Sequences

• A257617 → Pₙ + Pₙ₊₁
  3, 2 · 6, 38, 4 · 12, 424, 392, 8 … Σ 5, 48, 836, 20592, 653400, 25344000, …
  (−∞, ∞)nonnegative
• A229032 → Veronese 2 (j=1)
  4 · 16 · 40 · 80 … Σ 0, 0, 4, 16, 40, 80, 204, 736, …
  (−∞, 0]nonnegative
• A063967 → x ↦ x−12
  1 · -11, 1 · 110, -21, 1 · -1089, 319, -31, 1 … Σ 1, -10, 90, -800, 7100, -63000, 559000, …
  (7, 11]
• A038271 → basis A013611
  1 · 12, 20 · 144, 480, 400 · 1728, 8640, 14400, 8000 … Σ 1, 32, 1024, 32768, 1048576, 33554432, …
  (−∞, 0]nonnegativerational roots
• A038243 → basis A008277
  1 · 6, 1 · 36, 13, 1 · 216, 127, 21, 1 … Σ 1, 7, 50, 365, 2727, 20878, 163967, …
  (−∞, 0]nonnegative
• A344565 → (θ+1)²
  3 · 15, 60 · 45, 360, 405 · 105, 1260, 2835, 1680 … Σ 3, 75, 810, 5880, 33600, 163296, …
  (−∞, 0]nonnegative
• A288874: Row reversed version of triangle A201637 (second-order Eulerian triangle).
  A201637 → reverse (shift +1)
  1 · 0, 1 · 0, 2, 1 · 0, 6, 8, 1 … Σ 1, 1, 3, 15, 105, 945, 10395, 135135, …
  (−∞, 0]nonnegative
• A130123 → Veronese 2
  1 · 0, 4 · 0, 0, 16 · 0, 0, 0, 64 … Σ 1, 0, 4, 0, 16, 0, 64, 0, …
  (−∞, 0]nonnegativerational roots
• A085881 → γ
  1 · 1 · 3 · 15 … Σ 1, 1, 3, 15, 105, 945, 10395, 135135, …
  (−∞, 0]nonnegativerational roots
• A367270 → basis A013609
  1 · 1 · 3, 4 · 10, 24, 12 … Σ 1, 1, 7, 46, 307, 2086, 14374, 100108, …
  (−∞, 0]nonnegative
• A097806: Riordan array (1+x, 1) read by rows.
  1 · 1, 1 · 0, 1, 1 · 0, 0, 1, 1 … Σ 1, 2, 2, 2, 2, 2, 2, 2, …
  (−∞, 0]nonnegativerational roots
• basis-map coefficients of A026729, shifted → (θ+1)²
  1 · 0, -4 · 0, 0, 9 · 0, 0, 0, -16 … Σ 1, -4, 9, -16, 25, -36, 49, -64, …
  (−∞, 0]rational roots
• A274496 → θ+1
  1 · 2 · 2, 4 · 4, 8 … Σ 1, 2, 6, 12, 32, 64, 160, 320, …
  (−∞, 0]nonnegativerational roots
• A010054: a(n) = 1 if n is a triangular number, otherwise 0.
  1 · 1 · 1 · 1 … Σ 1, 1, 1, 1, 1, 1, 1, 1, …
  (−∞, −1][−1, 0][−3−2√2, −3+2√2]+2
• A122542 → basis A008277
  1 · 1, 1 · 3, 5, 1 · 7, 21, 10, 1 … Σ 1, 2, 9, 39, 186, 953, 5225, 30484, …
  (−∞, 0]nonnegative
• A026729: Square array of binomial coefficients T(n,k) = binomial(n,k), n >= 0, k >= 0, read by downward antidiagonals.
  1 · 0, 1 · 0, 1, 1 · 0, 0, 2, 1 … Σ 1, 1, 2, 3, 5, 8, 13, 21, …
  (−4, 0]nonnegative
• A269947 → basis A008277
  1 · 1, 1 · 2, 4, 1 · 18, 42, 15, 1 … Σ 1, 2, 7, 76, 2279, 152776, 19564357, …
  (−∞, 0]nonnegative
• A085841 → basis A013609
  1 · 7, 8 · 61, 144, 64 · 547, 2008, 2112, 512 … Σ 1, 15, 269, 5179, 102105, 2028071, …
  (−∞, 0]nonnegative
• A306364: Triangular array of the number of binary, rooted, leaf-labeled tree topologies with n leaves and k cherries, n >= 2, 1 <= k <= floor(n/2).
