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1381 sequences

• A113413 → D
  1 · 4, 2 · 8, 12, 3 · 12, 36, 24, 4 … row sums 0, 1, 6, 23, 76, 233, 682, 1935, …
  (−∞, 0] nonnegative
• A172431 → D
  2 · 4, 6 · 6, 20, 12 · 8, 42, 60, 20 … row sums 0, 2, 10, 38, 130, 420, 1308, 3970, …
  (−∞, 0] nonnegative
• A013610: Triangle of coefficients in expansion of (1+3*x)^n.
  1 · 1, 3 · 1, 6, 9 · 1, 9, 27, 27 … row sums 1, 4, 16, 64, 256, 1024, 4096, 16384, …
  A013610 (−∞, 0) [−1, 0] nonnegative rational roots
• A066325 → x ↦ x+1
  1 · 1, 1 · 0, 2, 1 · -2, 0, 3, 1 … row sums 1, 2, 3, 2, -5, -18, -11, 86, …
  (−∞, ∞)
• A143494: Triangle read by rows: 2-Stirling numbers of the second kind.
  1 · 2, 1 · 4, 5, 1 · 8, 19, 9, 1 … row sums 1, 3, 10, 37, 151, 674, 3263, 17007, …
  A143494 (−∞, 0) nonnegative
• A086645 → D
  1 · 6, 2 · 15, 30, 3 · 28, 140, 84, 4 … row sums 0, 1, 8, 48, 256, 1280, 6144, 28672, …
  (−∞, 0] nonnegative
• A091044 → ⊙ C(n+2,k+1) → x ↦ x/(x+1)
  1 · 1, 2 · 1, 7, 7 · 1, 17, 45, 30 … row sums 1, 3, 15, 93, 653, 4983, 40339, 341337, …
  [−1, 0] nonnegative
• A081580: Pascal-(1,5,1) array.
  1 · 1, 1 · 1, 7, 1 · 1, 13, 13, 1 … row sums 1, 2, 9, 28, 101, 342, 1189, 4088, …
  A081580 (−∞, 0) nonnegative
• A114656 → basis A007318
  1 · 3, 1 · 11, 8, 1 · 45, 51, 15, 1 … row sums 1, 4, 20, 112, 672, 4224, 27456, …
  (−∞, −1] nonnegative
• A207606 → D+1
  11, 11, 2 · 21, 38, 17, 2 · 36, 102, 81, 23, 2 … row sums 24, 78, 244, 743, 2218, 6521, 18942, …
  (−∞, 0] nonnegative
• A008278 → x ↦ x+1 (shift +1) → D+1
  1 · 3, 1 · 10, 7, 1 · 38, 43, 13, 1 … row sums 1, 4, 18, 95, 579, 3966, 29944, 246141, …
  (−∞, 0] nonnegative
• A010054 → reverse → θ+1
  1 · 0, 4 · 0, 0, 9 · 0, 0, 0, 16 … row sums 0, 1, 4, 9, 16, 25, 36, 49, …
  (−∞, 0] nonnegative rational roots
• A007318 → (1/2+(1/2)n)θ+1+n → D+1
  1 · 5, 3 · 12, 21, 6 · 22, 66, 54, 10 … row sums 1, 8, 39, 152, 520, 1632, 4816, 13568, …
  (−∞, 0] nonnegative
• A099097 → x ↦ x/(x+1)
  1 · 0, 3 · 0, 1, 10 · 0, 0, 6, 33 … row sums 1, 3, 11, 39, 139, 495, 1763, 6279, …
  [−1, 0] nonnegative
• A028326 → x ↦ x/(x+1)
  2 · 2, 4 · 2, 8, 8 · 2, 12, 24, 16 … row sums 2, 6, 18, 54, 162, 486, 1458, 4374, …
  [−1, 0] nonnegative rational roots
• A100862 → x ↦ x+1
  1 · 2, 1 · 5, 5, 1 · 14, 21, 9, 1 … row sums 1, 3, 11, 45, 201, 963, 4899, 26253, …
  (−∞, −1] nonnegative
• A110441 → basis A007318
  1 · 4, 1 · 14, 8, 1 · 48, 44, 12, 1 … row sums 1, 5, 23, 105, 479, 2185, 9967, 45465, …
