Sequences

• A038321 → basis A013609 → D+1
  828, 896, 196 · 19440, 34776, 18816, 2744 … Σ 1920, 75776, 2883584, 106954752, …
  (−∞, 0]nonnegativerational roots
• A172431 → basis A013609 → basis A013609
  1 · 7, 8 · 40, 88, 48 · 217, 696, 736, 256 … Σ 1, 15, 176, 1905, 19951, 205920, …
  (−∞, 0]nonnegative
• A008292 → γ (scale 1/4) (shift +1) → θ+1
  1 · 2 · 4, 4 · 8, 32 … Σ 1, 2, 8, 40, 240, 1680, 13440, 120960, …
  (−∞, 0]nonnegative
• A038303 → Pₙ + Pₙ₊₁
  11, 1 · 110, 21, 1 · 1100, 320, 31, 1 … Σ 12, 132, 1452, 15972, 175692, 1932612, …
  (−∞, ∞)nonnegativerational roots
• A081577 → basis A013609
  1 · 2, 2 · 6, 12, 4 · 16, 48, 40, 8 … Σ 1, 4, 22, 112, 580, 2992, 15448, 79744, …
  (−∞, 0]nonnegative
• A094816 → basis A013609 → x ↦ x+1
  1 · 4, 2 · 19, 18, 4 · 106, 142, 60, 8 … Σ 1, 6, 41, 316, 2721, 25946, 271801, …
  (−∞, −1]nonnegative
• A185263 → basis A013610
  1 · 1 · 2, 3 · 6, 15 … Σ 1, 1, 5, 21, 189, 1485, 19305, 225225, …
  (−∞, 0]nonnegative
• A129710 → basis A013610
  1 · 2 · 3, 3 · 5, 9 … Σ 1, 2, 6, 14, 38, 94, 246, 622, …
  (−∞, 0]nonnegative
• A269945 → θ+1
  1 · 0, 2 · 0, 2, 3 · 0, 2, 15, 4 … Σ 1, 2, 5, 21, 126, 1001, 10129, 126006, …
  (−∞, 0]nonnegative
• basis-map coefficients of A297191, shifted → basis A013609 → θ+1
  1 · 1, 8, 12 · 1, 16, 72, 128, 80 … Σ 1, 21, 297, 3645, 41553, 452709, …
  (−∞, 0]nonnegativerational roots
• A093562 → basis A013609
  1 · 6, 2 · 12, 16, 4 · 24, 56, 40, 8 … Σ 1, 8, 32, 128, 512, 2048, 8192, 32768, …
  (−∞, 0]nonnegativerational roots
• A038277 → x ↦ x+1 → basis A013610
  1 · 29, 33 · 841, 1914, 1089 … Σ 1, 62, 3844, 238328, 14776336, …
  (−∞, 0]nonnegativerational roots
• A159854 → Veronese 2
  0, 1 · 0, 1 · 0, 1, 1 · 0, 1, 3 … Σ 1, 1, 2, 4, 8, 16, 32, 64, …
  (−∞, 0]nonnegative
• A110552 → basis A013609
  1 · 3, 4 · 10, 26, 16 · 36, 136, 164, 64 … Σ 1, 7, 52, 400, 3136, 24832, 197632, …
  (−∞, 0]nonnegativerational roots
• A249248 → reverse → θ+1
  1 · 3, 2 · 3, 14, 3 · 3, 44, 36, 4 … Σ 1, 5, 20, 87, 367, 1615, 7206, 33149, …
  (−∞, 0]nonnegative
• Triangle read by rows: T(n, m) = S1(n, m)*6^(n-m), where S1 are the signed Stirling numbers of first kind A008275 (n >= 1, 1 <= m <= n).
