Sequences

• A166972 → x ↦ x/(x+1)
  1 · 1, 2 · 1, 12, 12 · 1, 86, 210, 126 … Σ 1, 3, 25, 423, 10045, 326931, 14166385, …
  [−1, 0]nonnegative
• A102547 → basis A013610 → x ↦ x+1
  1 · 1 · 1 · 5, 3 … Σ 1, 1, 1, 8, 15, 22, 78, 183, …
  (−∞, −1]nonnegative
• A272866 → basis A013609 → basis A013609
  1 · 19, 36, 16 · 361, 1368, 1904, 1152, 256 … Σ 1, 71, 5041, 357911, 25411681, …
  (−∞, 0]nonnegative
• A367270 → basis A013611 → D+1
  1 · 1 · 11, 8 · 58, 144, 48 … Σ 1, 1, 19, 250, 2979, 34206, 385646, …
  (−∞, 0]nonnegative
• A207607 → basis A013609 → basis A013611
  1 · 7, 16 · 34, 136, 128 · 163, 936, 1728, 1024 … Σ 1, 23, 298, 3851, 49765, 643094, …
  (−∞, 0]nonnegative
• A078812 → x ↦ x+1 → basis A013611
  1 · 4, 4 · 15, 32, 16 · 56, 184, 192, 64 … Σ 1, 8, 63, 496, 3905, 30744, 242047, …
  (−∞, 0]nonnegative
• A257623: Triangle read by rows: T(n,k) = t(n-k, k), where t(n,m) = f(m)*t(n-1,m) + f(n)*t(n,m-1) and f(n) = 5*n + 3.
  1 · 3, 3 · 9, 48, 9 · 27, 501, 501, 27 … Σ 1, 6, 66, 1056, 22176, 576576, …
  (−∞, 0)nonnegative
• basis-map coefficients of A030528, shifted → (θ+1)² → basis A013611
  1 · -4, -16 · 9, 72, 144 · -16, -192, -768, -1024 … Σ 1, -20, 225, -2000, 15625, -112500, …
  (−∞, 0]rational roots
• A166344 → D
  6, 2 · 15, 30, 3 · 34, 180, 102, 4 … Σ 8, 48, 320, 2400, 20160, 188160, …
  (−∞, 0]nonnegative
• A086645 → basis A013611 → θ+1
  1 · 2, 8 · 8, 64, 48 · 32, 384, 864, 256 … Σ 1, 10, 120, 1536, 19328, 237056, …
  (−∞, 0]nonnegative
• A209414 → x ↦ x/(x+1)
  1 · 1, 2 · 1, 6, 6 · 1, 10, 26, 18 … Σ 1, 3, 13, 55, 233, 987, 4181, 17711, …
  [−1, 0]nonnegative
• A094638 → basis A013610 → basis A013609
  1 · 5, 6 · 45, 114, 72 · 585, 2292, 2988, 1296 … Σ 1, 11, 231, 7161, 293601, 14973651, …
  (−∞, 0]nonnegativerational roots
• basis-map coefficients of A026729 → basis A013609 → D+1
  1 · 3, 2 · 5, 12, 4 · 7, 30, 36, 8 … Σ 1, 5, 21, 81, 297, 1053, 3645, 12393, …
  (−∞, 0]nonnegativerational roots
• A028326 → basis A007318
  2 · 4, 2 · 8, 8, 2 · 16, 24, 12, 2 … Σ 2, 6, 18, 54, 162, 486, 1458, 4374, …
  (−∞, −1]nonnegativerational roots
• A290319: Triangle read by rows: T(n, k) is the Sheffer triangle ((1 - 4*x)^(-1/4), (-1/4)*log(1 - 4*x)). A generalized Stirling1 triangle.
  1 · 1, 1 · 5, 6, 1 · 45, 59, 15, 1 … Σ 1, 2, 12, 120, 1680, 30240, 665280, …
  (−∞, 0)nonnegativerational roots
• A257609: Triangle read by rows: T(n,k) = t(n-k, k); t(n,m) = f(m)*t(n-1,m) + f(n)*t(n,m-1), where f(x) = 2*x + 2.
