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1381 sequences

• basis-map coefficients of A026729, shifted → D
  -1 · 0, 2 · 0, 0, -3 · 0, 0, 0, 4 … row sums 0, -1, 2, -3, 4, -5, 6, -7, …
  (−∞, 0] rational roots
• A113214 → x ↦ x−6
  1 · -4, 1 · 18, -9, 1 · -84, 62, -14, 1 … row sums 1, -3, 10, -35, 125, -450, 1625, -5875, …
  (2, 6]
• A059473 → x ↦ x/(x+1)
  1 · 2, 4 · 4, 18, 18 · 8, 56, 120, 80 … row sums 1, 6, 40, 264, 1744, 11520, 76096, …
  [−1, 0] nonnegative
• A099040 → x ↦ x−15
  1 · -30, 2 · 870, -118, 4 · -25200, 5160, -352, 8 … row sums 1, -28, 756, -20384, 549584, -14817600, …
  (13, 15]
• A049460: Generalized Stirling number triangle of first kind read by rows: T(n, k) = [x^k] Product_{m=1..n} (x - m - r), with r = 4.
  A028338 → x ↦ −2x+9
  1 · -5, 1 · 30, -11, 1 · -210, 107, -18, 1 … row sums 1, -4, 20, -120, 840, -6720, 60480, …
  A049460 [9/2, ∞) rational roots
• A062145 → x ↦ x/(x+1)
  1 · 1, 5 · 1, 12, 21 · 1, 21, 84, 84 … row sums 1, 6, 34, 190, 1059, 5908, 33028, …
  [−1, 0] nonnegative
• A086645 → x ↦ x/(x+1)
  1 · 1, 2 · 1, 8, 8 · 1, 18, 48, 32 … row sums 1, 3, 17, 99, 577, 3363, 19601, 114243, …
  [−1, 0] nonnegative
• A122076 → x ↦ x+1
  2 · 5, 2 · 17, 12, 2 · 65, 66, 21, 2 … row sums 2, 7, 31, 154, 799, 4207, 22258, …
  (−∞, ∞) nonnegative
• A063967 → x ↦ x−10
  1 · -9, 1 · 72, -17, 1 · -567, 207, -25, 1 … row sums 1, -8, 56, -384, 2624, -17920, 122368, …
  (5, 9]
• A062190 → x ↦ x/(x+1)
  1 · 1, 7 · 1, 16, 36 · 1, 27, 135, 165 … row sums 1, 8, 53, 328, 1966, 11584, 67582, …
  [−1, 0] nonnegative
• A038208 → D
  2 · 8, 8 · 24, 48, 24 · 64, 192, 192, 64 … row sums 0, 2, 16, 96, 512, 2560, 12288, 57344, …
  (−∞, 0] nonnegative rational roots
• A304236 → (θ+1)²
  1 · 1 · 1, 12 · 1, 24 … row sums 1, 1, 13, 25, 118, 292, 979, 2611, …
  (−∞, 0] nonnegative
• A114687 → D
  2 · 6, 8 · 12, 48, 24 · 20, 160, 240, 64 … row sums 0, 2, 14, 84, 484, 2750, 15546, 87752, …
  (−∞, 0] nonnegative
• A008292 → γ (scale 1/2) (shift +1) → (θ+1)²
  1 · 1 · 1, 4 · 1, 16 … row sums 1, 1, 5, 17, 81, 411, 2393, 15329, …
  (−∞, 0] nonnegative
• A114655 → x ↦ x+1
  2 · 6, 2 · 22, 16, 2 · 90, 102, 30, 2 … row sums 2, 8, 40, 224, 1344, 8448, 54912, …
  (−∞, −1] nonnegative
• A008292 → γ (scale 1/4) → D
  2 · 16 · 88, 32 · 416, 544 … row sums 0, 0, 2, 16, 120, 960, 8400, 80640, …
  (−∞, 0] nonnegative
• A038207 → (θ+1)²
  1 · 2, 4 · 4, 16, 9 · 8, 48, 54, 16 … row sums 1, 6, 29, 126, 513, 1998, 7533, 27702, …
  (−∞, 0] nonnegative
• A114687 → (θ+1)²
  1 · 1, 8 · 1, 24, 36 · 1, 48, 216, 128 … row sums 1, 9, 61, 393, 2481, 15473, 95677, …
  (−∞, 0] nonnegative
• A049444: Generalized Stirling number triangle of first kind read by rows: T(n, k) = [x^k] Product_{m=1..n} (x - m - r), with r = 1.
