Sequences

• A034870 → D+1
  1 · 3, 4, 1 · 5, 16, 18, 8, 1 … Σ 1, 8, 48, 256, 1280, 6144, 28672, …
  (−∞, 0]nonnegativerational roots
• A144442 → x ↦ x+1
  1 · 2, 1 · 19, 19, 1 · 238, 357, 121, 1 … Σ 1, 3, 39, 717, 18031, 580173, 22797479, …
  (−∞, −1]nonnegative
• A034870 → basis A013610 → basis A013609
  1 · 25, 60, 36 · 625, 3000, 5400, 4320, 1296 … Σ 1, 121, 14641, 1771561, 214358881, …
  (−∞, 0]nonnegativerational roots
• A038331 → basis A013611
  289, 680, 400 · 4913, 17340, 20400, 8000 … Σ 1369, 50653, 1874161, 69343957, …
  (−∞, 0]nonnegativerational roots
• A038329 → D
  72, 18 · 1296, 648, 81 · 20736, 15552, 3888, 324 … Σ 90, 2025, 40500, 759375, 13668750, …
  (−∞, 0]nonnegativerational roots
• A079621 → D
  1 · 12, 2 · 144, 48, 3 · 1920, 960, 120, 4 … Σ 0, 1, 14, 195, 3004, 51845, 998346, …
  (−∞, 0]nonnegative
• A178822 → basis A013610 → x ↦ x/(x+1)
  1 · 12, 30 · 84, 420, 525 · 448, 3360, 8400, 7000 … Σ 1, 42, 1029, 19208, 302526, 4235364, …
  [−1, 0]nonnegativerational roots
• A132393 → Veronese 2 → x ↦ x+1
  1 · 1, 1 · 3, 3 · 12, 13, 1 … Σ 1, 0, 2, 6, 26, 140, 896, 6636, …
  (−∞, −1]nonnegative
• A027467 → basis A013611
  1 · 16, 4 · 256, 128, 16 · 4096, 3072, 768, 64 … Σ 1, 20, 400, 8000, 160000, 3200000, …
  (−∞, 0]nonnegativerational roots
• A376827 → D
  1 · 6, 6 · 21, 42, 21 · 76, 228, 228, 76 … Σ 0, 1, 12, 84, 608, 4080, 27072, 176064, …
  (−∞, 0]nonnegativerational roots
• A371081 → reverse
  1 · 1, 16 · 1, 52, 400 · 1, 116, 2948, 14400 … Σ 1, 17, 453, 17465, 921233, 63789145, …
  (−∞, 0]nonnegative
• A207823 → basis A013609 → D+1
  1 · 7, 2 · 44, 28, 4 · 261, 266, 84, 8 … Σ 1, 9, 76, 619, 4915, 38296, 294069, …
  (−∞, 0]nonnegative
• A304236 → Veronese 2
  1 · 1 · 1 · 1 … Σ 1, 1, 1, 1, 10, 28, 55, 91, …
  (−∞, 0]nonnegative
• A085880 → x ↦ x+1 → reverse
  1 · 1, 2 · 2, 8, 8 · 5, 30, 60, 40 … Σ 1, 3, 18, 135, 1134, 10206, 96228, …
  (−∞, 0]nonnegativerational roots
• A109692 → basis A007318 → x ↦ x/(x+1)
  1 · 2, 3 · 8, 26, 21 · 48, 244, 412, 231 … Σ 1, 5, 55, 935, 21505, 623645, 21827575, …
  [−1, 0]nonnegativerational roots
• A172431 → D → D
  6 · 20, 24 · 42, 120, 60 · 72, 336, 420, 120 … Σ 0, 0, 6, 44, 222, 948, 3672, 13332, …
  (−∞, 0]nonnegative
• A169803 → basis A013610 → basis A007318
  1 · 5, 3 · 9, 6 · 29, 33, 9 … Σ 1, 8, 15, 71, 176, 673, 1905, 6616, …
  (−∞, −1]nonnegative
