Sequences

• A091044 → ⊙ C(n+2,k+1) → D+1
  1 · 2, 1 · 6, 7, 1 · 15, 42, 17, 1 … Σ 1, 3, 14, 75, 438, 2702, 17324, 114291, …
  (−∞, 0]nonnegative
• A154233 → θ+1
  1 · 1, 2 · 1, 14, 3 · 1, 38, 57, 4 … Σ 1, 3, 18, 100, 753, 5817, 54460, …
  (−∞, 0]nonnegative
• A269944 → x ↦ x+1 → reverse
  1 · 1, 1 · 1, 3, 2 · 1, 8, 17, 10 … Σ 1, 2, 6, 36, 396, 7128, 192456, …
  (−∞, 0]nonnegativerational roots
• A116414 → x ↦ x/(x+1)
  1 · 4, 5 · 13, 34, 22 · 40, 162, 216, 95 … Σ 1, 9, 69, 513, 3789, 27945, 206037, …
  [−1, 0)nonnegative
• A081578 → θ+1
  1 · 1, 2 · 1, 10, 3 · 1, 18, 27, 4 … Σ 1, 3, 14, 50, 183, 637, 2188, 7380, …
  (−∞, 0]nonnegative
• A137597 → D+1
  1 · 3, 1 · 10, 7, 1 · 37, 40, 12, 1 … Σ 1, 4, 18, 90, 494, 2946, 18926, 130066, …
  (−∞, −1]nonnegative
• A125092 → basis A007318
  1 · 5, 4 · 18, 26, 9 · 56, 114, 75, 16 … Σ 1, 9, 53, 261, 1161, 4833, 19197, …
  (−∞, −1]nonnegative
• A085478 → reverse → (θ+1)²
  1 · 1, 4 · 1, 12, 9 · 1, 20, 54, 16 … Σ 1, 5, 22, 91, 349, 1260, 4349, 14509, …
  (−∞, 0]nonnegative
• A225476 → (θ+1)²
  1 · 1, 4 · 1, 16, 18 · 1, 52, 162, 96 … Σ 1, 5, 35, 311, 3341, 42065, 607055, …
  (−∞, 0]nonnegative
• A038326 → basis A013609 → basis A007318
  1 · 47, 24 · 2209, 2256, 576 … Σ 1, 71, 5041, 357911, 25411681, …
  (−∞, −1]nonnegativerational roots
• A091044 → basis A013610 → reverse
  1 · 6, 4 · 27, 48, 16 · 108, 360, 288, 64 … Σ 1, 10, 91, 820, 7381, 66430, 597871, …
  (−∞, 0]nonnegative
• A152828 → D+1
  1 · 1 · 1 · 2, 1 … Σ 1, 1, 1, 3, 3, 3, 8, 8, …
  (−∞, 0]nonnegativerational roots
• A229032 → basis A013609
  1 · 2 · 7, 8 · 20, 32 … Σ 1, 2, 15, 52, 269, 1110, 5179, 22568, …
  (−∞, 0]nonnegative
• A093564 → basis A008277
  1 · 8, 1 · 16, 11, 1 · 32, 49, 15, 1 … Σ 1, 9, 28, 97, 373, 1580, 7307, 36585, …
  (−∞, 0]nonnegative
• A063007 → x ↦ x+1 → x ↦ x/(x+1)
  1 · 3, 5 · 13, 44, 37 · 63, 321, 543, 305 … Σ 1, 8, 94, 1232, 16966, 240368, 3468844, …
  [−1, −1/2)nonnegative
• A121574 → basis A013610 → x ↦ x/(x+1)
  1 · 3, 6 · 10, 41, 40 · 33, 204, 408, 264 … Σ 1, 9, 91, 909, 9091, 90909, 909091, …
  [−1, 0]nonnegative
• A206306 → basis A008277
  1 · 1, 1 · 4, 6, 1 · 14, 32, 12, 1 … Σ 1, 2, 11, 59, 332, 1969, 12287, 80490, …
  (−∞, 0]nonnegative
• A035607 → basis A013609 → basis A007318