  1 · 3 · 12, 3 · 60, 45 … Σ 1, 3, 15, 105, 945, 10395, 135135, …
  (−∞, 0)nonnegative
• A391533 → x ↦ x+1
  9, 6, 1 · 18, 21, 8, 1 · 36, 60, 37, 10, 1 … Σ 16, 48, 144, 432, 1296, 3888, 11664, …
  (−∞, −1]nonnegativerational roots
• A207824 → basis A013609
  1 · 6, 2 · 35, 24, 4 · 204, 212, 72, 8 … Σ 1, 8, 63, 496, 3905, 30744, 242047, …
  (−∞, 0]nonnegative
• A091044 → ⊙ C(n+2,k+1) → D+1
  1 · 2, 1 · 6, 7, 1 · 15, 42, 17, 1 … Σ 1, 3, 14, 75, 438, 2702, 17324, 114291, …
  (−∞, 0]nonnegative
• A116414 → x ↦ x/(x+1)
  1 · 4, 5 · 13, 34, 22 · 40, 162, 216, 95 … Σ 1, 9, 69, 513, 3789, 27945, 206037, …
  [−1, 0)nonnegative
• A081578 → θ+1
  1 · 1, 2 · 1, 10, 3 · 1, 18, 27, 4 … Σ 1, 3, 14, 50, 183, 637, 2188, 7380, …
  (−∞, 0]nonnegative
• A137597 → D+1
  1 · 3, 1 · 10, 7, 1 · 37, 40, 12, 1 … Σ 1, 4, 18, 90, 494, 2946, 18926, 130066, …
  (−∞, 0]nonnegative
• A125092 → x ↦ x+1
  1 · 5, 4 · 18, 26, 9 · 56, 114, 75, 16 … Σ 1, 9, 53, 261, 1161, 4833, 19197, …
  (−∞, −1]nonnegative
• A152828 → D+1
  1 · 1 · 1 · 2, 1 … Σ 1, 1, 1, 3, 3, 3, 8, 8, …
  (−∞, 0]nonnegativerational roots
• A082985 → θ+1
  1 · 1, 6 · 1, 10, 15 · 1, 14, 42, 28 … Σ 1, 7, 26, 85, 265, 804, 2393, 7019, …
  (−∞, 0]nonnegative
• A391533 → reverse
  1, 4, 4 · 1, 5, 8, 4 · 1, 6, 13, 12, 4 … Σ 9, 18, 36, 72, 144, 288, 576, 1152, …
  (−∞, 0]nonnegativerational roots
• A081577 → basis A013610
  1 · 2, 3 · 6, 18, 9 · 16, 72, 90, 27 … Σ 1, 5, 33, 205, 1289, 8085, 50737, …
  (−∞, 0]nonnegative
• A154986 → x ↦ x/(x+1)
  1 · 1, 2 · 1, 6, 6 · 1, 14, 36, 24 … Σ 1, 3, 13, 75, 537, 4611, 46053, 525483, …
  [−1, 0]nonnegative
• A136124 → basis A008277
  1 · 3, 1 · 12, 8, 1 · 60, 60, 15, 1 … Σ 1, 4, 21, 136, 1045, 9276, 93289, …
  (−∞, 0]nonnegative
• A327997 → basis A013610
  1 · 4, 3 · 17, 27, 9 · 78, 195, 135, 27 … Σ 1, 7, 53, 435, 3873, 37383, 390501, …
  (−∞, 0]nonnegative
• A053124: Triangle of coefficients of Chebyshev's U(n,2*x-1) polynomials (exponents of x in increasing order).
