Sequences

• A091044 → basis A013609
  1 · 4, 4 · 16, 32, 12 · 64, 192, 160, 32 … Σ 1, 8, 60, 448, 3344, 24960, 186304, …
  (−∞, 0]nonnegative
• A086645 → basis A013610 → basis A013611
  1 · 5, 12 · 41, 168, 144 · 365, 2196, 3888, 1728 … Σ 1, 17, 353, 8177, 198593, 4912337, …
  (−∞, 0]nonnegative
• A013612 → basis A008277
  36, 85, 25 · 216, 1115, 825, 125 … Σ 146, 2281, 40791, 816926, 18036311, …
  (−∞, 0]nonnegative
• A086645 → D → D+1
  1 · 8, 2 · 45, 36, 3 · 168, 308, 96, 4 … Σ 0, 1, 10, 84, 576, 3520, 19968, 107520, …
  (−∞, 0]nonnegative
• A038323 → basis A013610 → basis A013610
  1 · 47, 81 · 2209, 7614, 6561 … Σ 1, 128, 16384, 2097152, 268435456, …
  (−∞, 0]nonnegativerational roots
• A172431 → basis A013610 → D
  6 · 30, 54 · 114, 396, 324 · 390, 1998, 3240, 1620 … Σ 0, 6, 84, 834, 7248, 58878, 459468, …
  (−∞, 0]nonnegative
• Veronese parent of A098172 → θ+1
  1 · 0, 0, 3, 4 · 0, 0, 0, 0, 5, 12, 7 … Σ 1, 7, 24, 68, 176, 432, 1024, 2368, …
  (−∞, 0]nonnegativerational roots
• A156992 → basis A013611 → D
  8 · 96, 192 · 1152, 4608, 4608 … Σ 0, 8, 288, 10368, 414720, 18662400, …
  (−∞, 0]nonnegativerational roots
• A111006 → basis A008277
  1 · 1, 1 · 3, 7, 2 · 5, 27, 20, 3 … Σ 1, 2, 12, 55, 340, 2189, 15944, 124940, …
  (−∞, 0]nonnegative
• A094262 → D+1
  1 · 3, 4, 1 · 7, 30, 42, 22, 3 … Σ 1, 8, 104, 1888, 44032, 1254656, …
  (−∞, 0]nonnegative
• A133080 → basis A013609 → basis A013611
  1 · 4, 8 · 9, 48, 64 · 36, 264, 640, 512 … Σ 1, 12, 121, 1452, 14641, 175692, …
  (−∞, 0]nonnegativerational roots
• A113413 → basis A013610 → D+1
  1 · 6, 3 · 25, 36, 9 · 86, 231, 162, 27 … Σ 1, 9, 70, 506, 3494, 23394, 153182, …
  (−∞, 0]nonnegative
• A166972 → D
  1 · 10, 2 · 83, 82, 3 · 668, 2220, 366, 4 … Σ 0, 1, 12, 168, 3258, 83184, 2666952, …
  (−∞, 0]nonnegative
• A133087 → x ↦ x+1 → x ↦ x/(x+1)
  1 · 3, 4 · 4, 12, 9 · 12, 52, 75, 36 … Σ 1, 7, 25, 175, 625, 4375, 15625, …
  [−1, 0]nonnegativerational roots
• A091044 → basis A007318
  1 · 4, 2 · 16, 16, 3 · 64, 96, 40, 4 … Σ 1, 6, 35, 204, 1189, 6930, 40391, …
  (−∞, −1]nonnegative
• A207607 → basis A013610 → D
  6 · 27, 36 · 99, 270, 162 · 333, 1368, 1701, 648 … Σ 0, 6, 63, 531, 4050, 29172, 202473, …
  (−∞, 0]nonnegative
• A207606 → x ↦ x+1 → basis A013611
  26, 60, 32 · 97, 336, 368, 128 … Σ 118, 929, 7314, 57583, 453350, 3569217, …
