Sequences

• A103633 → (θ+1)²
  1 · 0, 4 · 0, 4, 9 · 0, 0, 9, 16 … Σ 1, 4, 13, 25, 66, 102, 248, 344, …
  (−∞, 0]nonnegative
• A013610 → basis A007318 → D
  3 · 24, 18 · 144, 216, 81 · 768, 1728, 1296, 324 … Σ 0, 3, 42, 441, 4116, 36015, 302526, …
  (−∞, −1]nonnegativerational roots
• A011973 → basis A013609 → basis A008277
  1 · 1 · 4, 2 · 7, 4 … Σ 1, 1, 6, 11, 45, 108, 393, 1093, …
  (−∞, 0]nonnegative
• A078812 → x ↦ x+1 → D+1
  1 · 4, 1 · 14, 8, 1 · 46, 43, 12, 1 … Σ 1, 5, 23, 102, 441, 1871, 7823, 32332, …
  (−∞, 0]nonnegative
• A063007 → x ↦ x+1 → basis A013609
  1 · 5, 4 · 37, 60, 24 · 305, 744, 600, 160 … Σ 1, 9, 121, 1809, 28401, 458649, …
  (−∞, 0]nonnegative
• A257612: 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) = 4*x + 2.
  1 · 2, 2 · 4, 24, 4 · 8, 184, 184, 8 … Σ 1, 4, 32, 384, 6144, 122880, 2949120, …
  (−∞, 0)nonnegative
• A166979 → D+1
  12, 13, 1 · 112, 171, 33, 1 · 1112, 2473, 855, 62, 1 … Σ 26, 317, 4503, 74074, 1400719, …
  (−∞, 0]nonnegative
• A249250 → x ↦ x+1 → reverse
  1 · 3, 4 · 3, 12, 10 · 3, 24, 48, 28 … Σ 1, 7, 25, 103, 409, 1639, 6553, 26215, …
  (−∞, 0]nonnegative
• A003506 → x ↦ x+1 → basis A013609
  1 · 6, 4 · 27, 36, 12 · 108, 216, 144, 32 … Σ 0, 1, 10, 75, 500, 3125, 18750, 109375, …
  (−∞, 0]nonnegativerational roots
• A039755 → (θ+1)²
  1 · 1, 4 · 1, 16, 9 · 1, 52, 81, 16 … Σ 1, 5, 26, 150, 964, 6836, 52936, …
  (−∞, 0]nonnegative
• A029653: Numbers in (2,1)-Pascal triangle (by row).
  1 · 2, 1 · 2, 3, 1 · 2, 5, 4, 1 … Σ 1, 3, 6, 12, 24, 48, 96, 192, …
  (−∞, 0)nonnegativerational roots
• A356546 → basis A013609 → basis A013610
  1 · 8, 12 · 96, 288, 216 · 1280, 5760, 8640, 4320 … Σ 1, 20, 600, 20000, 700000, 25200000, …
  (−∞, 0]nonnegativerational roots
• A038320 → x ↦ x+1 → (θ+1)²
  289, 816, 324 · 4913, 20808, 16524, 3456 … Σ 1429, 45701, 1384393, 40382273, …
  (−∞, 0]nonnegative
• A232535 → basis A007318 → θ+1
  1 · 3, 4 · 12, 28, 9 · 48, 160, 111, 16 … Σ 1, 7, 49, 335, 2241, 14743, 95729, …
  (−∞, 0]nonnegative
• A038321 → basis A007318 → basis A013610
  625, 1050, 441 · 15625, 39375, 33075, 9261 … Σ 2116, 97336, 4477456, 205962976, …
  (−∞, 0]nonnegativerational roots
• A193727 → basis A008277
  1 · 3, 1 · 21, 15, 2 · 147, 177, 52, 4 … Σ 1, 4, 38, 380, 4006, 44532, 521606, …
  (−∞, 0]nonnegative
• A086645 → basis A007318 → basis A008277
  1 · 3, 1 · 17, 11, 1 · 99, 109, 24, 1 … Σ 1, 4, 29, 233, 1972, 17475, 161829, …
  (−∞, 0]nonnegative
• A132200 → basis A013610
  1 · 8, 12 · 16, 48, 36 · 32, 144, 216, 108 … Σ 1, 20, 100, 500, 2500, 12500, 62500, …
  (−∞, 0]nonnegativerational roots
• A163932: Triangle related to the asymptotic expansion of E(x,m=3,n).