• A128813 → basis A013609 → D
  2 · 20, 24 · 236, 648, 432 … Σ 0, 2, 44, 1316, 55996, 3282616, …
  (−∞, 0]nonnegative
• A038321 → basis A013610 → θ+1
  324, 1512, 1323 · 5832, 40824, 71442, 37044 … Σ 3159, 155142, 7296237, 333135504, …
  (−∞, 0]nonnegativerational roots
• A159854 → x ↦ x+1
  1, 2, 1 · 2, 5, 4, 1 · 4, 12, 13, 6, 1 … Σ 4, 12, 36, 108, 324, 972, 2916, 8748, …
  (−∞, −1]nonnegativerational roots
• A085880 → basis A013610 → basis A008277
  1 · 5, 3 · 50, 78, 18 · 625, 1935, 1080, 135 … Σ 1, 8, 146, 3775, 122360, 4693962, …
  (−∞, 0]nonnegative
• A261711 → (θ+1)²
  1 · 4 · 15, 4 · 56, 32 … Σ 1, 4, 19, 88, 402, 1816, 8128, 36096, …
  (−∞, 0]nonnegative
• A026729 → basis A013610 → θ+1
  1 · 1, 6 · 2, 18, 27 · 3, 42, 135, 108 … Σ 1, 7, 47, 288, 1688, 9584, 53200, …
  (−∞, 0]nonnegative
• A207824 → basis A013610 → D
  3 · 36, 18 · 318, 324, 81 · 2484, 3834, 1944, 324 … Σ 0, 3, 54, 723, 8586, 95508, 1019466, …
  (−∞, 0]nonnegative
• Veronese parent of A098172 → D+1
  1, 1 · 0, 0, 3, 5, 1 · 0, 0, 0, 0, 5, 13, 9, 1 … Σ 2, 9, 28, 76, 192, 464, 1088, 2496, …
  (−∞, 0]nonnegative
• A257615 → γ
  1 · 5 · 25, 20 · 125, 340 … Σ 1, 5, 45, 465, 5865, 83565, 1346805, …
  (−∞, 0]nonnegative
• A028326 → D → basis A008277
  2 · 8, 4 · 24, 30, 6 · 64, 152, 72, 8 … Σ 0, 2, 12, 60, 296, 1510, 8088, 45682, …
  (−∞, 0]nonnegative
• Veronese parent of A098172 → D
  0, 2, 3 · 0, 0, 0, 4, 10, 6 … Σ 0, 5, 20, 60, 160, 400, 960, 2240, …
  (−∞, 0]nonnegativerational roots
• A091044 → basis A007318 → basis A013610
  1 · 6, 6 · 35, 66, 27 · 204, 564, 468, 108 … Σ 1, 12, 128, 1344, 14080, 147456, …
  (−∞, 0]nonnegative
• A249139 → basis A013610 → D
  3 · 6 · 27, 18 · 66, 54 … Σ 0, 3, 6, 45, 120, 555, 1674, 6393, …
  (−∞, 0]nonnegative
• A062190 → reverse → D+1
  1 · 7, 1 · 35, 16, 1 · 140, 132, 27, 1 … Σ 1, 8, 52, 300, 1595, 8008, 38584, …
  (−∞, 0]nonnegative
• A013610 → Veronese 2 → D
  9 · 27 · 54, 162 · 90, 810 … Σ 0, 0, 9, 27, 216, 900, 4752, 21168, …
  (−∞, 0]nonnegative
• A130123 → D → basis A013609
  2 · 8, 16 · 24, 96, 96 · 64, 384, 768, 512 … Σ 0, 2, 24, 216, 1728, 12960, 93312, …
  (−∞, 0]nonnegativerational roots
• A199881 → x ↦ x/(x+1)
  1, 2 · 0, 1, 2 · 0, 1, 4, 4 · 0, 0, 2, 7, 6 … Σ 3, 3, 9, 15, 33, 63, 129, 255, …
  [−1, 0]nonnegative
• A091044: One half of odd-numbered entries of even-numbered rows of Pascal's triangle A007318.
