0]nonnegative
• A069466 → basis A013611
  1 · 4, 8 · 36, 144, 96 · 400, 2400, 3840, 1280 … Σ 1, 12, 276, 7920, 252420, 8536752, …
  (−∞, 0]nonnegative
• A257180 → (θ+1)²
  9, 96, 81 · 27, 564, 1269, 432 … Σ 186, 2292, 29316, 394800, 5624640, …
  (−∞, 0]nonnegative
• A008459 → x ↦ x+1 → reverse
  1 · 1, 2 · 1, 6, 6 · 1, 12, 30, 20 … Σ 1, 3, 13, 63, 321, 1683, 8989, 48639, …
  (−∞, 0]nonnegative
• A085478 → reverse → D+1
  1 · 2, 1 · 4, 5, 1 · 6, 17, 9, 1 … Σ 1, 3, 10, 33, 105, 324, 977, 2895, …
  (−∞, 0]nonnegative
• A111006 → D+1
  1 · 1, 1 · 1, 5, 2 · 0, 4, 11, 3 … Σ 1, 2, 8, 18, 48, 110, 260, 586, …
  (−∞, 0]nonnegative
• A257606 → (θ+1)²
  1 · 4, 16 · 16, 160, 144 · 64, 1184, 2664, 1024 … Σ 1, 20, 320, 4936, 77184, 1247040, …
  (−∞, 0]nonnegative
• A159854 → basis A013609 → x ↦ x/(x+1)
  1, 6, 9 · 2, 16, 42, 36 · 4, 40, 148, 240, 144 … Σ 16, 96, 576, 3456, 20736, 124416, …
  [−1, 0]nonnegativerational roots
• A027465 → basis A008277 → x ↦ x+1
  1 · 5, 1 · 26, 11, 1 · 141, 94, 18, 1 … Σ 1, 6, 38, 254, 1790, 13278, 103470, …
  (−∞, −1]nonnegative
• A356546 → basis A013609 → D
  4 · 48, 48 · 480, 960, 480 · 4480, 13440, 13440, 4480 … Σ 0, 4, 96, 1920, 35840, 645120, …
  (−∞, 0]nonnegativerational roots
• basis-map coefficients of A026729 → basis A013610 → basis A013609
  1 · 4, 6 · 16, 48, 36 · 64, 288, 432, 216 … Σ 1, 10, 100, 1000, 10000, 100000, …
  (−∞, 0]nonnegativerational roots
• A144698 → Pₙ + Pₙ₊₁
  2, 4 · 2, 17, 16 · 2, 45, 129, 64 … Σ 6, 35, 240, 1890, 16800, 166320, …
  (−∞, ∞)nonnegative
• A081577 → basis A013611 → basis A013609
  1 · 6, 8 · 46, 112, 64 · 336, 1216, 1408, 512 … Σ 1, 14, 222, 3472, 54380, 851592, …
  (−∞, 0]nonnegative
• A133080 → D → θ+1
  1 · 0, 4 · 0, 4, 9 · 0, 0, 0, 16 … Σ 0, 1, 4, 13, 16, 41, 36, 85, …
  (−∞, 0]nonnegativerational roots
• A143491 → basis A008277
  12, 8, 1 · 60, 60, 15, 1 · 360, 480, 180, 24, 1 … Σ 21, 136, 1045, 9276, 93289, 1047376, …
  (−∞, 0]nonnegative
• Veronese parent of A109447 → basis A008277
  2, 4, 1 · 4, 5, 1 · 8, 46, 46, 13, 1 … Σ 7, 10, 114, 151, 2589, 3263, 77821, …
  (−∞, 0]nonnegative
• A344565 → basis A008277
  3 · 30, 15 · 180, 225, 45 · 840, 1995, 945, 105 … Σ 3, 45, 450, 3885, 31710, 254772, …
  (−∞, 0]nonnegative
• A001263 → θ+1 → x ↦ x/(x+1)
  1 · 1, 3 · 1, 8, 10 · 1, 15, 45, 35 … Σ 1, 4, 19, 96, 501, 2668, 14407, 78592, …
  [−1, 0]nonnegative
• A096956 → basis A013611
  6 · 7, 24 · 14, 76, 96 · 28, 208, 496, 384 … Σ 6, 31, 186, 1116, 6696, 40176, 241056, …
  (−∞, 0]nonnegativerational roots
• A144696 → x ↦ x+1