  1 · -2, 4 · 3, -16, 16 · -4, 40, -96, 64 … Σ 1, 2, 3, 4, 5, 6, 7, 8, …
  (0, 1)
• A030528 → (θ+1)²
  1 · 1, 4 · 0, 8, 9 · 0, 4, 27, 16 … Σ 1, 5, 17, 47, 116, 266, 579, 1213, …
  (−∞, 0]nonnegative
• A132200: Numbers in (4,4)-Pascal triangle .
  1 · 4, 4 · 4, 8, 4 · 4, 12, 12, 4 … Σ 1, 8, 16, 32, 64, 128, 256, 512, …
  (−∞, 0)nonnegativerational roots
• A130534 → Pₙ + Pₙ₊₁
  2, 1 · 3, 4, 1 · 8, 14, 7, 1 · 30, 61, 41, 11, 1 … Σ 3, 8, 30, 144, 840, 5760, 45360, …
  (−∞, ∞)nonnegativerational roots
• A039756 → D
  1 · 4, 2 · 9, 26, 3 · 16, 116, 120, 4 … Σ 0, 1, 6, 38, 256, 1844, 14296, 119160, …
  (−∞, 0]nonnegative
• A391045 → reverse
  1 · 1, 1 · 1, 4, 1 · 1, 10, 9, 1 … Σ 1, 2, 6, 21, 80, 322, 1347, 5798, …
  (−∞, 0]nonnegative
• narayana → basis A013611
  1 · 2, 4 · 5, 20, 16 · 14, 84, 144, 64 … Σ 1, 6, 41, 306, 2426, 20076, 171481, …
  (−∞, 0]nonnegative
• A121314: Triangle T(n,k), 0 <= k <= n, read by rows given by [0, 1, 0, 0, 0, 0, ...] DELTA [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, ...] where DELTA is the operator defi…
  1 · 0, 1 · 0, 1, 1 · 0, 1, 3, 1 … Σ 1, 1, 2, 5, 13, 34, 89, 233, …
  (−∞, 0]nonnegative
• A038326 → basis A013609
  1 · 23, 24 · 529, 1104, 576 … Σ 1, 47, 2209, 103823, 4879681, …
  (−∞, 0]nonnegativerational roots
• A038333 → basis A013611
  361, 1064, 784 · 6859, 30324, 44688, 21952 … Σ 2209, 103823, 4879681, 229345007, …
  (−∞, 0]nonnegativerational roots
• A232535 → basis A008277
  1 · 3, 2 · 12, 17, 3 · 48, 121, 49, 4 … Σ 1, 5, 32, 222, 1655, 13169, 111169, …
  (−∞, 0]nonnegative
• A090582: T(n, k) = Sum_{j=0..n-k} (-1)^j*binomial(n - k + 1, j)*(n - k + 1 - j)^n. Triangle read by rows, T(n, k) for 1 <= k <= n.
  1 · 2, 1 · 6, 6, 1 · 24, 36, 14, 1 … Σ 1, 3, 13, 75, 541, 4683, 47293, 545835, …
  (−∞, 0]nonnegative
• A136124 → Pₙ + Pₙ₊₁
  3, 1 · 8, 6, 1 · 30, 31, 10, 1 · 144, 180, 80, 15, 1 … Σ 4, 15, 72, 420, 2880, 22680, 201600, …
  (−∞, ∞)nonnegativerational roots
• A094305 → x ↦ x/(x+1)
  1 · 3, 6 · 6, 24, 24 · 10, 60, 120, 80 … Σ 1, 9, 54, 270, 1215, 5103, 20412, …
  [−1, 0]nonnegativerational roots
• A114687 → basis A013610
  1 · 3, 6 · 11, 42, 36 · 45, 252, 432, 216 … Σ 1, 9, 89, 945, 10577, 123129, 1476841, …
  (−∞, 0]nonnegative
• A124038 → D+1
  1 · -1, 1 · -3, 0, 1 · 0, -6, 1, 1 … Σ 1, 0, -2, -4, -3, 2, 7, 6, …
  (−∞, ∞)
• A108838 → x ↦ x+1
  2 · 5, 2 · 14, 12, 2 · 42, 56, 21, 2 … Σ 2, 7, 28, 121, 550, 2591, 12536, 61921, …
  (−∞, −1]nonnegative