  A130534 → D²∘x (shift +1)
  1 · 3, 3 · 11, 18, 6 · 50, 105, 60, 10 … Σ 1, 6, 35, 225, 1624, 13132, 118124, …
  (−∞, 0]nonnegative
• A106246 → basis A013611
  1 · 3, 4 · 6, 24, 16 · 10, 72, 144, 64 … Σ 1, 7, 46, 290, 1775, 10625, 62500, …
  (−∞, 0]nonnegative
• A039755 → x ↦ x+1
  1 · 2, 1 · 6, 6, 1 · 24, 34, 12, 1 … Σ 1, 3, 13, 71, 457, 3355, 27509, 248127, …
  (−∞, −1]nonnegative
• A116412 → D
  1 · 6, 2 · 21, 18, 3 · 60, 90, 36, 4 … Σ 0, 1, 8, 42, 190, 797, 3192, 12391, …
  (−∞, 0]nonnegative
• A135838 → (θ+1)²
  1 · 2, 8 · 2, 16, 18 · 4, 48, 108, 64 … Σ 1, 10, 36, 224, 640, 3456, 8960, 45056, …
  (−∞, 0]nonnegative
• A166972 → D+1
  1 · 2, 1 · 11, 12, 1 · 84, 165, 44, 1 … Σ 1, 3, 24, 294, 5160, 123036, 3759876, …
  (−∞, 0]nonnegative
• A120910 → Veronese 2 → x ↦ x+1
  3 · 6 · 15, 3 · 42, 18 … Σ 3, 6, 18, 60, 204, 696, 2376, 8112, …
  (−∞, −1]nonnegative
• A209414 → D+1
  1 · 2, 1 · 5, 6, 1 · 8, 25, 12, 1 … Σ 1, 3, 12, 46, 168, 594, 2052, 6966, …
  (−∞, 0]nonnegative
• A178822 → Veronese 2 (j=1) → basis A013610
  6 · 42 · 224, 168 · 1008, 1512 … Σ 0, 6, 42, 392, 2520, 15372, 84084, …
  (−∞, 0]nonnegative
• A132812 → basis A007318 → basis A007318
  1 · 6, 2 · 33, 21, 3 · 180, 168, 48, 4 … Σ 1, 8, 57, 400, 2810, 19824, 140497, …
  (−∞, −1]nonnegative
• A131689: Triangle of numbers T(n,k) = k!*Stirling2(n,k) = A000142(k)*A048993(n,k) read by rows, T(n, k) for 0 <= k <= n.
  1 · 0, 1 · 0, 1, 2 · 0, 1, 6, 6 … Σ 1, 1, 3, 13, 75, 541, 4683, 47293, …
  (−1, 0]nonnegative
• A208509 → basis A008277
  1 · 3 · 6, 1 · 12, 5 … Σ 1, 3, 7, 17, 42, 106, 273, 717, …
  (−∞, 0]nonnegative
• A216973 → θ+1 → D+1
  1 · 6, 4 · 15, 30, 9 · 28, 96, 84, 16 … Σ 0, 1, 10, 54, 224, 800, 2592, 7840, …
  (−∞, 0]nonnegative
• A123519 → basis A013611 → reverse
  64, 56, 11 · 512, 704, 304, 41 … Σ 131, 1561, 18601, 221651, 2641211, …
  (−∞, 0]nonnegative
• A038207 → basis A008277 → θ+1
  1 · 3, 2 · 9, 14, 3 · 27, 74, 36, 4 … Σ 1, 5, 26, 141, 799, 4736, 29371, …
  (−∞, 0]nonnegative
• A088996 → basis A013610 → x ↦ x/(x+1)
  1 · 1, 4 · 3, 21, 36 · 15, 147, 474, 504 … Σ 1, 5, 60, 1140, 29640, 978120, …
  [−1, 0]nonnegativerational roots
• A347056 → reverse
  1 · 4, 3 · 10, 16, 6 · 20, 50, 40, 10 … Σ 1, 7, 32, 120, 400, 1232, 3584, 9984, …