  (−∞, 0]nonnegative
• A153648 → basis A013610
  2 · 10, 15 · 50, 150, 18 · 250, 1125, 1161, 54 … Σ 2, 25, 218, 2590, 26030, 285550, …
  (−∞, 0]nonnegative
• A054142 → Veronese 2 (j=1)
  1 · 3 · 5, 1 · 7, 10 … Σ 0, 1, 3, 6, 17, 45, 116, 305, …
  (−∞, 0]nonnegative
• A290319 → basis A013609 → x ↦ x/(x+1)
  1 · 2, 4 · 12, 40, 32 · 120, 544, 800, 384 … Σ 1, 6, 84, 1848, 55440, 2106720, …
  [−1, 0]nonnegativerational roots
• A196347 → basis A013609 → D+1
  1 · 4, 2 · 24, 32, 8 · 192, 432, 288, 48 … Σ 1, 6, 64, 960, 18432, 430080, 11796480, …
  (−∞, 0]nonnegativerational roots
• A144438 → x ↦ x+1
  1 · 2, 1 · 7, 7, 1 · 30, 45, 17, 1 … Σ 1, 3, 15, 93, 703, 6285, 64983, 763533, …
  (−∞, −1]nonnegative
• A013610 → Veronese 2 → basis A013609
  1 · 1 · 10, 18 · 28, 54 … Σ 1, 1, 28, 82, 892, 3916, 31024, 163864, …
  (−∞, 0]nonnegative
• A304236 → basis A007318 → θ+1
  1 · 1 · 4, 6 · 7, 12 … Σ 1, 1, 10, 19, 100, 253, 1018, 2935, …
  (−∞, 0]nonnegative
• A013622 → basis A013609 → basis A007318
  1 · 18, 10 · 324, 360, 100 · 5832, 9720, 5400, 1000 … Σ 1, 28, 784, 21952, 614656, 17210368, …
  (−∞, −1]nonnegativerational roots
• A137320 → reverse → basis A008277
  1 · 2 · 6, 2 · 24, 24, 4 … Σ 1, 2, 8, 52, 512, 7248, 140536, …
  (−∞, 0]nonnegative
• A154986 → basis A013609
  1 · 2, 2 · 6, 12, 4 · 24, 72, 56, 8 … Σ 1, 4, 22, 160, 1432, 15328, 190192, …
  (−∞, 0]nonnegative
• A178820 → Veronese 2 (j=1) → basis A013610
  4 · 20 · 80, 60 · 280, 420 … Σ 0, 4, 20, 140, 700, 3416, 15288, 65640, …
  (−∞, 0]nonnegative
• basis-map coefficients of A297191, shifted → basis A013610 → D+1
  1 · 7, 24, 9 · 13, 120, 378, 432, 81 … Σ 1, 40, 1024, 22528, 458752, 8912896, …
  (−∞, 0]nonnegativerational roots
• A120910 → D → (θ+1)²
  3 · 12, 24 · 36, 144, 81 · 96, 576, 648, 192 … Σ 0, 3, 36, 261, 1512, 7695, 35964, …
  (−∞, 0]nonnegative
• A008303: Triangle read by rows: T(n,k) (n >= 1, 0 <= k <= ceiling(n/2)-1) = number of permutations of [n] with k peaks.
  A008292 → γ (scale 1/4) (shift +1)
  1 · 2 · 4, 2 · 8, 16 … Σ 1, 2, 6, 24, 120, 720, 5040, 40320, …
  (−∞, 0]nonnegative
• A060920 → D+1
  1 · 3, 1 · 10, 7, 1 · 33, 38, 12, 1 … Σ 1, 4, 18, 84, 390, 1784, 8042, 35804, …
  (−∞, 0]nonnegative
• A038231: Triangle whose (i,j)-th entry is binomial(i,j)*4^(i-j).
