Sequences

• A236471: Riordan array ((1-x)/(1-2*x), x(1-x)/(1-2*x)^2).
  1 · 1, 1 · 2, 4, 1 · 4, 13, 7, 1 … Σ 1, 2, 7, 25, 90, 325, 1175, 4250, …
  [−4, ∞)nonnegative
• A139548 → basis A013609 → D
  16, 16 · 256, 768, 768, 256 … Σ 0, 32, 2048, 98304, 4194304, 167772160, …
  (−∞, 0]nonnegativerational roots
• A038334 → basis A013609 → basis A013610
  1296, 3456, 2304 · 46656, 186624, 248832, 110592 … Σ 7056, 592704, 49787136, 4182119424, …
  (−∞, 0]nonnegativerational roots
• A330510 → basis A013610
  2 · 6, 9 · 18, 54, 36 · 54, 243, 333, 135 … Σ 2, 15, 108, 765, 5382, 37755, 264528, …
  (−∞, 0]nonnegative
• A052553 → basis A013609 → basis A013609
  1 · 1 · 4, 4 · 7, 8 … Σ 1, 1, 8, 15, 71, 176, 673, 1905, …
  (−∞, 0]nonnegative
• A086645 → D+1
  1 · 2, 1 · 7, 8, 1 · 16, 45, 18, 1 … Σ 1, 3, 16, 80, 384, 1792, 8192, 36864, …
  (−∞, 0]nonnegative
• A113413 → basis A013610
  1 · 3, 3 · 7, 18, 9 · 17, 69, 81, 27 … Σ 1, 6, 34, 194, 1106, 6306, 35954, …
  (−∞, 0]nonnegative
• A008278 → x ↦ x+1 (shift +1) → reverse
  1 · 1, 2 · 1, 5, 5 · 1, 10, 23, 15 … Σ 1, 3, 11, 49, 257, 1539, 10299, 75905, …
  [−1, 0]nonnegative
• A099097 → x ↦ x−15
  1 · -45, 3 · 2010, -269, 9 · -89775, 18045, -1209, 27 … Σ 1, -42, 1750, -72912, 3037804, …
  (131/9, 15]
• A257625: Triangle read by rows: T(n, k) = t(n-k, k), where t(0,0) = 1, t(n,m) = 0 if n < 0 or m < 0, else t(n,m) = f(m)*t(n-1,m) + f(n)*t(n,m-1), and f(n) = 6*…
  1 · 3, 3 · 9, 54, 9 · 27, 621, 621, 27 … Σ 1, 6, 72, 1296, 31104, 933120, …
  (−∞, 0)nonnegative
• A144697 → (θ+1)²
  1 · 1, 12 · 1, 40, 81 · 1, 100, 603, 432 … Σ 1, 13, 122, 1136, 11200, 118920, …
  (−∞, 0]nonnegative
• A029635 → basis A013610
  2 · 3, 6 · 6, 21, 18 · 12, 60, 99, 54 … Σ 2, 9, 45, 225, 1125, 5625, 28125, …
  (−∞, 0]nonnegativerational roots
• A113214 → D
  1 · 3, 2 · 2, 8, 3 · 0, 10, 15, 4 … Σ 0, 1, 5, 13, 29, 60, 118, 225, …
  (−∞, 0]nonnegative
• A110441 → reverse → x ↦ x+1
  1 · 4, 3 · 14, 20, 7 · 48, 100, 68, 15 … Σ 1, 7, 41, 231, 1289, 7175, 39913, …
  (−∞, −1]nonnegative
• A115951 → basis A008277
  1 · 2, 2 · 8, 20, 6 · 32, 176, 132, 20 … Σ 1, 4, 34, 360, 4570, 66616, 1088268, …
  (−∞, 0]nonnegative
• A116412 → basis A007318 → basis A013609
  1 · 5, 2 · 22, 20, 4 · 98, 138, 60, 8 … Σ 1, 7, 46, 304, 2008, 13264, 87616, …
  (−∞, 0]nonnegative
• A052553 → basis A013611 → basis A007318
  1 · 1 · 6, 4 · 11, 8 … Σ 1, 1, 10, 19, 109, 280, 1261, 3781, …
  (−∞, −1]nonnegative
• A132393 → θ+1 → D
  2 · 2, 6 · 4, 18, 12 · 12, 66, 72, 20 … Σ 0, 2, 8, 34, 170, 998, 6776, 52400, …
