Sequences

• A109692: Triangle of coefficients in expansion of (1+x)*(1+3x)*(1+5x)*(1+7x)*...*(1+(2n-1)x).
  1 · 1, 1 · 1, 4, 3 · 1, 9, 23, 15 … Σ 1, 2, 8, 48, 384, 3840, 46080, 645120, …
  (−∞, 0)nonnegativerational roots
• A039756 → x ↦ x+1 → θ+1
  1 · 2, 2 · 6, 12, 3 · 24, 76, 48, 4 … Σ 1, 4, 21, 152, 1361, 13956, 159701, …
  (−∞, 0]nonnegative
• basis-map coefficients of A026729 → basis A013611 → basis A013609
  1 · 5, 8 · 25, 80, 64 · 125, 600, 960, 512 … Σ 1, 13, 169, 2197, 28561, 371293, …
  (−∞, 0]nonnegativerational roots
• A130123 → basis A013610 → D+1
  1 · 8, 6 · 28, 96, 36 · 80, 504, 864, 216 … Σ 1, 14, 160, 1664, 16384, 155648, …
  (−∞, 0]nonnegativerational roots
• A104029 → D+1
  1 · 3, 1 · 8, 7, 1 · 17, 31, 12, 1 … Σ 1, 4, 16, 61, 223, 790, 2734, 9295, …
  (−∞, 0]nonnegative
• Triangle T(n,k) read by rows: T(n, k) = (m*n - m*k + 1)*T(n - 1, k - 1) + (9*k - 8)*(m*k - (m - 1))*T(n - 1, k) where m = 0.
  1, 11, 1 · 1, 111, 30, 1 · 1, 1111, 681, 58, 1 … Σ 13, 143, 1852, 27563, 473725, 9290396, …
  (−∞, 0)nonnegative
• A131689 → D
  1 · 1, 4 · 1, 12, 18 · 1, 28, 108, 96 … Σ 0, 1, 5, 31, 233, 2071, 21305, 249271, …
  (−∞, 0]nonnegative
• A130123 → basis A013610 → θ+1
  1 · 2, 12 · 4, 48, 108 · 8, 144, 648, 864 … Σ 1, 14, 160, 1664, 16384, 155648, …
  (−∞, 0]nonnegativerational roots
• A103327 → basis A013609 → basis A007318
  1 · 6, 2 · 44, 32, 4 · 328, 376, 120, 8 … Σ 1, 8, 80, 832, 8704, 91136, 954368, …
  (−∞, −1]nonnegative
• A249253 → basis A007318
  1 · 4, 1 · 17, 5 · 89, 30, 1 … Σ 1, 5, 22, 120, 764, 5588, 46232, …
  (−∞, −1]nonnegative
• A038327 → basis A013609 → D+1
  1 · 15, 2 · 221, 60, 4 · 3211, 1326, 180, 8 … Σ 1, 17, 285, 4725, 77625, 1265625, …
  (−∞, 0]nonnegativerational roots
• A119900 → basis A008277
  1 · 2, 2 · 4, 10, 3 · 8, 40, 28, 4 … Σ 1, 4, 17, 80, 415, 2348, 14351, 94016, …
  (−∞, 0]nonnegative
• A356546 → basis A013611 → basis A008277
  1 · 12, 8 · 216, 384, 96 · 4320, 15680, 9600, 1280 … Σ 1, 20, 696, 30880, 1622880, 97388928, …
  (−∞, 0]nonnegative
• A008306 → basis A008277
  1 · 2 · 9, 3 · 44, 20 … Σ 1, 2, 12, 64, 455, 3618, 33131, 338728, …
  (−∞, 0]nonnegative
• A013610 → basis A007318 → basis A013610
  1 · 7, 9 · 49, 126, 81 · 343, 1323, 1701, 729 … Σ 1, 16, 256, 4096, 65536, 1048576, …
  (−∞, 0]nonnegativerational roots
• A272866 → basis A007318 → D
  5, 2 · 50, 70, 30, 4 · 375, 900, 825, 360, 75, 6 … Σ 0, 7, 154, 2541, 37268, 512435, …