  1 · 3, 2 · 12, 15, 4 · 60, 108, 57, 8 … Σ 1, 5, 31, 233, 2071, 21305, 249271, …
  (−∞, −1]nonnegative
• A038220 → basis A013610 → (θ+1)²
  1 · 5, 24 · 25, 240, 324 · 125, 1800, 4860, 3456 … Σ 1, 29, 589, 10241, 162745, 2437061, …
  (−∞, 0]nonnegative
• A152842 → reverse → D+1
  1 · 4, 1 · 7, 6, 1 · 24, 29, 10, 1 … Σ 1, 5, 14, 64, 160, 704, 1664, 7168, …
  (−∞, 0]nonnegative
• A256890 → Pₙ + Pₙ₊₁
  12, 64, 56, 8 · 24, 248, 468, 204, 16 … Σ 140, 960, 7560, 67200, 665280, 7257600, …
  (−∞, ∞)nonnegative
• A013620 → basis A013610 → x ↦ x/(x+1)
  1 · 5, 14 · 25, 140, 196 · 125, 1050, 2940, 2744 … Σ 1, 19, 361, 6859, 130321, 2476099, …
  [−1, 0]nonnegativerational roots
• A144441 → γ
  1 · 1 · 1, 12 · 1, 80 … Σ 1, 1, 13, 81, 1117, 15537, 294733, …
  (−∞, 0]nonnegative
• A026729 → basis A013609
  1 · 1, 2 · 2, 6, 4 · 3, 14, 20, 8 … Σ 1, 3, 12, 45, 171, 648, 2457, 9315, …
  (−∞, 0]nonnegative
• A145597 → (θ+1)²
  1 · 3, 12 · 6, 60, 54 · 10, 180, 405, 160 … Σ 1, 15, 120, 755, 4191, 21567, 105560, …
  (−∞, 0]nonnegative
• A062190 → reverse → x ↦ x+1
  1 · 7, 1 · 36, 16, 1 · 165, 135, 27, 1 … Σ 1, 8, 53, 328, 1966, 11584, 67582, …
  (−∞, −1]nonnegative
• A035342 → θ+1
  1 · 3, 2 · 15, 18, 3 · 105, 174, 54, 4 … Σ 1, 5, 36, 337, 3875, 52776, 830095, …
  (−∞, 0]nonnegative
• A069466 → basis A007318 → θ+1
  1 · 4, 4 · 36, 72, 18 · 400, 1200, 720, 80 … Σ 1, 8, 126, 2400, 49350, 1055376, …
  (−∞, 0]nonnegative
• A110441 → reverse → θ+1
  1 · 1, 6 · 1, 12, 21 · 1, 18, 69, 60 … Σ 1, 7, 34, 148, 612, 2452, 9608, 37024, …
  (−∞, 0]nonnegative
• A395454: Triangle read by rows: T(n, k) = Sum_{j=0..n} C(-j-1, -n-1)*E2(j, n-k), E2 the Eulerian numbers A201637.
  1 · 0, 2 · 0, 6, 2 · 0, 24, 34, 2 … Σ 1, 0, 2, 8, 60, 544, 6040, 79008, …
  (−∞, 0]nonnegative
• A038277 → D+1
  1 · 18, 11 · 203, 396, 121 · 1960, 6699, 6534, 1331 … Σ 1, 29, 720, 16524, 361584, 7663248, …
  (−∞, 0]nonnegativerational roots
• A075497 → x ↦ x/(x+1)
  1 · 2, 3 · 4, 14, 11 · 8, 52, 92, 49 … Σ 1, 5, 29, 201, 1657, 15821, 170389, …
  [−1, 0]nonnegative
• A153649 → basis A013611
  2 · 14, 28 · 98, 392, 32 · 686, 4116, 5552, 128 … Σ 2, 42, 522, 10482, 154242, 2759802, …
  (−∞, 0]nonnegative
• A056242 → x ↦ x+1
  1 · 3, 2 · 10, 13, 4 · 34, 65, 40, 8 … Σ 1, 5, 27, 147, 801, 4365, 23787, …
  (−∞, −1]nonnegative
• basis-map coefficients of A026729, shifted → (θ+1)² → basis A013611
  1 · -4, -16 · 9, 72, 144 · -16, -192, -768, -1024 … Σ 1, -20, 225, -2000, 15625, -112500, …
  (−∞, 0]rational roots
• A241171 → reverse
  1 · 6, 1 · 90, 30, 1 · 2520, 1260, 126, 1 … Σ 1, 7, 121, 3907, 202741, 15430207, …
  (−∞, 0]nonnegative