  (−∞, 0]nonnegativerational roots
• Veronese parent of A109446 → Veronese 2 (j=1) → θ+1
  1 · 1 · 1, 2 · 3, 2 … Σ 1, 1, 3, 5, 16, 28, 80, 144, …
  (−∞, 0]nonnegative
• A136572 → basis A013611 → basis A008277
  1 · 5, 4 · 50, 112, 32 · 750, 3624, 2592, 384 … Σ 1, 9, 194, 7350, 423960, 34184760, …
  (−∞, 0]nonnegative
• image under θ+1 → θ+1 → D+1 → D
  4 · 18, 18 · 0, 96, 48 · 0, 0, 300, 100 … Σ 0, 4, 36, 144, 400, 900, 1764, 3136, …
  (−∞, 0]nonnegativerational roots
• A075499 → (θ+1)²
  16, 48, 9 · 64, 448, 216, 16 … Σ 73, 744, 8361, 102784, 1373121, …
  (−∞, 0]nonnegative
• A372868 → D+1
  1 · 2 · 5, 1 · 14, 6 … Σ 1, 2, 6, 20, 67, 222, 728, 2368, …
  (−∞, 0]nonnegative
• A272866 → basis A007318
  1 · 5, 5, 1 · 25, 50, 35, 10, 1 … Σ 1, 11, 121, 1331, 14641, 161051, …
  (−∞, −1]nonnegative
• A126216 → basis A013610 → D+1
  1 · 6, 3 · 32, 39, 9 · 171, 342, 189, 27 … Σ 1, 9, 80, 729, 6806, 64746, 624694, …
  (−∞, 0]nonnegative
• basis-map coefficients of A021012 → (θ+1)²
  1 · 0, -4 · 0, 0, 18 · 0, 0, 0, -96 … Σ 1, -4, 18, -96, 600, -4320, 35280, …
  (−∞, 0]rational roots
• A106246 → θ+1 → x ↦ x/(x+1)
  1 · 2, 4 · 1, 10, 12 · 0, 6, 30, 28 … Σ 1, 6, 23, 64, 141, 266, 451, 708, …
  [−1, 0]nonnegative
• A196347 → basis A013610 → basis A013609
  1 · 5, 6 · 50, 120, 72 · 750, 2700, 3240, 1296 … Σ 1, 11, 242, 7986, 351384, 19326120, …
  (−∞, 0]nonnegativerational roots
• A038322 → basis A007318 → D+1
  1 · 27, 8 · 665, 432, 64 · 15523, 15960, 5184, 512 … Σ 1, 35, 1161, 37179, 1161297, 35606547, …
  (−∞, 0]nonnegativerational roots
• A185263 → basis A008277
  1 · 1 · 2, 1 · 6, 5 … Σ 1, 1, 3, 11, 71, 491, 5186, 55258, …
  (−∞, 0]nonnegative
• A144445: Triangle, read by rows, T(n,k) = (7*n-7*k+1)*T(n-1, k-2) + (7*k-6)*T(n-1, k) + 7*T(n-2, k-1) with T(n, 1) = T(n, n) = 1.
  1 · 1, 1 · 1, 23, 1 · 1, 206, 206, 1 … Σ 1, 2, 25, 414, 9697, 293808, 10938775, …
  (−∞, 0)nonnegative
• A132393 → basis A013609 → basis A013610
  1 · 3, 6 · 12, 42, 36 · 60, 282, 432, 216 … Σ 1, 9, 90, 990, 11880, 154440, 2162160, …
  (−∞, 0]nonnegativerational roots
• A091044 → basis A013609 → x ↦ x/(x+1)
  1 · 4, 8 · 16, 64, 60 · 64, 384, 736, 448 … Σ 1, 12, 140, 1632, 19024, 221760, …
  [−1, 0]nonnegative