  1 · 2, 2 · 3, 10, 3 · 4, 28, 28, 4 … Σ 1, 4, 16, 64, 256, 1024, 4096, 16384, …
  (−∞, 0)nonnegative
• A033282 → x ↦ x+1 → D+1
  1 · 5, 2 · 26, 25, 5 · 138, 219, 105, 14 … Σ 1, 7, 56, 476, 4187, 37645, 343630, …
  (−∞, 0]nonnegative
• A038331 → Pₙ + Pₙ₊₁
  1872, 2280, 925, 125 · 22464, 36720, 22500, 6125, 625 … Σ 5202, 88434, 1503378, 25557426, …
  (−∞, ∞)nonnegativerational roots
• Triangle T(n, k) = coefficients of ( t(n, x) ) where t(n, x) = (1-x)^(n+1)*p(n, x)/x, p(n, x) = x*D( p(n-1, x) ), with p(1, x) = x/(1-x)^2, p(2, x) = x*(1+x)/(…
  1, 8, 1 · 1, 19, 19, 1 · 1, 42, 114, 42, 1 … Σ 10, 40, 200, 1200, 8400, 67200, 604800, …
  (−∞, 0)nonnegative
• A059473 → x ↦ x+1 → D+1
  1 · 6, 2 · 36, 26, 4 · 200, 232, 80, 8 … Σ 1, 8, 66, 520, 3992, 30048, 222784, …
  (−∞, 0]nonnegative
• A131222 → D+1
  1 · 1, 1 · 3, 5, 1 · 14, 32, 12, 1 … Σ 1, 2, 9, 59, 506, 5354, 67344, 981336, …
  (−∞, 0]nonnegative
• A038255: Triangle whose (i,j)-th entry is binomial(i,j)*6^(i-j).
  1 · 6, 1 · 36, 12, 1 · 216, 108, 18, 1 … Σ 1, 7, 49, 343, 2401, 16807, 117649, …
  (−∞, −1]nonnegativerational roots
• A064861 → Veronese 2 → D
  2 · 8 · 13, 8 · 25, 56 … Σ 2, 8, 21, 81, 189, 675, 1512, 5184, …
  (−∞, 0]nonnegative
• A030528 → basis A013610
  1 · 2, 3 · 3, 12, 9 · 5, 30, 54, 27 … Σ 1, 5, 24, 116, 560, 2704, 13056, 63040, …
  (−∞, 0]nonnegative
• A038330 → basis A013609 → reverse
  64, 256, 256 · 512, 3072, 6144, 4096 … Σ 576, 13824, 331776, 7962624, 191102976, …
  (−∞, 0]nonnegativerational roots
• basis-map coefficients of A026729, shifted → D
  -1 · 0, 2 · 0, 0, -3 · 0, 0, 0, 4 … Σ 0, -1, 2, -3, 4, -5, 6, -7, …
  (−∞, 0]rational roots
• A086915 → x ↦ x+1
  2 · 8, 4 · 44, 40, 8 · 304, 384, 144, 16 … Σ 2, 12, 92, 848, 9072, 110048, 1488608, …
  (−∞, −1]nonnegative
• A038330 → basis A013610 → basis A008277
  784, 816, 144 · 21952, 42048, 17280, 1728 … Σ 1744, 83008, 4301824, 241533952, …
  (−∞, 0]nonnegative
• A209599 → basis A013610
  1 · 2 · 4, 3 · 8, 9 … Σ 1, 2, 7, 17, 52, 137, 397, 1082, …
  (−∞, 0]nonnegative
• A113214 → x ↦ x−6
  1 · -4, 1 · 18, -9, 1 · -84, 62, -14, 1 … Σ 1, -3, 10, -35, 125, -450, 1625, -5875, …
  (2, 6]
• A178822 → basis A013609 → basis A013610
  1 · 24, 36 · 336, 1008, 756 … Σ 1, 60, 2100, 56000, 1260000, 25200000, …
  (−∞, 0]nonnegativerational roots