  (−7, −1) nonnegative
• A082985 → x ↦ x/(x+1)
  1 · 1, 4 · 1, 7, 11 · 1, 10, 31, 29 … row sums 1, 5, 19, 71, 265, 989, 3691, 13775, …
  [−1, 0] nonnegative
• A099040 → x ↦ x−12
  1 · -24, 2 · 552, -94, 4 · -12672, 3264, -280, 8 … row sums 1, -22, 462, -9680, 202796, -4248552, …
  (10, 12]
• A106800 → reverse (shift +1) → θ+1
  1 · 0, 2 · 0, 2, 3 · 0, 2, 9, 4 … row sums 1, 2, 5, 15, 52, 203, 877, 4140, …
  (−∞, 0] nonnegative
• A008288 → (θ+1)²
  1 · 1, 4 · 1, 12, 9 · 1, 20, 45, 16 … row sums 1, 5, 22, 82, 283, 923, 2892, 8788, …
  (−∞, 0] nonnegative
• A274498 → D+1
  1 · 3 · 9, 6 · 27, 18 … row sums 1, 3, 15, 45, 189, 567, 2187, 6561, …
  (−∞, 0] nonnegative rational roots
• A035607 → D
  2 · 4, 4 · 6, 16, 6 · 8, 36, 36, 8 … row sums 0, 0, 2, 8, 28, 88, 262, 752, …
  (−∞, 0] nonnegative
• A106800 → reverse (shift +1) → (θ+1)²
  1 · 0, 4 · 0, 4, 9 · 0, 4, 27, 16 … row sums 1, 4, 13, 47, 188, 825, 3937, 20270, …
  (−∞, 0] nonnegative
• A367270 → D+1
  1 · 1 · 3, 2 · 7, 12, 3 … row sums 1, 1, 5, 22, 95, 406, 1722, 7260, …
  (−∞, 0] nonnegative
• A178820 → D+1
  1 · 8, 4 · 30, 40, 10 · 80, 180, 120, 20 … row sums 1, 12, 80, 400, 1680, 6272, 21504, …
  (−∞, 0] nonnegative rational roots
• A102547 → x ↦ x+1
  1 · 1 · 1 · 2, 1 … row sums 1, 1, 1, 3, 5, 7, 13, 23, …
  (−∞, −1] nonnegative
• A030528 → x ↦ x−15
  1 · -14, 1 · 195, -28, 1 · -2715, 586, -42, 1 … row sums 1, -13, 168, -2170, 28028, -362012, …
  (11, 15]
• A274496 → D+1
  1 · 2 · 4, 2 · 8, 4 … row sums 1, 2, 6, 12, 32, 64, 160, 320, …
  (−∞, 0] nonnegative rational roots
• A173018 → D+1
  1 · 1 · 2, 1 · 5, 6, 1 … row sums 1, 1, 3, 12, 60, 360, 2520, 20160, …
  (−∞, 0] nonnegative
• A249252 → D
  4 · 8, 16 · 12, 64, 48 · 16, 144, 288, 128 … row sums 0, 4, 24, 124, 576, 2532, 10728, 44300, …
  (−∞, 0] nonnegative
• A172431 → ⊙ C(n,k+1) (shift -1) → x ↦ x+1
  1 · 2, 1 · 6, 6, 1 · 21, 32, 13, 1 … row sums 1, 3, 13, 67, 377, 2243, 13877, 88371, …
  (−∞, −1] nonnegative
• chebyshev_t → D
  1 · 0, 4 · -3, 0, 12 · 0, -16, 0, 32 … row sums 0, 1, 4, 9, 16, 25, 36, 49, …
  (−∞, ∞)
• A232535 → D+1
  1 · 3, 2 · 9, 14, 3 · 19, 68, 37, 4 … row sums 1, 5, 26, 128, 608, 2816, 12800, 57344, …
  (−∞, 0] nonnegative
• narayana → basis A007318
  1 · 2, 1 · 5, 5, 1 · 14, 21, 9, 1 … row sums 1, 3, 11, 45, 197, 903, 4279, 20793, …
  (−∞, −1] nonnegative
• A023531: a(n) = 1 if n is of the form m(m+3)/2, otherwise 0.