  (−∞, 0]nonnegative
• A085880 → x ↦ x+1 → (θ+1)²
  1 · 2, 4 · 8, 32, 18 · 40, 240, 270, 80 … Σ 1, 6, 58, 630, 7182, 83916, 994356, …
  (−∞, 0]nonnegative
• A130123 → basis A013610 → basis A013610
  1 · 8, 18 · 64, 288, 324 · 512, 3456, 7776, 5832 … Σ 1, 26, 676, 17576, 456976, 11881376, …
  (−∞, 0]nonnegativerational roots
• A013622 → basis A013610 → θ+1
  1 · 8, 30 · 64, 480, 675 · 512, 5760, 16200, 13500 … Σ 1, 38, 1219, 35972, 1009861, 27424418, …
  (−∞, 0]nonnegativerational roots
• A120986: Triangle read by rows: T(n,k) is the number of ternary trees with n edges and having k middle edges (n >= 0, k >= 0).
  1 · 2, 1 · 5, 6, 1 · 14, 28, 12, 1 … Σ 1, 3, 12, 55, 273, 1428, 7752, 43263, …
  (−∞, 0)nonnegative
• A088996 → basis A013611 → basis A013610
  1 · 5, 12 · 55, 252, 288 · 935, 6264, 13968, 10368 … Σ 1, 17, 595, 31535, 2238985, 199269665, …
  (−∞, 0]nonnegativerational roots
• basis-map coefficients of A112227 → (θ+1)² → basis A013609
  9, 36, 36 · 16, 96, 192, 128 · 25, 200, 600, 800, 400 … Σ 81, 432, 2025, 8748, 35721, 139968, …
  (−∞, 0]nonnegativerational roots
• A003506 → (θ+1)² → (θ+1)²
  1 · 2, 32 · 3, 96, 243 · 4, 192, 972, 1024 … Σ 0, 1, 34, 342, 2192, 11000, 47232, …
  (−∞, 0]nonnegative
• A196347 → basis A013610 → x ↦ x/(x+1)
  1 · 2, 5 · 8, 40, 50 · 48, 360, 900, 750 … Σ 1, 7, 98, 2058, 57624, 2016840, …
  [−1, 0]nonnegativerational roots
• A249139 → Veronese 2 (j=1)
  1 · 2 · 7 · 16 … Σ 0, 1, 2, 7, 16, 42, 98, 237, …
  (−∞, 0]nonnegative
• A119808 → (θ+1)²
  1 · 2, 4 · 4, 20 · 8, 68, 18 … Σ 1, 6, 24, 94, 356, 1314, 4752, 16902, …
  (−∞, 0]nonnegative
• A111577 → (θ+1)²
  1 · 1, 4 · 1, 20, 9 · 1, 84, 108, 16 … Σ 1, 5, 30, 209, 1663, 14856, 146695, …
  (−∞, 0]nonnegative
• A143494 → x ↦ x+1 → D
  1 · 7, 2 · 40, 24, 3 · 221, 206, 54, 4 … Σ 0, 1, 9, 67, 485, 3571, 27181, 215195, …
  (−∞, 0]nonnegative
• A106246 → D+1 → x ↦ x/(x+1)
  1 · 3, 4 · 5, 16, 12 · 3, 24, 48, 28 … Σ 1, 7, 33, 103, 241, 471, 817, 1303, …
  [−1, 0]nonnegative
• A145596 → Pₙ + Pₙ₊₁
  3, 2 · 5, 10, 3 · 7, 28, 23, 4 · 9, 60, 95, 44, 5 … Σ 5, 18, 62, 213, 737, 2574, 9074, 32266, …
  (−∞, ∞)nonnegative
• A130123 → θ+1 → reverse
  1 · 4 · 12 · 32 … Σ 1, 4, 12, 32, 80, 192, 448, 1024, …
  (−∞, 0]nonnegativerational roots
• A059364 → basis A013609 → reverse
  1 · 2, 3 · 8, 22, 15 · 48, 188, 244, 105 … Σ 1, 5, 45, 585, 9945, 208845, 5221125, …
  (−∞, 0]nonnegativerational roots
• A convolution triangle of numbers obtained from A036224.
