Sequences

• A091044 → basis A007318 → x ↦ x/(x+1)
  1 · 4, 6 · 16, 48, 35 · 64, 288, 424, 204 … Σ 1, 10, 99, 980, 9701, 96030, 950599, …
  [−1, 0]nonnegative
• A145324 → basis A013611
  1 · 3, 8 · 12, 68, 96 · 60, 532, 1568, 1536 … Σ 1, 11, 176, 3696, 96096, 2978976, …
  (−∞, 0]nonnegativerational roots
• A081580 → D
  1 · 7, 2 · 13, 26, 3 · 19, 122, 57, 4 … Σ 0, 1, 9, 42, 202, 855, 3567, 14308, …
  (−∞, 0]nonnegative
• A143494 → (θ+1)²
  1 · 2, 4 · 4, 20, 9 · 8, 76, 81, 16 … Σ 1, 6, 33, 181, 1020, 5977, 36589, …
  (−∞, 0]nonnegative
• A091044 → basis A013610 → D+1
  1 · 10, 6 · 64, 102, 27 · 352, 1008, 684, 108 … Σ 1, 16, 193, 2152, 23065, 240808, …
  (−∞, 0]nonnegative
• A055151 → D → D
  4 · 20 · 60, 30 · 140, 210 … Σ 0, 0, 0, 0, 4, 20, 90, 350, …
  (−∞, 0]nonnegative
• A137597 → reverse → x ↦ x+1
  1 · 3, 2 · 11, 15, 5 · 47, 98, 67, 15 … Σ 1, 5, 31, 227, 1897, 17693, 181351, …
  (−∞, −1]nonnegative
• A038271 → x ↦ x/(x+1) → x ↦ x/(x+1)
  1 · 7, 19 · 49, 266, 361 · 343, 2793, 7581, 6859 … Σ 1, 26, 676, 17576, 456976, 11881376, …
  [−1, 0]nonnegativerational roots
• A156289 → x ↦ x/(x+1)
  1 · 1, 4 · 1, 17, 31 · 1, 66, 339, 379 … Σ 1, 5, 49, 785, 18121, 563045, 22458409, …
  [−1, 0]nonnegative
• A038305 → basis A013610 → basis A013610
  484, 1188, 729 · 10648, 39204, 48114, 19683 … Σ 2401, 117649, 5764801, 282475249, …
  (−∞, 0]nonnegativerational roots
• A125662 → basis A013610 → basis A008277
  1 · 7, 3 · 48, 51, 9 · 329, 651, 270, 27 … Σ 1, 10, 108, 1277, 16478, 230715, …
  (−∞, 0]nonnegative
• A156289 → θ+1
  1 · 1, 6 · 1, 30, 45 · 1, 126, 630, 420 … Σ 1, 7, 76, 1177, 24451, 650992, …
  (−∞, 0]nonnegative
• A136124 → basis A013609 → θ+1
  1 · 3, 4 · 12, 28, 12 · 60, 188, 144, 32 … Σ 1, 7, 52, 424, 3812, 37668, 406920, …
  (−∞, 0]nonnegative
• A099040 → basis A007318 → D+1
  1 · 4, 2 · 16, 18, 4 · 56, 104, 56, 8 … Σ 1, 6, 38, 224, 1280, 7136, 39072, …
  (−∞, 0]nonnegative
• A063967 → x ↦ x−4
  1 · -3, 1 · 6, -5, 1 · -9, 15, -7, 1 … Σ 1, -2, 2, 0, -4, 8, -8, 0, …
  (−1, 3]
• A159854 → basis A013611 → basis A013609
  25, 80, 64 · 150, 680, 1024, 512 … Σ 169, 2366, 33124, 463736, 6492304, …
