Sequences

• A059473 → x ↦ x/(x+1)
  1 · 2, 4 · 4, 18, 18 · 8, 56, 120, 80 … Σ 1, 6, 40, 264, 1744, 11520, 76096, …
  [−1, 0]nonnegative
• A100862 → x ↦ x+1 → D+1
  1 · 3, 1 · 10, 7, 1 · 35, 39, 12, 1 … Σ 1, 4, 18, 87, 447, 2418, 13692, 80769, …
  (−∞, 0]nonnegative
• A286718 → D+1
  1 · 2, 1 · 9, 7, 1 · 67, 63, 15, 1 … Σ 1, 3, 17, 146, 1686, 24484, 428548, …
  (−∞, 0]nonnegative
• A064861 → reverse → x ↦ x/(x+1)
  2, 7, 6 · 4, 20, 33, 18 · 4, 28, 73, 84, 36 … Σ 15, 75, 225, 1125, 3375, 16875, 50625, …
  [−1, 0]nonnegativerational roots
• A099040 → x ↦ x−15
  1 · -30, 2 · 870, -118, 4 · -25200, 5160, -352, 8 … Σ 1, -28, 756, -20384, 549584, -14817600, …
  (13, 15]
• basis-map coefficients of A026729, shifted → θ+1 → D
  -2 · 0, 6 · 0, 0, -12 · 0, 0, 0, 20 … Σ 0, -2, 6, -12, 20, -30, 42, -56, …
  (−∞, 0]rational roots
• A102413 → basis A013611
  1 · 2, 4 · 6, 24, 16 · 14, 84, 144, 64 … Σ 1, 6, 46, 306, 2066, 13926, 93886, …
  (−∞, 0]nonnegative
• Veronese parent of A098172 → basis A013611
  1, 8, 16 · 2, 36, 256, 896, 1536, 1024 … Σ 25, 3750, 562500, 84375000, …
  (−∞, 0]nonnegativerational roots
• A272867 → basis A013610 → D
  18, 18 · 216, 864, 972, 324 … Σ 0, 36, 2376, 117612, 5174928, …
  (−∞, 0]nonnegative
• A156992 → basis A013609 → D+1
  1 · 8, 4 · 72, 96, 24 · 768, 1728, 1152, 192 … Σ 1, 12, 192, 3840, 92160, 2580480, …
  (−∞, 0]nonnegativerational roots
• basis-map coefficients of A026729, shifted → basis A013609 → basis A008288
  1 · -3, -2 · 9, 16, 4 · -27, -82, -52, -8 … Σ 1, -5, 29, -169, 985, -5741, 33461, …
  [−3−2√2, −3+2√2]
• A200536 → reverse
  1 · 2, 3, 1 · 4, 12, 13, 6, 1 … Σ 1, 6, 36, 216, 1296, 7776, 46656, …
  (−∞, 0]nonnegativerational roots
• A027465 → basis A008277 → x ↦ x/(x+1)
  1 · 4, 5 · 16, 41, 26 · 64, 253, 329, 141 … Σ 1, 9, 83, 787, 7697, 77865, 816627, …
  [−1, 0]nonnegative
• A038337 → D+1
  408, 506, 121 · 6480, 13464, 8349, 1331 … Σ 1035, 29624, 815189, 21827598, …
  (−∞, 0]nonnegativerational roots
• A136124 → basis A013611 → basis A013609
  1 · 7, 8 · 56, 120, 64 · 504, 1528, 1536, 512 … Σ 1, 15, 240, 4080, 73440, 1395360, …
  (−∞, 0]nonnegativerational roots
• A204420 → basis A013609
  1 · 1, 2 · 9, 24, 12 · 225, 690, 540, 120 … Σ 1, 3, 45, 1575, 99225, 9823275, …
  (−∞, 0]nonnegativerational roots
• A030528 → basis A013609 → basis A008277