  1 · 2, 2 · 4, 16, 4 · 8, 88, 88, 8 … Σ 1, 4, 24, 192, 1920, 23040, 322560, …
  (−∞, 0)nonnegative
• A232535 → basis A013610 → basis A013610
  1 · 9, 18 · 81, 288, 243 · 729, 3690, 5913, 2916 … Σ 1, 27, 612, 13248, 282816, 6011136, …
  (−∞, 0]nonnegative
• A059473 → γ → basis A013611
  1 · 2 · 6, 8 · 16, 32 … Σ 1, 2, 14, 48, 236, 952, 4264, 18048, …
  (−∞, 0]nonnegative
• A013620 → basis A008288 → x ↦ x+1
  1 · 8, 3 · 73, 57, 9 · 674, 792, 270, 27 … Σ 1, 11, 139, 1763, 22363, 283667, …
  (−∞, −1]nonnegative
• A200536 → basis A013610 → D+1
  1 · 27, 57, 18 · 288, 1566, 2925, 2052, 324 … Σ 1, 102, 7155, 437400, 24877125, …
  (−∞, 0]nonnegative
• A126216 → basis A013610 → D
  3 · 21, 18 · 126, 216, 81 · 726, 1872, 1458, 324 … Σ 0, 3, 39, 423, 4380, 44670, 453213, …
  (−∞, 0]nonnegative
• A038327 → basis A013611 → x ↦ x+1
  1 · 17, 4 · 289, 136, 16 · 4913, 3468, 816, 64 … Σ 1, 21, 441, 9261, 194481, 4084101, …
  (−∞, −1]nonnegativerational roots
• A106246 → θ+1
  1 · 2, 2 · 1, 8, 3 · 0, 6, 18, 4 … Σ 1, 4, 12, 28, 55, 96, 154, 232, …
  (−∞, 0]nonnegative
• A038305 → basis A013610 → x ↦ x/(x+1)
  169, 572, 484 · 2197, 11154, 18876, 10648 … Σ 1225, 42875, 1500625, 52521875, …
  [−1, 0]nonnegativerational roots
• A156992 → basis A008277 → x ↦ x/(x+1)
  1 · 4, 6 · 24, 78, 60 · 192, 1032, 1704, 888 … Σ 1, 10, 162, 3816, 123000, 5199120, …
  [−1, 0]nonnegative
• A038314 → basis A013609 → D
  1056, 1152 · 34848, 76032, 41472 … Σ 2208, 152352, 9344256, 537294720, …
  (−∞, 0]nonnegativerational roots
• A196347 → basis A013610 → basis A013610
  1 · 5, 9 · 50, 180, 162 · 750, 4050, 7290, 4374 … Σ 1, 14, 392, 16464, 921984, 64538880, …
  (−∞, 0]nonnegativerational roots
• A347056 → basis A008277
  1 · 7, 4 · 32, 46, 10 · 120, 330, 170, 20 … Σ 1, 11, 88, 640, 4545, 32459, 236348, …
  (−∞, 0]nonnegative
• A257180 → Pₙ + Pₙ₊₁
  36, 165, 150, 27 · 108, 867, 1551, 753, 81 … Σ 378, 3360, 33264, 362880, 4324320, …
  (−∞, ∞)nonnegative
• A078812 → basis A013611 → reverse
  1 · 4, 3 · 16, 24, 8 · 64, 144, 100, 21 … Σ 1, 7, 48, 329, 2255, 15456, 105937, …
  (−∞, 0]nonnegative
• A257615 → (θ+1)²
  1 · 5, 20 · 25, 280, 225 · 125, 2860, 6435, 2000 … Σ 1, 25, 530, 11420, 259680, 6296640, …
  (−∞, 0]nonnegative
• A038331 → basis A013609 → basis A013609
  729, 1080, 400 · 19683, 43740, 32400, 8000 … Σ 2209, 103823, 4879681, 229345007, …
  (−∞, 0]nonnegativerational roots
• A120910 → basis A013611 → θ+1
  3 · 9, 24 · 27, 144, 144 · 81, 648, 1296, 768 … Σ 3, 33, 315, 2793, 23667, 194481, …
