Sequences

• A063007 → basis A008288
  1 · 3, 2 · 13, 24, 6 · 63, 202, 130, 20 … Σ 1, 5, 43, 415, 4201, 43741, 463891, …
  [−3−2√2, −3+2√2]nonnegative
• A121574 → basis A013610
  1 · 3, 3 · 10, 21, 9 · 33, 105, 99, 27 … Σ 1, 6, 40, 264, 1744, 11520, 76096, …
  (−∞, 0]nonnegative
• A038326 → basis A008277
  1 · 23, 12 · 529, 696, 144 … Σ 1, 35, 1369, 59723, 2883889, 152682227, …
  (−∞, 0]nonnegative
• A122431 → D
  3, 6, 3 · 1, 6, 9, 4 · 0, 2, 9, 12, 5 … Σ 12, 20, 28, 36, 44, 52, 60, 68, …
  (−∞, 0]nonnegativerational roots
• Triangle read by rows: T(n, m) = S1(n, m)*9^(n-m), where S1 are the signed Stirling numbers of first kind A008275 (n >= 1, 1 <= m <= n).
  162, -27, 1 · -4374, 891, -54, 1 … Σ 136, -3536, 123760, -5445440, …
  [9/2, ∞)rational roots
• A178822 → x ↦ x+1
  1 · 12, 6 · 84, 84, 21 · 448, 672, 336, 56 … Σ 1, 18, 189, 1512, 10206, 61236, 336798, …
  (−∞, −1]nonnegativerational roots
• A130123 → reverse
  1 · 2 · 4 · 8 … Σ 1, 2, 4, 8, 16, 32, 64, 128, …
  (−∞, 0]nonnegativerational roots
• A106246 → x ↦ x+1
  1 · 3, 1 · 6, 6, 1 · 10, 18, 9, 1 … Σ 1, 4, 13, 38, 104, 272, 688, 1696, …
  (−∞, −1]nonnegative
• A133080 → basis A008277
  1 · 2, 1 · 1, 3, 1 · 2, 10, 7, 1 … Σ 1, 3, 5, 20, 52, 255, 877, 5017, …
  (−∞, 0]nonnegative
• A038284 → Pₙ + Pₙ₊₁
  576, 1248, 900, 216 · 4608, 13440, 14688, 7128, 1296 … Σ 2940, 41160, 576240, 8067360, …
  (−∞, ∞)nonnegativerational roots
• Triangle of Sulanke numbers: T(n,k) = T(n,k-1) + a(n-1,k) for n+k even and a(n,k) = a(n,k-1) + 2*a(n-1,k) for n+k odd.
  1, 3, 2 · 1, 5, 8, 4 · 1, 6, 13, 12, 4 … Σ 6, 18, 36, 108, 216, 648, 1296, 3888, …
  (−∞, 0]nonnegativerational roots
• A334218 → x ↦ x+1
  1 · 1 · 2, 2 · 6, 9, 3 … Σ 1, 1, 4, 18, 104, 750, 6492, 65562, …
  (−∞, −1]nonnegative
• A013610 → Pₙ + Pₙ₊₁
  2, 3 · 2, 9, 9 · 2, 15, 36, 27 · 2, 21, 81, 135, 81 … Σ 5, 20, 80, 320, 1280, 5120, 20480, …
  (−∞, ∞)nonnegativerational roots
• A132774 → x ↦ x+1
  1 · 5, 3 · 9, 14, 5 · 13, 33, 27, 7 … Σ 1, 8, 28, 80, 208, 512, 1216, 2816, …
  (−∞, −1]nonnegativerational roots
• A358735 → basis A008277
  1 · 2, 1 · 7, 10, 2 · 33, 100, 52, 6 … Σ 1, 3, 19, 191, 2779, 55247, 1436433, …
  (−∞, 0]nonnegative
• A345013: Triangle read by rows, related to clusters of type D.