  1 · 4, 2 · 15, 20, 4 · 57, 148, 72, 8 … Σ 1, 6, 39, 285, 2308, 20509, 198033, …
  (−∞, 0]nonnegative
• A013613 → x ↦ x+1 → θ+1
  1 · 7, 12 · 49, 168, 108 · 343, 1764, 2268, 864 … Σ 1, 19, 325, 5239, 81289, 1228123, …
  (−∞, 0]nonnegativerational roots
• A272866 → D → D
  2 · 22, 36, 12 · 60, 270, 360, 180, 30 … Σ 0, 2, 70, 900, 8500, 68750, 506250, …
  (−∞, 0]nonnegative
• A166960 → D+1
  1 · 2, 1 · 7, 8, 1 · 28, 69, 24, 1 … Σ 1, 3, 16, 122, 1272, 17204, 291028, …
  (−∞, 0]nonnegative
• A088996 → x ↦ x/(x+1)
  1 · 0, 1 · 0, 1, 3 · 0, 2, 11, 15 … Σ 1, 1, 4, 28, 280, 3640, 58240, 1106560, …
  [−1, 0]nonnegativerational roots
• A038319 → Pₙ + Pₙ₊₁
  1452, 1925, 850, 125 · 15972, 28435, 18975, 5625, 625 … Σ 4352, 69632, 1114112, 17825792, …
  (−∞, ∞)nonnegativerational roots
• A052553 → basis A008277 → D+1
  1 · 1 · 3, 1 · 5, 2 … Σ 1, 1, 4, 7, 20, 43, 113, 267, …
  (−∞, 0]nonnegative
• narayana → basis A013610 → D
  3 · 15, 18 · 63, 162, 81 · 252, 1008, 1134, 324 … Σ 0, 3, 33, 306, 2718, 23805, 207495, …
  (−∞, 0]nonnegative
• A207823 → basis A013609 → D
  2 · 20, 8 · 146, 120, 24 · 940, 1176, 480, 64 … Σ 0, 2, 28, 290, 2660, 22840, 188132, …
  (−∞, 0]nonnegative
• A038335 → basis A013609 → basis A013609
  1 · 39, 36 · 1521, 2808, 1296 … Σ 1, 75, 5625, 421875, 31640625, …
  (−∞, 0]nonnegativerational roots
• A143685 → γ → D
  9 · 18 · 27, 162 · 36, 486 … Σ 0, 0, 9, 18, 189, 522, 3204, 10422, …
  (−∞, 0]nonnegative
• A111006 → basis A007318
  1 · 1, 1 · 3, 5, 2 · 5, 13, 11, 3 … Σ 1, 2, 10, 32, 124, 440, 1624, 5888, …
  (−∞, −1]nonnegative
• A136124 → basis A013611 → basis A013610
  1 · 7, 12 · 56, 180, 144 · 504, 2292, 3456, 1728 … Σ 1, 19, 380, 7980, 175560, 4037880, …
  (−∞, 0]nonnegativerational roots
• A013610 → Veronese 2 (j=1) → x ↦ x+1
  3 · 6 · 36, 27 · 120, 108 … Σ 0, 3, 6, 63, 228, 1527, 6930, 39819, …
  (−∞, −1]nonnegative
• A391533 → Pₙ + Pₙ₊₁ → basis A013610
  27, 81, 81, 27 · 54, 243, 405, 297, 81 … Σ 216, 1080, 5400, 27000, 135000, 675000, …
  (−∞, 0]nonnegativerational roots
• A145597 → γ → D+1
  1 · 3 · 9, 3 · 25, 15 … Σ 1, 3, 12, 40, 132, 420, 1316, 4068, …
  (−∞, 0]nonnegative
• A115951 → basis A007318
  1 · 2, 2 · 8, 14, 6 · 32, 84, 72, 20 … Σ 1, 4, 28, 208, 1624, 13024, 106336, …
  (−∞, −1]nonnegative
• A094305 → basis A013611
  1 · 6, 12 · 24, 96, 96 · 80, 480, 960, 640 … Σ 1, 18, 216, 2160, 19440, 163296, …