  (−∞, 0]nonnegativerational roots
• type_b_eulerian → γ (scale 1/4) → x ↦ x+1 → D+1
  1 · 1 · 3, 1 · 11, 5 … Σ 1, 1, 4, 16, 95, 663, 5590, 54218, …
  (−∞, 0]nonnegative
• A271703 → θ+1
  1 · 0, 2 · 0, 4, 3 · 0, 12, 18, 4 … Σ 1, 2, 7, 34, 209, 1546, 13327, 130922, …
  (−∞, 0]nonnegative
• A125092 → θ+1 → (θ+1)²
  1 · 1, 32 · 1, 64, 243 · 1, 96, 729, 1024 … Σ 1, 33, 308, 1850, 8808, 36232, 134656, …
  (−∞, 0]nonnegative
• A038319 → basis A013609 → basis A013610
  676, 1560, 900 · 17576, 60840, 70200, 27000 … Σ 3136, 175616, 9834496, 550731776, …
  (−∞, 0]nonnegativerational roots
• A209599 → basis A013611
  1 · 2 · 4, 4 · 8, 12 … Σ 1, 2, 8, 20, 68, 188, 596, 1724, …
  (−∞, 0]nonnegative
• A269944 → basis A013609 → D+1
  1 · 3, 2 · 8, 14, 4 · 44, 98, 56, 8 … Σ 1, 5, 26, 206, 2640, 52176, 1499232, …
  (−∞, 0]nonnegative
• basis-map coefficients of A030528, shifted → basis A013609 → basis A013610
  1 · -3, -6 · 9, 36, 36 · -27, -162, -324, -216 … Σ 1, -9, 81, -729, 6561, -59049, 531441, …
  (−∞, 0]rational roots
• A013610 → basis A013611 → x ↦ x+1
  1 · 16, 12 · 256, 384, 144 · 4096, 9216, 6912, 1728 … Σ 1, 28, 784, 21952, 614656, 17210368, …
  (−∞, −1]nonnegativerational roots
• A008278 → x ↦ x+1 (shift +1) → x ↦ x+1 → reverse
  1 · 1, 3 · 1, 7, 11 · 1, 13, 46, 49 … Σ 1, 4, 19, 109, 742, 5815, 51193, …
  (−∞, 0]nonnegative
• A131431 → θ+1 → basis A013609
  1 · 8, 16 · 21, 84, 84 · 40, 240, 480, 320 … Σ 1, 24, 189, 1080, 5265, 23328, 96957, …
  (−∞, 0]nonnegativerational roots
• A069466 → θ+1
  1 · 2, 4 · 6, 48, 18 · 20, 360, 540, 80 … Σ 1, 6, 72, 1000, 14700, 222264, 3415104, …
  (−∞, 0]nonnegative
• A136157 → (θ+1)²
  3 · 1, 12 · 0, 4, 27 · 0, 0, 9, 48 … Σ 3, 13, 31, 57, 91, 133, 183, 241, …
  (−∞, 0]nonnegativerational roots
• A110441 → basis A007318 → basis A013609
  1 · 5, 2 · 23, 20, 4 · 105, 142, 60, 8 … Σ 1, 7, 47, 315, 2111, 14147, 94807, …
  (−∞, 0]nonnegative
• A052553 → basis A013611 → D
  4 · 8 · 20, 32 · 40, 96 … Σ 0, 0, 4, 8, 52, 136, 560, 1624, …
  (−∞, 0]nonnegative
• A386789: Triangle read by rows: T(n, k) = binomial(n - 1, k - 1)*binomial(n + k, k).