  72, -18, 1 · -1296, 396, -36, 1 … Σ 55, -935, 21505, -623645, 21827575, …
  [0, ∞)rational roots
• A257617 → Pₙ + Pₙ₊₁
  3, 2 · 6, 38, 4 · 12, 424, 392, 8 … Σ 5, 48, 836, 20592, 653400, 25344000, …
  (−∞, ∞)nonnegative
• A116414 → basis A013609 → basis A013609
  1 · 7, 4 · 46, 56, 16 · 301, 564, 336, 64 … Σ 1, 11, 118, 1265, 13561, 145376, …
  (−∞, 0]nonnegative
• A132393 → basis A013611 → x ↦ x+1
  1 · 5, 4 · 30, 44, 16 · 210, 428, 288, 64 … Σ 1, 9, 90, 990, 11880, 154440, 2162160, …
  (−∞, −1]nonnegativerational roots
• A130534 → basis A008277 → x ↦ x/(x+1)
  1 · 2, 3 · 6, 18, 13 · 24, 108, 156, 73 … Σ 1, 5, 37, 361, 4361, 62701, 1044205, …
  [−1, 0]nonnegative
• A135065 → x ↦ x+1 → D+1
  1 · 12, 4 · 72, 54, 9 · 320, 384, 144, 16 … Σ 1, 16, 135, 864, 4725, 23328, 107163, …
  (−∞, 0]nonnegativerational roots
• A001263 → basis A013610 → basis A013609
  1 · 5, 6 · 29, 66, 36 · 185, 612, 648, 216 … Σ 1, 11, 131, 1661, 22101, 305151, …
  (−∞, 0]nonnegative
• A229032 → Veronese 2 (j=1)
  4 · 16 · 40 · 80 … Σ 0, 0, 4, 16, 40, 80, 204, 736, …
  (−∞, 0]nonnegative
• A038320 → x ↦ x/(x+1)
  121, 374, 289 · 1331, 6171, 9537, 4913 … Σ 784, 21952, 614656, 17210368, …
  [−1, 0]nonnegativerational roots
• A038303 → basis A013610 → reverse
  1 · 3, 11 · 9, 66, 121 · 27, 297, 1089, 1331 … Σ 1, 14, 196, 2744, 38416, 537824, …
  (−∞, 0]nonnegativerational roots
• A013620 → Veronese 2 → D+1
  1 · 2 · 13, 9 · 62, 54 … Σ 1, 2, 22, 116, 691, 3902, 21880, …
  (−∞, 0]nonnegative
• A063967 → x ↦ x−12
  1 · -11, 1 · 110, -21, 1 · -1089, 319, -31, 1 … Σ 1, -10, 90, -800, 7100, -63000, 559000, …
  (7, 11]
• A128099 → basis A013611 → basis A008277
  1 · 1 · 11, 8 · 21, 16 … Σ 1, 1, 19, 37, 443, 1237, 12219, 43189, …
  (−∞, 0]nonnegative
• A201701 → D+1
  1 · 1 · 3, 1 · 7, 3 … Σ 1, 1, 4, 10, 27, 71, 186, 484, …
  (−∞, 0]nonnegative
• A038271 → basis A013611
  1 · 12, 20 · 144, 480, 400 · 1728, 8640, 14400, 8000 … Σ 1, 32, 1024, 32768, 1048576, 33554432, …
  (−∞, 0]nonnegativerational roots
• A173018 → reverse (shift +1) → reverse → θ+1
  1 · 1 · 1, 2 · 1, 8, 3 … Σ 1, 1, 3, 12, 60, 360, 2520, 20160, …
  (−∞, 0]nonnegative
• A193685 → D+1
  1 · 6, 1 · 36, 13, 1 · 216, 127, 21, 1 … Σ 1, 7, 50, 365, 2727, 20878, 163967, …
  (−∞, 0]nonnegative
• A143495 → D+1 → θ+1
  1 · 4, 2 · 16, 18, 3 · 64, 122, 45, 4 … Σ 1, 6, 37, 235, 1540, 10427, 73013, …