  1 · 4, 3 · 15, 20, 6 · 56, 105, 60, 10 … Σ 1, 7, 41, 231, 1289, 7183, 40081, …
  (−∞, −1]nonnegative
• A161198 → Pₙ + Pₙ₊₁
  2, 2 · 4, 10, 4 · 18, 54, 40, 8 … Σ 4, 18, 120, 1050, 11340, 145530, …
  (−∞, ∞)nonnegativerational roots
• A125662 → basis A013610
  1 · 4, 3 · 15, 24, 9 · 56, 138, 108, 27 … Σ 1, 7, 48, 329, 2255, 15456, 105937, …
  (−∞, 0]nonnegative
• A033282 → x ↦ x/(x+1)
  1 · 1, 3 · 1, 7, 11 · 1, 12, 42, 45 … Σ 1, 4, 19, 100, 562, 3304, 20071, …
  [−1, 0)nonnegative
• A111125 → D+1
  1 · 4, 1 · 10, 7, 1 · 21, 28, 10, 1 … Σ 1, 5, 18, 60, 191, 589, 1775, 5257, …
  (−∞, 0]nonnegative
• A152830 → basis A008277
  1 · 1 · 1 · 1 … Σ 1, 1, 1, 1, 3, 3, 3, 3, …
  (−∞, 0]nonnegative
• A128100 → θ+1
  1 · 1 · 2, 2 · 3, 4 … Σ 1, 1, 4, 7, 18, 37, 84, 179, …
  (−∞, 0]nonnegative
• A113413 → basis A008277
  1 · 3, 1 · 7, 7, 1 · 17, 33, 12, 1 … Σ 1, 4, 15, 63, 288, 1427, 7605, 43314, …
  (−∞, 0]nonnegative
• A114656 → basis A013610
  1 · 3, 3 · 11, 24, 9 · 45, 153, 135, 27 … Σ 1, 6, 44, 360, 3152, 28896, 273856, …
  (−∞, 0]nonnegative
• A099093 → θ+1
  1 · 0, 6 · 0, 6, 27 · 0, 0, 54, 108 … Σ 1, 6, 33, 162, 756, 3402, 14931, 64314, …
  (−∞, 0]nonnegative
• A344565 → Veronese 2 (j=1)
  15 · 90 · 315, 105 · 840, 840 … Σ 0, 15, 90, 420, 1680, 6048, 20160, …
  (−∞, 0]nonnegative
• A225468 → Pₙ + Pₙ₊₁
  3, 1 · 6, 8, 1 · 12, 46, 16, 1 · 24, 242, 174, 27, 1 … Σ 4, 15, 75, 468, 3429, 28539, 264870, …
  (−∞, ∞)nonnegative
• A257617: 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) = 7*x + 2.
  1 · 2, 2 · 4, 36, 4 · 8, 388, 388, 8 … Σ 1, 4, 44, 792, 19800, 633600, 24710400, …
  (−∞, 0)nonnegative
• A112493: Triangle read by rows, T(n, k) = Sum_{j=0..n} C(n-j, n-k)*E2(n, j), where E2 are the second-order Eulerian numbers A201637, for n >= 0 and 0 <= k <= n.
  1 · 1, 1 · 1, 4, 3 · 1, 11, 25, 15 … Σ 1, 2, 8, 52, 472, 5504, 78416, 1320064, …
  [−1, 0)nonnegative
• A099040 → x ↦ x−1
  1 · -2, 2 · 2, -6, 4 · 0, 8, -16, 8 … Σ 1, 0, 0, 0, 0, 0, 0, 0, …
  (−1, 1]
• A225470 → basis A013610
  1 · 3, 3 · 18, 27, 9 · 162, 297, 162, 27 … Σ 1, 6, 54, 648, 9720, 174960, 3674160, …
  (−∞, 0]nonnegativerational roots
• A094646: Triangle of generalized Stirling numbers of the first kind read by rows: T(n, k) = (-1)^(n+k)*Sum_{m=0..n} Stirling1(n, m) * binomial(m, k) * 2^(m-k),…
  1 · -2, 1 · 2, -3, 1 · 0, 2, -3, 1 … Σ 1, -1, 0, 0, 0, 0, 0, 0, …
  (−∞, 5/2]rational roots
• A274498 → θ+1
  1 · 3 · 3, 12 · 9, 36 … Σ 1, 3, 15, 45, 189, 567, 2187, 6561, …
  (−∞, 0]nonnegativerational roots
• A249248 → x ↦ x+1
  1 · 4, 3 · 11, 13, 3 · 38, 65, 31, 3 … Σ 1, 7, 27, 137, 681, 3687, 20595, …
  (−∞, −1]nonnegative
• A391045: Triangle read by rows: T(n,k) = binomial(n+1,k+1)*binomial(2*n-k+1,k)/(n+1), 0<=k<=n.
