Sequences

• A143683 → basis A013611
  1 · 2, 4 · 12, 48, 16 · 40, 240, 352, 64 … Σ 1, 6, 76, 696, 7216, 71136, 715456, …
  (−∞, 0]nonnegative
• A120909 → Pₙ + Pₙ₊₁
  6, 6 · 6, 18, 12 · 6, 30, 48, 24 … Σ 12, 36, 108, 324, 972, 2916, 8748, …
  (−∞, ∞)nonnegativerational roots
• A144439 → γ
  1 · 1 · 1, 6 · 1, 28 … Σ 1, 1, 7, 29, 223, 1773, 18287, 210509, …
  (−∞, 0]nonnegative
• A133214 → basis A013611
  13, 64, 64 · 63, 456, 960, 512 … Σ 141, 1991, 29761, 460251, 7272861, …
  (−∞, 0]nonnegative
• A181289: Triangle read by rows: T(n,k) is the number of 2-compositions of n having length k (0 <= k <= n).
  1 · 0, 2 · 0, 3, 4 · 0, 4, 12, 8 … Σ 1, 2, 7, 24, 82, 280, 956, 3264, …
  [−1, ∞)nonnegative
• A137338: Triangle read by rows: T(n,k), 0 <= k <= n, gives the coefficients of the Charlier polynomials (with parameter a=1), ordered by rising powers.
  1 · -1, 1 · 0, -3, 1 · 3, 6, -6, 1 … Σ 1, 0, -2, 4, -4, -4, 44, -236, …
  (−∞, ∞)
• A038331 → basis A007318
  289, 170, 25 · 4913, 4335, 1275, 125 … Σ 484, 10648, 234256, 5153632, 113379904, …
  (−∞, 0]nonnegativerational roots
• A093375 → x ↦ x+1
  1 · 3, 1 · 8, 6, 1 · 20, 24, 9, 1 … Σ 1, 4, 15, 54, 189, 648, 2187, 7290, …
  (−∞, −1]nonnegativerational roots
• A089627: T(n,k) = binomial(n,2*k)*binomial(2*k,k) for 0 <= k <= n, triangle read by rows.
  1 · 1 · 1, 2 · 1, 6 … Σ 1, 1, 3, 7, 19, 51, 141, 393, …
  (−∞, 0)nonnegative
• A257609 → Pₙ + Pₙ₊₁
  3, 2 · 6, 18, 4 · 12, 104, 92, 8 … Σ 5, 28, 216, 2112, 24960, 345600, …
  (−∞, ∞)nonnegative
• A038321 → basis A013611
  324, 1008, 784 · 5832, 27216, 42336, 21952 … Σ 2116, 97336, 4477456, 205962976, …
  (−∞, 0]nonnegativerational roots
• A026729 → D+1
  1 · 1, 1 · 1, 3, 1 · 0, 4, 5, 1 … Σ 1, 2, 5, 10, 20, 38, 71, 130, …
  (−∞, 0]nonnegative
• A232535 → Veronese 2
  1 · 1 · 1, 3 · 1, 25 … Σ 1, 1, 4, 26, 104, 376, 1504, 6176, …
  (−∞, 0]nonnegative
• basis-map coefficients of Triangular array read by rows: T(n,k) = binomial(n,2)*binomial(n,k), n>=0, 0<=k<=n.
  0, 0, 1 · 0, 0, 0, 3 · 0, 0, 0, 0, 6 … Σ 0, 0, 1, 3, 6, 10, 15, 21, …
  (−∞, 0]nonnegativerational roots
• A121574 → (θ+1)²
  1 · 2, 4 · 4, 20, 9 · 8, 64, 72, 16 … Σ 1, 6, 33, 160, 726, 3144, 13159, 53652, …
  (−∞, 0]nonnegative
• A038208 → Pₙ + Pₙ₊₁
  3, 2 · 6, 10, 4 · 12, 32, 28, 8 · 24, 88, 120, 72, 16 … Σ 5, 20, 80, 320, 1280, 5120, 20480, …
  (−∞, ∞)nonnegativerational roots
• A008288 → basis A013609
  1 · 2, 2 · 5, 10, 4 · 12, 36, 32, 8 … Σ 1, 4, 19, 88, 409, 1900, 8827, 41008, …
  (−∞, 0]nonnegative
• A038305 → basis A007318
  169, 78, 9 · 2197, 1521, 351, 27 … Σ 256, 4096, 65536, 1048576, 16777216, …
  (−∞, 0]nonnegativerational roots
• A054142 → reverse
  1 · 1, 1 · 1, 3, 1 · 1, 6, 5, 1 … Σ 1, 2, 5, 13, 34, 89, 233, 610, …
  (−∞, 0]nonnegative
• A285061: Sheffer triangle S2[4,1] = (exp(x), exp(4*x) - 1).