  A028338 → x ↦ −2x+3
  1 · -2, 1 · 6, -5, 1 · -24, 26, -9, 1 … row sums 1, -1, 2, -6, 24, -120, 720, -5040, …
  A049444 [3/2, ∞) rational roots
• A143683 → x ↦ x/(x+1)
  1 · 1, 2 · 1, 12, 12 · 1, 22, 60, 40 … row sums 1, 3, 25, 123, 769, 4275, 25129, …
  [−1, 0] nonnegative
• A052553 → D+1
  1 · 1 · 2, 1 · 3, 2 … row sums 1, 1, 3, 5, 10, 18, 33, 59, …
  (−∞, 0] nonnegative
• basis-map coefficients of A026729 → basis A056242 → D+1
  1 · 3, 2 · 6, 13, 4 · 10, 41, 40, 8 … row sums 1, 5, 23, 99, 408, 1632, 6388, 24596, …
  (−∞, 0] nonnegative
• A102662 → reverse
  1 · 3, 1 · 3, 5, 1 · 3, 11, 7, 1 … row sums 1, 4, 9, 22, 53, 128, 309, 746, …
  (−∞, 0] nonnegative
• A145597 → (θ+1)²
  1 · 3, 12 · 6, 60, 54 · 10, 180, 405, 160 … row sums 1, 15, 120, 755, 4191, 21567, 105560, …
  (−∞, 0] nonnegative
• A075497 → x ↦ x/(x+1)
  1 · 2, 3 · 4, 14, 11 · 8, 52, 92, 49 … row sums 1, 5, 29, 201, 1657, 15821, 170389, …
  [−1, 0] nonnegative
• basis-map coefficients of A026729 → basis A056242 → x ↦ x+1
  1 · 3, 2 · 10, 13, 4 · 34, 65, 40, 8 … row sums 1, 5, 27, 147, 801, 4365, 23787, …
  (−∞, −1] nonnegative
• A227450 → x ↦ x/(x+1)
  2 · 2, 6 · 2, 16, 22 · 2, 34, 110, 94 … row sums 2, 8, 40, 240, 1664, 12992, 112256, …
  [−1, 0] nonnegative
• A007318 → (1/3+(1/2)n+(1/6)n²)θ+1+(3/2)n+(1/2)n² → D
  4 · 16, 20 · 40, 100, 60 · 80, 300, 360, 140 … row sums 0, 4, 36, 200, 880, 3360, 11648, 37632, …
  (−∞, 0] nonnegative rational roots
• A172431 → (θ+1)²
  1 · 1, 8 · 1, 16, 27 · 1, 24, 90, 64 … row sums 1, 9, 44, 179, 667, 2352, 7973, 26229, …
  (−∞, 0] nonnegative
• A030528 → x ↦ x−1
  1 · 0, 1 · -1, 0, 1 · 1, -2, 0, 1 … row sums 1, 1, 0, 0, 0, 0, 0, 0, …
  (−3, 1]
• A062190 → θ+1
  1 · 1, 12 · 1, 28, 63 · 1, 48, 252, 224 … row sums 1, 13, 92, 525, 2695, 13013, 60424, …
  (−∞, 0] nonnegative
• A173018 → θ+1
  1 · 1 · 1, 2 · 1, 8, 3 … row sums 1, 1, 3, 12, 60, 360, 2520, 20160, …
  (−∞, 0] nonnegative
• A105070: T(n,k) = 2^k*binomial(n,2k+1), where 0 <= k <= floor((n-1)/2), n >= 1.