  (−∞, 0]nonnegative
• A137320 → x ↦ x+1 → θ+1
  1 · 2, 4 · 6, 20, 12 · 24, 104, 108, 32 … Σ 1, 6, 38, 268, 2116, 18608, 180912, …
  (−∞, 0]nonnegative
• A344565 → (θ+1)²
  3 · 15, 60 · 45, 360, 405 · 105, 1260, 2835, 1680 … Σ 3, 75, 810, 5880, 33600, 163296, …
  (−∞, 0]nonnegative
• A104684 → D → (θ+1)²
  1 · 6, 8 · 30, 96, 27 · 140, 720, 540, 64 … Σ 0, 1, 14, 153, 1464, 12825, 105678, …
  (−∞, 0]nonnegative
• A046716 → basis A013610 → reverse
  1 · 3, 2 · 9, 15, 5 · 27, 99, 75, 16 … Σ 1, 5, 29, 217, 2297, 34349, 674965, …
  (−∞, 0]nonnegative
• A038319 → basis A013611 → basis A008288
  1296, 1840, 400 · 46656, 112960, 59200, 8000 … Σ 3536, 226816, 14576896, 937035776, …
  [−3−2√2, −3+2√2]nonnegative
• A288874: Row reversed version of triangle A201637 (second-order Eulerian triangle).
  A201637 → reverse (shift +1)
  1 · 0, 1 · 0, 2, 1 · 0, 6, 8, 1 … Σ 1, 1, 3, 15, 105, 945, 10395, 135135, …
  (−∞, 0]nonnegative
• A128813 → basis A007318 → D+1
  1 · 3, 1 · 18, 16, 3 · 174, 280, 135, 18 … Σ 1, 4, 37, 607, 15477, 565782, 28060809, …
  (−∞, 0]nonnegative
• A038320 → D+1
  253, 204, 36 · 3509, 4554, 1836, 216 … Σ 493, 10115, 201433, 3925487, 75252421, …
  (−∞, 0]nonnegativerational roots
• A094816 → basis A013610 → x ↦ x+1
  1 · 5, 3 · 29, 33, 9 · 193, 312, 162, 27 … Σ 1, 8, 71, 694, 7421, 86276, 1084483, …
  (−∞, −1]nonnegative
• A130123 → Veronese 2
  1 · 0, 4 · 0, 0, 16 · 0, 0, 0, 64 … Σ 1, 0, 4, 0, 16, 0, 64, 0, …
  (−∞, 0]nonnegativerational roots
• A104684 → basis A013609 → θ+1
  1 · 3, 4 · 13, 32, 12 · 63, 228, 180, 32 … Σ 1, 7, 57, 503, 4577, 42135, 389625, …
  (−∞, 0]nonnegative
• A085881 → γ
  1 · 1 · 3 · 15 … Σ 1, 1, 3, 15, 105, 945, 10395, 135135, …
  (−∞, −1][−1, 0][−3−2√2, −3+2√2]+2
• A038323 → D
  9 · 198, 162 · 3267, 5346, 2187 … Σ 0, 9, 360, 10800, 288000, 7200000, …
  (−∞, 0]nonnegativerational roots
• A113953 → basis A013611 → θ+1
  1 · 1, 8 · 3, 32, 48 · 5, 88, 336, 256 … Σ 1, 9, 83, 685, 5435, 41725, 313275, …
  (−∞, 0]nonnegative
• A367270 → basis A013609
  1 · 1 · 3, 4 · 10, 24, 12 … Σ 1, 1, 7, 46, 307, 2086, 14374, 100108, …
  (−∞, 0]nonnegative
• A114656 → basis A013609 → D+1
  1 · 5, 2 · 27, 24, 4 · 147, 222, 84, 8 … Σ 1, 7, 55, 461, 4013, 35795, 324715, …
  (−∞, 0]nonnegative
• A229032 → x ↦ x+1 → θ+1
  1 · 2 · 7, 8 · 20, 32 … Σ 1, 2, 15, 52, 253, 1014, 4395, 18088, …
  (−∞, 0]nonnegative