  1 · 0, 1 · 0, 0, 1 · 0, 0, 0, 1 … row sums 1, 1, 1, 1, 1, 1, 1, 1, …
  A023531 [−1, 0] [0, ∞) nonnegative rational roots
• A051523: Generalized Stirling number triangle of first kind read by rows: T(n, k) = [x^k] Product_{m=1..n} (x - m - r), with r = 9.
  A028338 → x ↦ −2x+19
  1 · -10, 1 · 110, -21, 1 · -1320, 362, -33, 1 … row sums 1, -9, 90, -990, 11880, -154440, …
  A051523 [19/2, ∞) rational roots
• A128099 → θ+1
  1 · 1 · 1, 4 · 1, 8 … row sums 1, 1, 5, 9, 25, 53, 125, 273, …
  (−∞, 0] nonnegative
• A013610 → (θ+1)²
  1 · 1, 12 · 1, 24, 81 · 1, 36, 243, 432 … row sums 1, 13, 106, 712, 4288, 24064, 128512, …
  (−∞, 0] nonnegative
• A106800 → reverse (shift +1) → reverse
  1 · 1 · 1, 1 · 1, 3, 1 … row sums 1, 1, 2, 5, 15, 52, 203, 877, …
  (−∞, 0] nonnegative
• A152830 → x ↦ x+1
  1 · 1 · 1 · 1 … row sums 1, 1, 1, 1, 3, 3, 3, 3, …
  (−∞, −1] nonnegative rational roots
• A133087 → D+1
  1 · 3, 1 · 3, 4, 1 · 7, 13, 7, 1 … row sums 1, 4, 8, 28, 48, 160, 256, 832, …
  (−∞, 0] nonnegative
• A013609: Triangle of coefficients in expansion of (1+2*x)^n.
  1 · 1, 2 · 1, 4, 4 · 1, 6, 12, 8 … row sums 1, 3, 9, 27, 81, 243, 729, 2187, …
  A013609 (−∞, 0) [−1, 0] nonnegative rational roots
• A120910 → x ↦ x/(x+1)
  3 · 6, 9 · 12, 36, 27 · 24, 108, 162, 81 … row sums 3, 15, 75, 375, 1875, 9375, 46875, …
  [−1, 0] nonnegative rational roots
• A008277 → θ+1 → reverse
  1 · 2, 1 · 3, 6, 1 · 4, 18, 14, 1 … row sums 1, 3, 10, 37, 151, 674, 3263, 17007, …
  (−∞, 0] nonnegative
• A008278 → θ+1
  1 · 1, 2 · 1, 6, 3 · 1, 12, 21, 4 … row sums 1, 3, 10, 38, 161, 747, 3753, 20253, …
  (−∞, 0] nonnegative
• A188440 → (θ+1)²
  1 · 1 · 1, 8 · 1, 8 … row sums 1, 1, 9, 9, 53, 53, 261, 261, …
  (−∞, 0] nonnegative
• chebyshev_u → D
  2 · 0, 8 · -4, 0, 24 · 0, -24, 0, 64 … row sums 0, 2, 8, 20, 40, 70, 112, 168, …
  (−∞, ∞)
• A133087 → x ↦ x/(x+1)
  1 · 2, 3 · 1, 4, 4 · 2, 11, 20, 12 … row sums 1, 5, 9, 45, 81, 405, 729, 3645, …
  [−1, 0] nonnegative rational roots
• A143683 → D
  1 · 10, 2 · 19, 38, 3 · 28, 236, 84, 4 … row sums 0, 1, 12, 60, 352, 1680, 8256, 38080, …
  (−∞, 0] nonnegative