  1 · 1 · 7, 4 · 31, 32, 8 … Σ 1, 1, 11, 71, 481, 3241, 21851, 147311, …
  (−∞, 0]nonnegative
• A013609 → basis A008288 → θ+1
  1 · 3, 4 · 9, 32, 12 · 27, 164, 156, 32 … Σ 1, 7, 53, 379, 2617, 17631, 116621, …
  (−∞, 0]nonnegative
• A082985 → θ+1
  1 · 1, 6 · 1, 10, 15 · 1, 14, 42, 28 … Σ 1, 7, 26, 85, 265, 804, 2393, 7019, …
  (−∞, 0]nonnegative
• A013610 → Veronese 2 (j=1) → basis A013610
  3 · 6 · 36, 81 · 120, 324 … Σ 0, 3, 6, 117, 444, 4983, 25506, 225417, …
  (−∞, 0]nonnegative
• A391533 → reverse
  1, 4, 4 · 1, 5, 8, 4 · 1, 6, 13, 12, 4 … Σ 9, 18, 36, 72, 144, 288, 576, 1152, …
  (−∞, 0]nonnegativerational roots
• A081577 → basis A013610 → reverse
  1 · 3, 2 · 9, 18, 6 · 27, 90, 72, 16 … Σ 1, 5, 33, 205, 1289, 8085, 50737, …
  (−∞, 0]nonnegative
• A114687 → basis A013610 → basis A013609
  1 · 9, 12 · 89, 228, 144 · 945, 3528, 4320, 1728 … Σ 1, 21, 461, 10521, 248201, 6020301, …
  (−∞, 0]nonnegative
• A130123 → θ+1 → basis A007318
  1 · 4, 4 · 12, 24, 12 · 32, 96, 96, 32 … Σ 1, 8, 48, 256, 1280, 6144, 28672, …
  (−∞, −1]nonnegativerational roots
• A228955 → θ+1
  1 · 1, 2 · 2, 12 · 6, 72, 18 … Σ 1, 3, 14, 96, 864, 9600, 126720, …
  (−∞, 0]nonnegative
• A122542 → reverse → x ↦ x+1
  1 · 1 · 3, 2 · 7, 8, 2 … Σ 1, 1, 5, 17, 61, 217, 773, 2753, …
  (−∞, −1]nonnegative
• A367270 → D → θ+1
  2 · 6, 12 · 12, 72, 36 · 20, 240, 360, 80 … Σ 0, 0, 2, 18, 120, 700, 3780, 19404, …
  (−∞, 0]nonnegative
• A099040 → basis A007318 → (θ+1)²
  1 · 2, 8 · 6, 40, 36 · 16, 160, 288, 128 … Σ 1, 10, 82, 592, 3976, 25408, 156608, …
  (−∞, 0]nonnegative
• A028326 → basis A013610 → basis A013609
  2 · 10, 12 · 50, 120, 72 · 250, 900, 1080, 432 … Σ 2, 22, 242, 2662, 29282, 322102, …
  (−∞, 0]nonnegativerational roots
• A081577 → basis A013610
  1 · 2, 3 · 6, 18, 9 · 16, 72, 90, 27 … Σ 1, 5, 33, 205, 1289, 8085, 50737, …
  (−∞, 0]nonnegative
• A028338 → x ↦ x+1 → basis A013611
  1 · 3, 4 · 15, 32, 16 · 105, 284, 240, 64 … Σ 1, 7, 63, 693, 9009, 135135, 2297295, …
  (−∞, 0]nonnegativerational roots
• A112493 → reverse
  1 · 1, 1 · 3, 4, 1 · 15, 25, 11, 1 … Σ 1, 2, 8, 52, 472, 5504, 78416, 1320064, …
  (−∞, 0]nonnegative
• A153653 → basis A007318
  2 · 38, 19 · 722, 722, 2 · 13718, 20577, 6863, 2 … Σ 2, 57, 1446, 41160, 1057596, 29762148, …