  A011973 → x ↦ (1/2)x−1/4
  1 · 2 · 3, 2 · 4, 8 … row sums 1, 2, 5, 12, 29, 70, 169, 408, …
  A105070 (−∞, 1/2] nonnegative
• A091042 → basis A007318
  1 · 4, 3 · 16, 20, 5 · 64, 112, 56, 7 … row sums 1, 7, 41, 239, 1393, 8119, 47321, …
  (−∞, −1] nonnegative
• A081581 → D
  1 · 8, 2 · 15, 30, 3 · 22, 156, 66, 4 … row sums 0, 1, 10, 48, 248, 1100, 4872, 20608, …
  (−∞, 0] nonnegative
• A102547 → reverse → D
  1 · 0, 2 · 0, 0, 3 · 0, 0, 3, 4 … row sums 1, 2, 3, 7, 13, 21, 36, 61, …
  (−∞, 0] nonnegative
• A008277 → θ+2 (shift +1) → x ↦ x/(x+1)
  2 · 2, 5 · 2, 13, 15 · 2, 27, 72, 52 … row sums 2, 7, 30, 153, 898, 5919, 43102, …
  [−1, 0] nonnegative
• narayana → D
  1 · 3, 2 · 6, 12, 3 · 10, 40, 30, 4 … row sums 0, 1, 5, 21, 84, 330, 1287, 5005, …
  (−∞, 0] nonnegative
• A075497 → D
  1 · 6, 2 · 28, 24, 3 · 120, 200, 60, 4 … row sums 0, 1, 8, 55, 384, 2841, 22504, 190863, …
  (−∞, 0] nonnegative
• A008277 → θ+1 → x ↦ x/(x+1)
  1 · 1, 3 · 1, 8, 10 · 1, 17, 49, 37 … row sums 1, 4, 19, 104, 641, 4380, 32803, …
  [−1, 0] nonnegative
• A232535 → D
  2 · 8, 6 · 18, 50, 12 · 32, 196, 168, 20 … row sums 0, 2, 14, 80, 416, 2048, 9728, 45056, …
  (−∞, 0] nonnegative
• A063967 → x ↦ x−9
  1 · -8, 1 · 56, -15, 1 · -384, 160, -22, 1 … row sums 1, -7, 42, -245, 1421, -8232, 47677, …
  (4, 8]
• narayana
  1 · 1, 1 · 1, 3, 1 · 1, 6, 6, 1 … row sums 1, 2, 5, 14, 42, 132, 429, 1430, …
  (−∞, 0) nonnegative
• delannoy → x ↦ x+1
  1 · 2, 1 · 5, 5, 1 · 12, 18, 8, 1 … row sums 1, 3, 11, 39, 139, 495, 1763, 6279, …
  (−∞, −1] nonnegative
• A207606 → D
  7, 4 · 16, 22, 6 · 30, 72, 45, 8 … row sums 11, 44, 155, 510, 1608, 4924, 14761, …
  (−∞, 0] nonnegative
• A154986 → θ+1
  1 · 1, 2 · 1, 8, 3 · 1, 22, 33, 4 … row sums 1, 3, 12, 60, 360, 2520, 20160, 181440, …
  (−∞, 0] nonnegative
• A304236 → θ+1
  1 · 1 · 1, 6 · 1, 12 … row sums 1, 1, 7, 13, 46, 106, 301, 739, …
  (−∞, 0] nonnegative
• A113214 → x ↦ x−7
  1 · -5, 1 · 28, -11, 1 · -161, 93, -17, 1 … row sums 1, -4, 18, -84, 396, -1872, 8856, …
  (3, 7]
• A116414 → D+1
  1 · 5, 1 · 21, 10, 1 · 82, 66, 15, 1 … row sums 1, 6, 32, 164, 819, 4012, 19363, 92352, …
  (−∞, 0] nonnegative
• A131689 → D
  1 · 1, 4 · 1, 12, 18 · 1, 28, 108, 96 … row sums 0, 1, 5, 31, 233, 2071, 21305, 249271, …
  (−∞, 0] nonnegative