  1 · 1, 4 · 1, 24, 16 · 1, 124, 240, 64 … Σ 1, 5, 41, 429, 5329, 75989, 1215481, …
  (−∞, 0)nonnegative
• A144697: Triangle of 3-Eulerian numbers.
  1 · 1, 3 · 1, 10, 9 · 1, 25, 67, 27 … Σ 1, 4, 20, 120, 840, 6720, 60480, …
  (−∞, 0)nonnegative
• A099093 → x ↦ x−6
  1 · -18, 3 · 306, -105, 9 · -5184, 2700, -468, 27 … Σ 1, -15, 210, -2925, 40725, -567000, …
  (14/3, 6]
• A091044 → (θ+1)²
  1 · 2, 8 · 3, 40, 27 · 4, 112, 252, 64 … Σ 1, 10, 70, 432, 2464, 13312, 69120, …
  (−∞, 0]nonnegative
• A100861 → D
  1 · 3 · 6, 6 · 10, 30 … Σ 0, 0, 1, 3, 12, 40, 150, 546, …
  (−∞, 0]nonnegative
• A290319 → Pₙ + Pₙ₊₁
  2, 1 · 6, 7, 1 · 50, 65, 16, 1 · 630, 871, 269, 29, 1 … Σ 3, 14, 132, 1800, 31920, 695520, …
  (−∞, ∞)nonnegativerational roots
• A124038: Triangle read by rows: T(n, k) = T(n-1, k-1) - T(n-2, k), with T(n, n) = 1, T(n, n-1) = -2.
  1 · -2, 1 · -1, -2, 1 · 2, -2, -2, 1 … Σ 1, -1, -2, -1, 1, 2, 1, -1, …
  (−2, 3)
• A062196: Triangle read by rows, T(n, k) = binomial(n, k)*binomial(n + 2, k).
  1 · 1, 3 · 1, 8, 6 · 1, 15, 30, 10 … Σ 1, 4, 15, 56, 210, 792, 3003, 11440, …
  (−∞, 0)nonnegative
• A207607 → D+1
  1 · 3, 2 · 6, 9, 2 · 10, 27, 15, 2 … Σ 1, 5, 17, 54, 166, 499, 1475, 4303, …
  (−∞, 0]nonnegative
• A357367: Triangle read by rows. T(n, k) = binomial(n - 1, k - 1)*(n + k)! / k!.