  (−∞, −1]nonnegative
• A227450 → θ+1
  2 · 2, 8 · 2, 24, 24 · 2, 56, 144, 64 … Σ 2, 10, 50, 266, 1522, 9354, 61490, …
  (−∞, 0]nonnegative
• A091042 → basis A013610 → basis A013609
  1 · 13, 18 · 121, 300, 180 · 1093, 3822, 4284, 1512 … Σ 1, 31, 601, 10711, 186961, 3245551, …
  (−∞, 0]nonnegative
• A161198 → θ+1
  1 · 1, 4 · 3, 16, 12 · 15, 92, 108, 32 … Σ 1, 5, 31, 247, 2433, 28653, 393279, …
  (−∞, 0]nonnegative
• A038243 → reverse
  1 · 1, 5 · 1, 10, 25 · 1, 15, 75, 125 … Σ 1, 6, 36, 216, 1296, 7776, 46656, …
  (−∞, 0]nonnegativerational roots
• A062145 → x ↦ x+1 → D+1
  1 · 9, 4 · 51, 50, 10 · 252, 378, 165, 20 … Σ 1, 13, 111, 815, 5573, 36633, 234979, …
  (−∞, 0]nonnegative
• A078812 → basis A013609 → basis A013611
  1 · 5, 8 · 24, 80, 64 · 115, 584, 960, 512 … Σ 1, 13, 168, 2171, 28055, 362544, …
  (−∞, 0]nonnegative
• A028326 → basis A013610 → basis A008277
  2 · 10, 6 · 50, 78, 18 · 250, 774, 432, 54 … Σ 2, 16, 146, 1510, 17480, 223522, …
  (−∞, 0]nonnegative
• A257606 → D
  4 · 40, 32 · 296, 592, 192 · 1928, 7104, 5784, 1024 … Σ 0, 4, 72, 1080, 15840, 237600, 3706560, …
  (−∞, 0]nonnegative
• A196347 → Pₙ + Pₙ₊₁
  2, 1 · 3, 5, 2 · 8, 22, 20, 6 · 30, 114, 162, 102, 24 … Σ 3, 10, 56, 432, 4224, 49920, 691200, …
  (−∞, ∞)nonnegativerational roots
• Triangle whose (i,j)-th entry is binomial(i,j)*11^(i-j)*5^j.
  121, 110, 25 · 1331, 1815, 825, 125 … Σ 256, 4096, 65536, 1048576, 16777216, …
  (−∞, −1]nonnegativerational roots
• A093644: (9,1) Pascal triangle.
  1 · 9, 1 · 9, 10, 1 · 9, 19, 11, 1 … Σ 1, 10, 20, 40, 80, 160, 320, 640, …
  (−∞, 0)nonnegativerational roots
• A156992 → basis A008277 → (θ+1)²
  1 · 4, 8 · 24, 120, 54 · 192, 1824, 1944, 384 … Σ 1, 12, 198, 4344, 122400, 4303440, …
  (−∞, 0]nonnegative
• A003506 → x ↦ x+1 → D+1
  1 · 6, 2 · 24, 18, 3 · 80, 96, 36, 4 … Σ 0, 1, 8, 45, 216, 945, 3888, 15309, …
  (−∞, 0]nonnegativerational roots
• A132812 → basis A007318 → x ↦ x/(x+1)
  1 · 4, 6 · 15, 45, 33 · 56, 252, 372, 180 … Σ 1, 10, 93, 860, 7985, 74550, 699685, …
  [−1, 0]nonnegative
• A116412 → Veronese 2 (j=1)
  1 · 6 · 21, 1 · 60, 12 … Σ 0, 1, 6, 22, 72, 235, 774, 2557, …
  (−∞, 0]nonnegative
• A054142 → Veronese 2 → D+1
  1 · 1 · 2, 1 · 7, 6 … Σ 1, 1, 3, 13, 34, 102, 305, 875, …
  (−∞, 0]nonnegative
• A081580 → basis A013611 → x ↦ x+1
  1 · 6, 4 · 61, 68, 16 · 516, 872, 448, 64 … Σ 1, 10, 145, 1900, 25525, 340750, …
  (−∞, −1]nonnegative