  1 · 4, 1 · 16, 8, 1 · 64, 48, 12, 1 … Σ 1, 5, 25, 125, 625, 3125, 15625, 78125, …
  (−∞, −1]nonnegativerational roots
• A059344 → basis A013610 → basis A013610
  1 · 1 · 9, 18 · 25, 54 … Σ 1, 1, 27, 79, 2185, 10401, 294451, …
  (−∞, 0]nonnegative
• A038291: Triangle whose (i,j)-th entry is binomial(i,j)*9^(i-j)*1^j.
  1 · 9, 1 · 81, 18, 1 · 729, 243, 27, 1 … Σ 1, 10, 100, 1000, 10000, 100000, …
  (−∞, −1]nonnegativerational roots
• A207607 → reverse → x ↦ x+1
  1 · 3, 1 · 8, 7, 1 · 21, 30, 12, 1 … Σ 1, 4, 16, 64, 256, 1024, 4096, 16384, …
  (−∞, −1]nonnegative
• A085881 → (θ+1)²
  1 · 1, 4 · 3, 24, 27 · 15, 180, 405, 240 … Σ 1, 5, 54, 840, 16800, 408240, 11642400, …
  (−∞, 0]nonnegative
• A034870 → basis A013611 → basis A013610
  1 · 36, 144, 144 · 1296, 10368, 31104, 41472, 20736 … Σ 1, 324, 104976, 34012224, 11019960576, …
  (−∞, 0]nonnegativerational roots
• A102662 → basis A013609
  1 · 4, 6 · 9, 22, 12 · 22, 76, 80, 24 … Σ 1, 10, 43, 202, 937, 4354, 20227, …
  (−∞, 0]nonnegative
• A021010: Triangle of coefficients of Laguerre polynomials L_n(x) (powers of x in decreasing order).
  A144084 → x ↦ −x (shift -1)
  1 · -1, 1 · 1, -4, 2 · -1, 9, -18, 6 … Σ 1, 0, -1, -4, -15, -56, -185, -204, …
  [0, ∞)
• A093644 → basis A013609
  1 · 10, 2 · 20, 24, 4 · 40, 88, 56, 8 … Σ 1, 12, 48, 192, 768, 3072, 12288, …
  (−∞, 0]nonnegativerational roots
• A038331 → basis A013611 → basis A013609
  1369, 2960, 1600 · 50653, 164280, 177600, 64000 … Σ 5929, 456533, 35153041, 2706784157, …
  (−∞, 0]nonnegativerational roots
• A013611 → basis A013611
  1 · 5, 16 · 25, 160, 256 · 125, 1200, 3840, 4096 … Σ 1, 21, 441, 9261, 194481, 4084101, …
  (−∞, 0]nonnegativerational roots
• A125092 → D
  4 · 8, 18 · 12, 54, 48 · 16, 108, 192, 100 … Σ 0, 4, 26, 114, 416, 1360, 4128, 11872, …
  (−∞, 0]nonnegative
• A038328 → basis A008277
  196, 60, 4 · 2744, 1352, 192, 8 … Σ 260, 4296, 72256, 1238368, 21646912, …
  (−∞, 0]nonnegative
• A137320 → reverse
  1 · 2 · 4, 2 · 8, 12, 4 … Σ 1, 2, 6, 24, 120, 720, 5040, 40320, …
  (−∞, 0]nonnegativerational roots
• A204420 → basis A013610 → x ↦ x/(x+1)
  1 · 1, 4 · 9, 54, 72 · 225, 1710, 3960, 2880 … Σ 1, 5, 135, 8775, 1044225, 197358525, …
  [−1, 0]nonnegativerational roots
• A100861 → (θ+1)²
  1 · 1 · 1, 4 · 1, 12 … Σ 1, 1, 5, 13, 52, 176, 706, 2710, …
  (−∞, 0]nonnegative
• A122542 → reverse → D
  2 · 4, 4 · 6, 16, 6 · 8, 36, 36, 8 … Σ 0, 0, 2, 8, 28, 88, 262, 752, …
  (−∞, 0]nonnegative
• A034867 → basis A008277
  1 · 2 · 4, 1 · 8, 4 … Σ 1, 2, 5, 12, 30, 76, 197, 520, …
  (−∞, 0]nonnegative