  1 · 0, 2 · 0, 6, 12 · 0, 24, 120, 120 … Σ 1, 2, 18, 264, 5400, 141840, 4551120, …
  (−∞, 0]nonnegative
• A169803 → θ+1
  1 · 1, 2 · 1, 4 · 1, 6, 3 … Σ 1, 3, 5, 10, 18, 33, 59, 105, …
  (−∞, 0]nonnegative
• A008288 → Veronese 2
  1 · 1 · 1, 1 · 1, 5 … Σ 1, 1, 2, 6, 15, 35, 84, 204, …
  (−∞, 0]nonnegative
• A111125 → basis A008277
  1 · 4, 1 · 11, 8, 1 · 29, 42, 13, 1 … Σ 1, 5, 20, 85, 391, 1941, 10341, 58800, …
  (−∞, 0]nonnegative
• A139548 → basis A007318
  1 · 8, 8, 2 · 64, 128, 96, 32, 4 … Σ 1, 18, 324, 5832, 104976, 1889568, …
  (−∞, 0]nonnegativerational roots
• A091042 → D
  3 · 10, 10 · 21, 70, 21 · 36, 252, 252, 36 … Σ 0, 3, 20, 112, 576, 2816, 13312, 61440, …
  (−∞, 0]nonnegative
• A094638: Triangle read by rows: T(n,k) = |s(n,n+1-k)|, where s(n,k) are the signed Stirling numbers of the first kind A008276 (1 <= k <= n; in other words, the…
  1 · 1, 1 · 1, 3, 2 · 1, 6, 11, 6 … Σ 1, 2, 6, 24, 120, 720, 5040, 40320, …
  (−∞, 0)nonnegativerational roots
• narayana → x ↦ x/(x+1)
  1 · 1, 2 · 1, 5, 5 · 1, 9, 21, 14 … Σ 1, 3, 11, 45, 197, 903, 4279, 20793, …
  [−1, 0]nonnegative
• A121574 → Veronese 2
  1 · 2 · 4, 1 · 8, 8 … Σ 1, 2, 5, 16, 54, 180, 595, 1964, …
  (−∞, 0]nonnegative
• A078812 → x ↦ x/(x+1)
  1 · 2, 3 · 3, 10, 8 · 4, 22, 38, 21 … Σ 1, 5, 21, 85, 341, 1365, 5461, 21845, …
  [−1, 0)nonnegative
• A114656 → basis A013609
  1 · 3, 2 · 11, 16, 4 · 45, 102, 60, 8 … Σ 1, 5, 31, 215, 1597, 12425, 99955, …
  (−∞, 0]nonnegative
• A116414 → θ+1
  1 · 4, 2 · 13, 16, 3 · 40, 84, 36, 4 … Σ 1, 6, 32, 164, 819, 4012, 19363, 92352, …
  (−∞, 0]nonnegative
• A304236 → basis A007318
  1 · 1 · 4, 3 · 7, 6 … Σ 1, 1, 7, 13, 55, 133, 463, 1261, …
  (−∞, −1]nonnegative
• A152198 → basis A013611
  1 · 1 · 2, 4 · 2, 4 … Σ 1, 1, 6, 6, 36, 36, 216, 216, …
  (−∞, 0]nonnegativerational roots
• A128813 → basis A013610
  1 · 2, 3 · 8, 30, 27 · 56, 354, 729, 486 … Σ 1, 5, 65, 1625, 66625, 4064125, …
  (−∞, 0]nonnegativerational roots
• A352880 → reverse
  8 · 18, 12 · 32, 64, 16 · 50, 200, 150, 20 … Σ 8, 30, 112, 420, 1584, 6006, 22880, …
  (−∞, 0]nonnegative
• A356546 → basis A013611
  1 · 4, 8 · 24, 96, 96 · 160, 960, 1920, 1280 … Σ 1, 12, 216, 4320, 90720, 1959552, …
  (−∞, 0]nonnegativerational roots
• A026374 → D
  1 · 3, 2 · 4, 8, 3 · 6, 22, 18, 4 … Σ 0, 1, 5, 15, 50, 125, 375, 875, …
  (−∞, 0]nonnegative
• A082985 → Veronese 2
  1 · 1 · 1, 5 · 1, 14 … Σ 1, 1, 6, 15, 37, 100, 261, 681, …
  (−∞, 0]nonnegative
• A135065 → (θ+1)²
  1 · 4, 16 · 9, 72, 81 · 16, 192, 432, 256 … Σ 1, 20, 162, 896, 4000, 15552, 54880, …
  (−∞, 0]nonnegative
• A090452: Scaled array A078740 ((3,2)-Stirling2).
  1 · 1, 3, 2 · 1, 7, 16, 15, 5 … Σ 1, 6, 44, 360, 3152, 28896, 273856, …
  (−∞, 0)nonnegative
• A038323: Triangle whose (i,j)-th entry is binomial(i,j)*11^(i-j)*9^j.
  1 · 11, 9 · 121, 198, 81 · 1331, 3267, 2673, 729 … Σ 1, 20, 400, 8000, 160000, 3200000, …
  (−∞, 0)nonnegativerational roots