Sequences

• A103633 → basis A013611
  1 · 1, 4 · 2, 12, 16 · 2, 20, 64, 64 … Σ 1, 5, 30, 150, 900, 4500, 27000, …
  (−∞, 0]nonnegativerational roots
• A114655 → reverse
  2 · 2, 4 · 2, 12, 8 · 2, 24, 48, 16 … Σ 2, 6, 22, 90, 394, 1806, 8558, 41586, …
  (−∞, 0]nonnegative
• A103633 → D+1
  1 · 1, 1 · 1, 3, 1 · 0, 2, 4, 1 … Σ 1, 2, 5, 7, 16, 20, 44, 52, …
  (−∞, 0]nonnegative
• A094646 → Pₙ + Pₙ₊₁
  -1, 1 · 0, -2, 1 · 2, -1, -2, 1 · 0, 4, -4, -1, 1 … Σ 0, -1, 0, 0, 0, 0, 0, 0, …
  (−∞, ∞)rational roots
• A152842 → Veronese 2 (j=1)
  3 · 4 · 7, 9 · 8, 24 … Σ 0, 3, 4, 16, 32, 128, 256, 1024, …
  (−∞, 0]nonnegative
• A059473 → x ↦ x+1
  1 · 4, 2 · 18, 18, 4 · 80, 120, 56, 8 … Σ 1, 6, 40, 264, 1744, 11520, 76096, …
  (−∞, −1]nonnegative
• A152830 → basis A013609
  1 · 1 · 1 · 1 … Σ 1, 1, 1, 1, 4, 4, 4, 4, …
  (−∞, 0]nonnegativerational roots
• A106800 → θ+1
  1 · 1 · 1, 2 · 1, 6, 3 … Σ 1, 1, 3, 10, 38, 161, 747, 3753, …
  (−∞, 0]nonnegative
• Triangle whose (i,j)-th entry is binomial(i,j)*10^(i-j)*3^j.
  100, 60, 9 · 1000, 900, 270, 27 … Σ 169, 2197, 28561, 371293, 4826809, …
  (−∞, 0)nonnegativerational roots
• A086645 → γ
  1 · 1 · 1, 4 · 1, 12 … Σ 1, 1, 5, 13, 41, 121, 365, 1093, …
  (−∞, 0]nonnegative
• A136572 → basis A013609
  1 · 1, 2 · 2, 8, 8 · 6, 36, 72, 48 … Σ 1, 3, 18, 162, 1944, 29160, 524880, …
  (−∞, 0]nonnegativerational roots
• A013618 → basis A013609
  144, 528, 484 · 1728, 9504, 17424, 10648 … Σ 1156, 39304, 1336336, 45435424, …
  (−∞, 0]nonnegativerational roots
• A159854 → basis A013609
  1, 4, 4 · 2, 10, 16, 8 · 4, 24, 52, 48, 16 … Σ 9, 36, 144, 576, 2304, 9216, 36864, …
  (−∞, 0]nonnegativerational roots
• A001263 → (θ+1)²
  1 · 1, 4 · 1, 12, 9 · 1, 24, 54, 16 … Σ 1, 5, 22, 95, 406, 1722, 7260, 30459, …
  (−∞, 0]nonnegative
• chebyshev_t → D+1
  1 · 1, 1 · -1, 4, 2 · -3, -3, 12, 4 … Σ 1, 2, 5, 10, 17, 26, 37, 50, …
  (−∞, ∞)
• A257613 → γ
  1 · 4 · 16, 16 · 64, 224 … Σ 1, 4, 32, 288, 3264, 41856, 615168, …
  (−∞, 0]nonnegative
• A135065 → D+1
  1 · 8, 4 · 27, 36, 9 · 64, 144, 96, 16 … Σ 1, 12, 72, 320, 1200, 4032, 12544, …
  (−∞, 0]nonnegativerational roots
• 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
• 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, …
  (−∞, 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
• A113214 → D
  1 · 3, 2 · 2, 8, 3 · 0, 10, 15, 4 … Σ 0, 1, 5, 13, 29, 60, 118, 225, …
  (−∞, 0]nonnegative
• 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
• A249139 → Veronese 2 (j=1)
  1 · 2 · 7 · 16 … Σ 0, 1, 2, 7, 16, 42, 98, 237, …
  (−∞, 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
• A convolution triangle of numbers obtained from A036224.