  (−∞, 0]nonnegativerational roots
• A136572 → (θ+1)² → basis A007318
  1 · 4, 4 · 18, 36, 18 · 96, 288, 288, 96 … Σ 1, 8, 72, 768, 9600, 138240, 2257920, …
  (−∞, −1]nonnegativerational roots
• A130123 → θ+1 → basis A013611
  1 · 4, 16 · 12, 96, 192 · 32, 384, 1536, 2048 … Σ 1, 20, 300, 4000, 50000, 600000, …
  (−∞, 0]nonnegativerational roots
• A357367 → basis A008277
  1 · 2, 2 · 18, 42, 12 · 264, 1224, 840, 120 … Σ 1, 4, 72, 2448, 130800, 9940320, …
  (−∞, 0]nonnegative
• A038333 → basis A013609 → x ↦ x/(x+1)
  361, 1254, 1089 · 6859, 35739, 62073, 35937 … Σ 2704, 140608, 7311616, 380204032, …
  [−1, 0]nonnegativerational roots
• A063007 → basis A013610 → basis A013609
  1 · 9, 12 · 121, 324, 216 · 1809, 7272, 9720, 4320 … Σ 1, 21, 661, 23121, 849201, 32081301, …
  (−∞, 0]nonnegative
• A091042 → basis A013609 → θ+1
  1 · 4, 12 · 16, 80, 60 · 64, 448, 672, 224 … Σ 1, 16, 156, 1408, 12304, 105216, …
  (−∞, 0]nonnegative
• A269947 → θ+1
  1 · 0, 2 · 0, 2, 3 · 0, 16, 27, 4 … Σ 1, 2, 5, 47, 1334, 87214, 11021724, …
  (−∞, 0]nonnegative
• A232535 → basis A007318 → D
  2 · 14, 6 · 80, 74, 12 · 416, 592, 228, 20 … Σ 0, 2, 20, 166, 1256, 9002, 62268, …
  (−∞, 0]nonnegative
• A085841 → x ↦ x/(x+1)
  1 · 3, 7 · 5, 50, 61 · 7, 161, 637, 547 … Σ 1, 10, 116, 1352, 15760, 183712, …
  [−1, 0]nonnegative
• delannoy → Veronese 2 (j=1)
  1 · 3 · 5, 1 · 7, 7 … Σ 0, 1, 3, 6, 14, 35, 85, 204, …
  (−∞, 0]nonnegative
• A120986 → D
  1 · 6, 2 · 28, 24, 3 · 120, 180, 60, 4 … Σ 0, 1, 8, 55, 364, 2380, 15504, 100947, …
  (−∞, 0]nonnegative
• A142075: Triangle T(n, k) = 2^(k-1) * E(n, k-1) where E(n,k) are the Eulerian numbers A173018, read by rows.
  1 · 1, 2 · 1, 8, 4 · 1, 22, 44, 8 … Σ 1, 3, 13, 75, 541, 4683, 47293, 545835, …
  (−∞, 0)nonnegative
• A091044 → basis A013610 → x ↦ x/(x+1)
  1 · 4, 10 · 16, 80, 91 · 64, 480, 1128, 820 … Σ 1, 14, 187, 2492, 33205, 442442, …
  [−1, 0]nonnegative
• A225471 → basis A007318 → (θ+1)²
  1 · 4, 4 · 32, 48, 9 · 384, 704, 216, 16 … Σ 1, 8, 89, 1320, 24649, 556352, …
  (−∞, 0]nonnegative
• A178821 → basis A013609 → basis A013610
  1 · 20, 30 · 240, 720, 540 · 2240, 10080, 15120, 7560 … Σ 1, 50, 1500, 35000, 700000, 12600000, …
  (−∞, 0]nonnegativerational roots
• A266213 → basis A013610
  1 · 1 · 3, 6 · 7, 24, 18 … Σ 1, 1, 9, 49, 281, 1601, 9129, 52049, …
  (−∞, 0]nonnegative
• A257627 → x ↦ x/(x+1)
  1 · 3, 6 · 9, 78, 78 · 27, 834, 2340, 1560 … Σ 1, 9, 165, 4761, 185565, 9103329, …
  [−1, 0]nonnegative