  (−∞, 0]nonnegative
• A154986 → x ↦ x/(x+1)
  1 · 1, 2 · 1, 6, 6 · 1, 14, 36, 24 … Σ 1, 3, 13, 75, 537, 4611, 46053, 525483, …
  [−1, 0]nonnegative
• A136124 → basis A008277
  1 · 3, 1 · 12, 8, 1 · 60, 60, 15, 1 … Σ 1, 4, 21, 136, 1045, 9276, 93289, …
  (−∞, 0]nonnegative
• A147644 → basis A013610
  1 · 2, 3 · 4, 12, 9 · 12, 54, 72, 27 … Σ 1, 5, 25, 165, 825, 4125, 20625, …
  (−∞, 0]nonnegative
• A178820 → Veronese 2 (j=1) → basis A013609
  4 · 20 · 80, 40 · 280, 280 … Σ 0, 4, 20, 120, 560, 2464, 10080, 39360, …
  (−∞, 0]nonnegative
• A038335 → x ↦ x+1 → basis A008277
  1 · 30, 9 · 900, 621, 81 · 27000, 32319, 9477, 729 … Σ 1, 39, 1602, 69525, 3192615, 155127798, …
  (−∞, 0]nonnegative
• A038301 → basis A013609 → (θ+1)²
  400, 3520, 4356 · 8000, 105600, 261360, 170368 … Σ 8276, 545328, 32916240, 1874722752, …
  (−∞, 0]nonnegative
• A243662 → x ↦ x+1
  1 · 4, 1 · 21, 10, 1 · 126, 88, 18, 1 … Σ 1, 5, 32, 233, 1833, 15180, 130392, …
  (−∞, −1]nonnegative
• A038328 → basis A013609 → x ↦ x+1
  324, 144, 16 · 5832, 3888, 864, 64 … Σ 484, 10648, 234256, 5153632, 113379904, …
  (−∞, −1]nonnegativerational roots
• reversed rows → D
  2 · 3 · 4, 4 · 5, 10 … Σ 0, 2, 3, 8, 15, 30, 56, 104, …
  (−∞, 0]nonnegative
• A327997 → basis A013610
  1 · 4, 3 · 17, 27, 9 · 78, 195, 135, 27 … Σ 1, 7, 53, 435, 3873, 37383, 390501, …
  (−∞, 0]nonnegative
• A095660 → basis A013609
  3 · 4, 6 · 8, 20, 12 · 16, 56, 64, 24 … Σ 3, 10, 40, 160, 640, 2560, 10240, …
  (−∞, 0]nonnegativerational roots
• A133080 → basis A013609 → x ↦ x+1
  1 · 4, 2 · 9, 12, 4 · 36, 66, 40, 8 … Σ 1, 6, 25, 150, 625, 3750, 15625, 93750, …
  (−∞, −1]nonnegativerational roots
• A130534 → Veronese 2 → basis A013610
  1 · 1 · 3, 3 · 12, 18 … Σ 1, 1, 6, 30, 180, 1260, 10080, 90720, …
  (−∞, 0]nonnegative
• A053124: Triangle of coefficients of Chebyshev's U(n,2*x-1) polynomials (exponents of x in increasing order).
  1 · -2, 4 · 3, -16, 16 · -4, 40, -96, 64 … Σ 1, 2, 3, 4, 5, 6, 7, 8, …
  (0, 1)
• A038328 → x ↦ x+1 → θ+1
  196, 112, 12 · 2744, 2352, 504, 32 … Σ 320, 5632, 98304, 1703936, 29360128, …
  (−∞, 0]nonnegativerational roots
• A109692 → basis A013610 → D+1
  1 · 5, 3 · 38, 84, 27 · 348, 1524, 1827, 405 … Σ 1, 8, 149, 4104, 147681, 6532992, …
  (−∞, 0]nonnegative