  1 · 0, 2 · 0, 3, 6 · 0, 4, 20, 20 … Σ 1, 2, 9, 44, 225, 1182, 6321, 34232, …
  (−∞, 0]nonnegative
• A059364 → basis A013609 → basis A013609
  1 · 5, 4 · 45, 76, 32 · 585, 1528, 1328, 384 … Σ 1, 9, 153, 3825, 126225, 5175225, …
  (−∞, 0]nonnegativerational roots
• A178821 → Veronese 2 → basis A008277
  1 · 5 · 30, 15 · 140, 105 … Σ 1, 5, 45, 245, 1260, 5796, 25410, …
  (−∞, 0]nonnegative
• A013622 → basis A013611 → basis A008277
  1 · 28, 20 · 784, 1520, 400 … Σ 1, 48, 2704, 176192, 13014016, …
  (−∞, 0]nonnegative
• A204420 → basis A007318 → D+1
  1 · 2, 1 · 21, 18, 3 · 570, 615, 180, 15 … Σ 1, 3, 42, 1380, 82320, 7771680, …
  (−∞, 0]nonnegative
• A125092 → reverse → basis A013609
  1 · 5, 2 · 18, 20, 4 · 56, 108, 60, 8 … Σ 1, 7, 42, 232, 1216, 6144, 30208, …
  (−∞, 0]nonnegative
• A048854 → D
  1 · 12, 2 · 180, 60, 3 · 3360, 1680, 168, 4 … Σ 0, 1, 14, 243, 5212, 133925, 4016106, …
  (−∞, 0]nonnegative
• basis-map coefficients of A113214, shifted → x ↦ x+1 → (θ+1)²
  1 · -2, -4 · 4, 16, 9 · -8, -48, -54, -16 … Σ 1, -6, 29, -126, 513, -1998, 7533, …
  (−∞, 0]
• A085478 → basis A013610 → basis A013609
  1 · 1 · 5, 6 · 29, 66, 36 … Σ 1, 1, 11, 131, 1561, 18601, 221651, …
  (−∞, 0]nonnegative
• A120910 → Veronese 2 (j=1) → basis A008277
  3 · 12 · 39, 3 · 120, 24 … Σ 0, 3, 12, 42, 144, 495, 1716, 6009, …
  (−∞, 0]nonnegative
• A391533 → basis A013609
  9, 12, 4 · 18, 42, 32, 8 · 36, 120, 148, 80, 16 … Σ 25, 100, 400, 1600, 6400, 25600, …
  (−∞, 0]nonnegativerational roots
• A166962 → x ↦ x+1
  1 · 2, 1 · 14, 14, 1 · 174, 244, 72, 1 … Σ 1, 3, 29, 491, 12893, 472947, 22873821, …
  (−∞, −1]nonnegative
• A145324: Triangle read by rows: coefficients of 1; 1(X+2); 1(X+2)(X+3); 1(X+2)(X+3)(X+4); ....
  1 · 1, 2 · 1, 5, 6 · 1, 9, 26, 24 … Σ 1, 3, 12, 60, 360, 2520, 20160, 181440, …
  (−∞, 0)[−1, 0]nonnegative+1
• A064861 → D
  3, 4 · 5, 16, 12 · 6, 26, 36, 16 … Σ 7, 33, 84, 324, 756, 2700, 6048, 20736, …
  (−∞, 0]nonnegativerational roots
• A200536 → basis A013610
  1 · 6, 21, 18 · 36, 252, 657, 756, 324 … Σ 1, 45, 2025, 91125, 4100625, 184528125, …
  (−∞, 0]nonnegativerational roots
• A038326 → θ+1
  1 · 11, 24 · 121, 528, 432 · 1331, 8712, 14256, 6912 … Σ 1, 35, 1081, 31211, 863857, 23226803, …
  (−∞, 0]nonnegativerational roots
• A121574 → D+1
  1 · 3, 1 · 9, 7, 1 · 24, 32, 11, 1 … Σ 1, 4, 17, 68, 264, 1002, 3739, 13768, …
  (−∞, 0]nonnegative
• A001263 → basis A013611 → D
  4 · 20, 32 · 84, 288, 192 · 336, 1792, 2688, 1024 … Σ 0, 4, 52, 564, 5840, 59560, 604284, …
  (−∞, 0]nonnegative
• A119900 → basis A013609
  1 · 2, 4 · 4, 14, 12 · 8, 40, 64, 32 … Σ 1, 6, 30, 144, 684, 3240, 15336, 72576, …
  (−∞, 0]nonnegative
• A038326 → basis A013609 → x ↦ x/(x+1)
  1 · 23, 47 · 529, 2162, 2209 … Σ 1, 70, 4900, 343000, 24010000, …
  [−1, 0]nonnegativerational roots