  1 · 1, 1 · 1, 4, 1 · 1, 9, 10, 1 … Σ 1, 2, 6, 21, 80, 322, 1347, 5798, …
  (−∞, 0)nonnegative
• A172431 → basis A008277
  1 · 3, 2 · 8, 13, 3 · 21, 64, 34, 4 … Σ 1, 5, 24, 123, 682, 4079, 26159, …
  (−∞, 0]nonnegative
• A166345: Triangle T(n, k) = coefficients of ( t(n, x) ) where t(n, x) = (1-x)^(n+1)*p(n, x)/x, p(n, x) = x*D( p(n-1, x) ), with p(1, x) = x/(1-x)^2, p(2, x) = …
  1 · 1, 1 · 1, 2, 1 · 1, 7, 7, 1 … Σ 1, 2, 4, 16, 80, 480, 3360, 26880, …
  (−∞, 0)nonnegative
• A249251 → basis A013610
  1 · 4, 9 · 13, 54, 54 · 43, 261, 513, 324 … Σ 1, 13, 121, 1141, 10753, 101341, …
  (−∞, 0]nonnegative
• A049029: Triangle read by rows, the Bell transform of the quartic factorial numbers A007696(n+1) without column 0.
  1 · 5, 1 · 45, 15, 1 · 585, 255, 30, 1 … Σ 1, 6, 61, 871, 15996, 358891, 9509641, …
  (−∞, 0)nonnegative
• basis-map coefficients of A297191, shifted → basis A013609
  1 · 1, 4, 4 · 1, 8, 24, 32, 16 … Σ 1, 9, 81, 729, 6561, 59049, 531441, …
  (−∞, 0]nonnegativerational roots
• A188440 → Veronese 2
  1 · 1 · 1 · 1 … Σ 1, 1, 1, 1, 5, 5, 13, 13, …
  (−∞, 0]nonnegative
• A120910 → Pₙ + Pₙ₊₁
  9, 3 · 18, 15, 3 · 36, 48, 21, 3 · 72, 132, 90, 27, 3 … Σ 12, 36, 108, 324, 972, 2916, 8748, …
  (−∞, ∞)nonnegativerational roots
• Triangle whose (i,j)-th entry is binomial(i,j)*12^(i-j)*7^j.
  144, 168, 49 · 1728, 3024, 1764, 343 … Σ 361, 6859, 130321, 2476099, 47045881, …
  (−∞, 0)nonnegativerational roots
• A137320 → x ↦ x/(x+1)
  1 · 0, 2 · 0, 2, 6 · 0, 4, 20, 24 … Σ 1, 2, 8, 48, 384, 3840, 46080, 645120, …
  [−1, 0]nonnegativerational roots
• A286718 → Pₙ + Pₙ₊₁
  2, 1 · 5, 6, 1 · 32, 44, 13, 1 · 308, 457, 171, 23, 1 … Σ 3, 12, 90, 960, 13200, 221760, 4398240, …
  (−∞, ∞)nonnegativerational roots
• A085478 → basis A008277
  1 · 1 · 2, 1 · 5, 6, 1 … Σ 1, 1, 3, 12, 53, 253, 1297, 7103, …
  (−∞, 0]nonnegative
• A091044 → ⊙ C(n+2,k+1) → D
  1 · 5, 2 · 14, 28, 3 · 30, 168, 90, 4 … Σ 0, 1, 7, 45, 292, 1930, 12993, 88893, …
  (−∞, 0]nonnegative
• A099097: Riordan array (1, 3+x).
  1 · 0, 3 · 0, 1, 9 · 0, 0, 6, 27 … Σ 1, 3, 10, 33, 109, 360, 1189, 3927, …
  (−4/9, 0]nonnegative
• A109692 → basis A008277
  1 · 2, 1 · 8, 13, 3 · 48, 183, 113, 15 … Σ 1, 3, 24, 359, 8563, 295114, 13765813, …
  (−∞, 0]nonnegative
• A249248 → basis A013609
  1 · 4, 6 · 11, 26, 12 · 38, 130, 124, 24 … Σ 1, 10, 49, 316, 1999, 13684, 96715, …
  (−∞, 0]nonnegative