  (−∞, 0]nonnegativerational roots
• A108426 → D
  1 · 5, 4 · 28, 42, 15 · 165, 360, 252, 56 … Σ 0, 1, 9, 85, 833, 8361, 85305, 880685, …
  (−∞, 0]nonnegative
• A038325 → basis A013609 → θ+1
  1 · 22, 44 · 484, 1936, 1452 … Σ 1, 66, 3872, 212960, 11244288, …
  (−∞, 0]nonnegativerational roots
• A038329 → Pₙ + Pₙ₊₁
  1872, 1368, 333, 27 · 22464, 22032, 8100, 1323, 81 … Σ 3600, 54000, 810000, 12150000, …
  (−∞, ∞)nonnegativerational roots
• A133214 → D
  8, 8 · 18, 72, 24 · 32, 288, 384, 64 … Σ 16, 114, 768, 5010, 32016, 201698, …
  (−∞, 0]nonnegative
• A027467 → D
  1 · 30, 2 · 675, 90, 3 · 13500, 2700, 180, 4 … Σ 0, 1, 32, 768, 16384, 327680, 6291456, …
  (−∞, 0]nonnegativerational roots
• A027467 → x ↦ x+1 → (θ+1)²
  1 · 16, 4 · 256, 128, 9 · 4096, 3072, 432, 16 … Σ 1, 20, 393, 7616, 145945, 2770932, …
  (−∞, 0]nonnegative
• A038321 → basis A013610 → basis A013609
  1521, 3276, 1764 · 59319, 191646, 206388, 74088 … Σ 6561, 531441, 43046721, 3486784401, …
  (−∞, 0]nonnegativerational roots
• A085881 → Pₙ + Pₙ₊₁
  2, 1 · 4, 7, 3 · 18, 51, 48, 15 … Σ 3, 14, 132, 1800, 31920, 695520, …
  (−∞, ∞)nonnegativerational roots
• A152830 → basis A013609 → basis A013609
  1 · 1 · 1 · 1 … Σ 1, 1, 1, 1, 8, 8, 8, 8, …
  (−∞, 0]nonnegativerational roots
• A049460: Generalized Stirling number triangle of first kind read by rows: T(n, k) = [x^k] Product_{m=1..n} (x - m - r), with r = 4.
  1 · -5, 1 · 30, -11, 1 · -210, 107, -18, 1 … Σ 1, -4, 20, -120, 840, -6720, 60480, …
  [9/2, ∞)rational roots
• A062145 → x ↦ x/(x+1)
  1 · 1, 5 · 1, 12, 21 · 1, 21, 84, 84 … Σ 1, 6, 34, 190, 1059, 5908, 33028, …
  [−1, 0]nonnegative
• A103327 → Veronese 2 (j=1)
  1 · 10 · 35, 1 · 84, 36 … Σ 0, 1, 10, 36, 120, 496, 2080, 8256, …
  (−∞, 0]nonnegative
• A172431 → basis A013610 → basis A013611
  1 · 9, 24 · 65, 336, 432 · 441, 3336, 8352, 6912 … Σ 1, 33, 833, 19041, 415105, 8823969, …
  (−∞, 0]nonnegative
• A038284 → basis A013611 → D
  672, 1152 · 14112, 48384, 41472 … Σ 1824, 103968, 5267712, 250216320, …
  (−∞, 0]nonnegativerational roots
• A122542 → basis A013610 → basis A013609
  1 · 4, 6 · 24, 60, 36 · 136, 492, 576, 216 … Σ 1, 10, 120, 1420, 16820, 199220, …
  (−∞, 0]nonnegative
• A048993 → θ+1 → D+1
  1 · 2, 2 · 2, 8, 3 · 2, 20, 21, 4 … Σ 1, 4, 13, 47, 188, 825, 3937, 20270, …
  (−∞, 0]nonnegative