  336, 42, 1 · 4536, 1113, 63, 1 … Σ 379, 5713, 80032, 1080325, 14354557, …
  [−36, 0)nonnegative
• A274496 → (θ+1)²
  1 · 2 · 2, 8 · 4, 16 … Σ 1, 2, 10, 20, 72, 144, 448, 896, …
  (−∞, 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
• A121574 → basis A013611
  1 · 3, 4 · 10, 28, 16 · 33, 140, 176, 64 … Σ 1, 7, 54, 413, 3161, 24192, 185149, …
  (−∞, 0]nonnegative
• A013612 → basis A007318
  36, 60, 25 · 216, 540, 450, 125 … Σ 121, 1331, 14641, 161051, 1771561, …
  (−∞, 0]nonnegativerational roots
• A008277 → x ↦ x+1
  1 · 2, 1 · 5, 5, 1 · 15, 22, 9, 1 … Σ 1, 3, 11, 47, 227, 1215, 7107, 44959, …
  (−∞, −1]nonnegative
• A113953 → x ↦ x−4
  1 · -4, 1 · 8, -6, 1 · 0, 16, -8, 1 … Σ 1, -3, 3, 9, -45, 81, 27, -567, …
  (−4, 4]
• A038328 → Pₙ + Pₙ₊₁
  1872, 912, 148, 8 · 22464, 14688, 3600, 392, 16 … Σ 2940, 41160, 576240, 8067360, …
  (−∞, ∞)nonnegativerational roots
• A120909 → x ↦ x/(x+1)
  3 · 3, 9 · 3, 18, 27 · 3, 27, 81, 81 … Σ 3, 12, 48, 192, 768, 3072, 12288, …
  [−1, 0]nonnegativerational roots
• A099097 → reverse
  1 · 3 · 9, 1 · 27, 6 … Σ 1, 3, 10, 33, 109, 360, 1189, 3927, …
  (−∞, 0]nonnegative
• A172431 → basis A013611
  1 · 3, 8 · 8, 40, 48 · 21, 152, 352, 256 … Σ 1, 11, 96, 781, 6191, 48576, 379561, …
  (−∞, 0]nonnegative
• A111125 → basis A013609
  1 · 4, 2 · 11, 14, 4 · 29, 62, 40, 8 … Σ 1, 6, 29, 139, 666, 3191, 15289, 73254, …
  (−∞, 0]nonnegative
• A130534 → Veronese 2
  1 · 1 · 2, 1 · 6, 6 … Σ 1, 1, 3, 12, 60, 360, 2520, 20160, …
  (−∞, 0]nonnegative
• A035607 → basis A013609
  1 · 1 · 3, 4 · 7, 16, 8 … Σ 1, 1, 7, 31, 145, 673, 3127, 14527, …
  (−∞, 0]nonnegative
• A026729 → basis A008277
  1 · 1, 1 · 2, 4, 1 · 3, 13, 8, 1 … Σ 1, 2, 7, 25, 102, 456, 2219, 11640, …
  (−∞, 0]nonnegative
• A130850: Triangle read by rows, 0 <= k <= n, T(n,k) = Sum_{j=0..n} A(n,j)*binomial(n-j,k) where A(n,j) are the Eulerian numbers A173018.
  1 · 1, 1 · 2, 3, 1 · 6, 12, 7, 1 … Σ 1, 2, 6, 26, 150, 1082, 9366, 94586, …
  (−∞, −1]nonnegative
• A027465 → θ+1
  1 · 3, 2 · 9, 12, 3 · 27, 54, 27, 4 … Σ 1, 5, 24, 112, 512, 2304, 10240, 45056, …
  (−∞, 0]nonnegativerational roots
• A099097 → D
  3 · 1, 18 · 0, 12, 81 · 0, 2, 81, 324 … Σ 0, 3, 19, 93, 407, 1674, 6618, 25455, …
  (−∞, 0]nonnegative
• A094816 → (θ+1)²
  1 · 1, 4 · 1, 12, 9 · 1, 32, 54, 16 … Σ 1, 5, 22, 103, 543, 3273, 22512, …
  (−∞, 0]nonnegative
• A225472 → Pₙ + Pₙ₊₁
  3, 3 · 6, 24, 18 · 12, 138, 288, 162 … Σ 6, 48, 600, 10200, 218328, 5627928, …
  (−∞, ∞)nonnegative
• A099097 → basis A008277
  1 · 3, 3 · 10, 28, 9 · 33, 207, 168, 27 … Σ 1, 6, 47, 435, 4622, 55080, 724371, …
  (−∞, 0]nonnegative
• A130123 → basis A013609
  1 · 2, 4 · 4, 16, 16 · 8, 48, 96, 64 … Σ 1, 6, 36, 216, 1296, 7776, 46656, …
  (−∞, 0]nonnegativerational roots
• A063007: T(n,k) = binomial(n,k)*binomial(n+k,k), 0 <= k <= n, triangle read by rows.
  1 · 1, 2 · 1, 6, 6 · 1, 12, 30, 20 … Σ 1, 3, 13, 63, 321, 1683, 8989, 48639, …
  (−1, 0)nonnegative