  336, 42, 1 · 4536, 1113, 63, 1 … Σ 379, 5713, 80032, 1080325, 14354557, …
  [−36, 0)nonnegative
• A155112 → basis A007318
  1 · 1, 1 · 3, 4, 1 · 8, 14, 7, 1 … Σ 1, 2, 8, 30, 114, 432, 1638, 6210, …
  (−∞, 0]nonnegative
• A103633 → basis A007318 → D+1
  1 · 2, 1 · 5, 5, 1 · 7, 13, 7, 1 … Σ 1, 3, 11, 28, 96, 228, 756, 1728, …
  (−∞, 0]nonnegative
• A274496 → (θ+1)²
  1 · 2 · 2, 8 · 4, 16 … Σ 1, 2, 10, 20, 72, 144, 448, 896, …
  (−∞, 0]nonnegative
• A038305 → x ↦ x+1 → basis A013610
  256, 288, 81 · 4096, 6912, 3888, 729 … Σ 625, 15625, 390625, 9765625, 244140625, …
  (−∞, 0]nonnegativerational roots
• A105278 → reverse
  1 · 1, 2 · 1, 6, 6 · 1, 12, 36, 24 … Σ 1, 3, 13, 73, 501, 4051, 37633, 394353, …
  (−∞, 0]nonnegative
• A081580 → basis A008277
  1 · 2, 1 · 9, 10, 1 · 28, 59, 19, 1 … Σ 1, 3, 20, 107, 681, 4454, 31263, …
  (−∞, 0]nonnegative
• A395972 → D
  16, 16 · 72, 288, 144 · 256, 2304, 4608, 1536 … Σ 32, 504, 8704, 167200, 3561984, …
  (−∞, 0]nonnegative
• A207823 → basis A013611 → basis A007318
  1 · 9, 4 · 80, 72, 16 · 711, 964, 432, 64 … Σ 1, 13, 168, 2171, 28055, 362544, …
  (−∞, 0]nonnegative
• A121574 → basis A013611
  1 · 3, 4 · 10, 28, 16 · 33, 140, 176, 64 … Σ 1, 7, 54, 413, 3161, 24192, 185149, …
  (−∞, 0]nonnegative
• A038220 → basis A013610 → x ↦ x/(x+1)
  1 · 5, 11 · 25, 110, 121 · 125, 825, 1815, 1331 … Σ 1, 16, 256, 4096, 65536, 1048576, …
  [−1, 0]nonnegativerational roots
• A106246 → θ+1 → D+1
  1 · 4, 2 · 9, 14, 3 · 6, 42, 30, 4 … Σ 1, 6, 26, 82, 207, 446, 856, 1506, …
  (−∞, 0]nonnegative
• A113413 → basis A013610 → basis A013609
  1 · 6, 6 · 34, 72, 36 · 194, 624, 648, 216 … Σ 1, 12, 142, 1682, 19922, 235962, …
  (−∞, 0]nonnegative
• A038243 → basis A013611 → D
  4 · 48, 32 · 432, 576, 192 · 3456, 6912, 4608, 1024 … Σ 0, 4, 80, 1200, 16000, 200000, 2400000, …
  (−∞, 0]nonnegativerational roots
• A274498 → D → (θ+1)²
  6 · 18 · 36, 288 · 108, 864 … Σ 0, 0, 6, 18, 324, 972, 8586, 25758, …
  (−∞, 0]nonnegative
• A038284 → basis A013611 → basis A008277
  1444, 2400, 576 · 54872, 183456, 107136, 13824 … Σ 4420, 359288, 32816656, 3319287776, …
  (−∞, 0]nonnegative