• A286718 → basis A013611 → θ+1
  1 · 2, 8 · 10, 56, 48 · 80, 528, 720, 256 … Σ 1, 10, 114, 1584, 26352, 513216, …
  (−∞, 0]nonnegative
• A167884 → D+1
  1 · 2, 1 · 19, 20, 1 · 180, 537, 182, 1 … Σ 1, 3, 40, 900, 28080, 1113840, …
  (−∞, 0]nonnegative
• A130123 → basis A008277 → θ+1
  1 · 2, 4 · 4, 24, 12 · 8, 112, 144, 32 … Σ 1, 6, 40, 296, 2416, 21568, 208832, …
  (−∞, 0]nonnegative
• A116414 → basis A013609 → D+1
  1 · 7, 2 · 42, 28, 4 · 233, 258, 84, 8 … Σ 1, 9, 74, 583, 4461, 33416, 246289, …
  (−∞, 0]nonnegative
• A145324 → basis A013611 → x ↦ x/(x+1)
  1 · 3, 11 · 12, 92, 176 · 60, 712, 2812, 3696 … Σ 1, 14, 280, 7280, 232960, 8852480, …
  [−1, 0]nonnegativerational roots
• A081579 → x ↦ x+1 → basis A013610
  1 · 3, 3 · 17, 30, 9 · 75, 201, 153, 27 … Σ 1, 6, 56, 456, 3856, 32256, 270656, …
  (−∞, 0]nonnegative
• A137597 → x ↦ x+1 → x ↦ x/(x+1)
  1 · 3, 4 · 11, 29, 19 · 47, 184, 239, 103 … Σ 1, 7, 59, 573, 6241, 74887, 977419, …
  [−1, 0]nonnegative
• A111125 → D → x ↦ x+1
  1 · 7, 2 · 31, 20, 3 · 115, 120, 39, 4 … Σ 0, 1, 9, 54, 278, 1323, 6003, 26380, …
  (−∞, −1]nonnegative
• A249252 → basis A013609
  1 · 5, 8 · 17, 48, 32 · 61, 248, 320, 128 … Σ 1, 13, 97, 757, 5881, 45709, 355249, …
  (−∞, 0]nonnegative
• A079510 → (θ+1)²
  1 · 0, 8 · 0, 12, 54 · 0, 0, 180, 384 … Σ 1, 8, 66, 564, 5215, 52380, 571228, …
  (−∞, 0]nonnegative
• veronese parent of Table read by rows: 1 if x = y, 0 otherwise, where (x,y) = (0,0),(0,1),(1,0),(0,2),(1,1),(2,0),...
  0, 1 · 0, 0, -1 · 0, 0, 0, 1 · 0, 0, 0, 0, -1 … Σ 1, -1, 1, -1, 1, -1, 1, -1, …
  (−∞, 0]rational roots
• A124932 → reverse
  1 · 3, 2 · 6, 9, 3 · 10, 24, 18, 4 … Σ 1, 5, 18, 56, 160, 432, 1120, 2816, …
  (−∞, 0]nonnegativerational roots
• A038322 → basis A008277
  1 · 19, 8 · 361, 368, 64 · 6859, 12824, 5184, 512 … Σ 1, 27, 793, 25379, 883057, 33250795, …
  (−∞, 0]nonnegative
• Veronese parent of A109447 → basis A013610
  2, 9, 9 · 4, 12, 9 · 8, 60, 162, 189, 81 … Σ 20, 25, 500, 625, 12500, 15625, 312500, …
  (−∞, 0]nonnegativerational roots
• A038255 → basis A013610 → basis A008277
  1 · 10, 3 · 100, 69, 9 · 1000, 1197, 351, 27 … Σ 1, 13, 178, 2575, 39415, 638386, …
  (−∞, 0]nonnegative
• A113413 → x ↦ x+1 → basis A013609
  1 · 4, 2 · 14, 16, 4 · 50, 88, 48, 8 … Σ 1, 6, 34, 194, 1106, 6306, 35954, …
  (−∞, 0]nonnegative
• A143495 → (θ+1)²
  1 · 3, 4 · 9, 28, 9 · 27, 148, 108, 16 … Σ 1, 7, 46, 299, 1967, 13248, 91903, …
  (−∞, 0]nonnegative