Sequences

3,043 sequences

• 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]
• A204420 → basis A013609
  1 · 1, 2 · 9, 24, 12 · 225, 690, 540, 120 … row sums 1, 3, 45, 1575, 99225, 9823275, …
  (−∞, 0] nonnegative rational roots
• A038319 → Pₙ + Pₙ₊₁
  1452, 1925, 850, 125 · 15972, 28435, 18975, 5625, 625 … row sums 4352, 69632, 1114112, 17825792, …
  (−∞, ∞) nonnegative rational roots
• A038329 → Pₙ + Pₙ₊₁
  1872, 1368, 333, 27 · 22464, 22032, 8100, 1323, 81 … row sums 3600, 54000, 810000, 12150000, …
  (−∞, ∞) nonnegative rational roots
• A085881 → Pₙ + Pₙ₊₁
  2, 1 · 4, 7, 3 · 18, 51, 48, 15 … row sums 3, 14, 132, 1800, 31920, 695520, …
  (−∞, ∞) nonnegative rational roots
• 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
• A103327 → Veronese 2 (j=1)
  1 · 10 · 35, 1 · 84, 36 … row sums 0, 1, 10, 36, 120, 496, 2080, 8256, …
  (−∞, 0] nonnegative
• A013620 → basis A008277
  1 · 5, 3 · 25, 39, 9 · 125, 387, 216, 27 … row sums 1, 8, 73, 755, 8740, 111761, 1560817, …
  (−∞, 0] nonnegative
• A102662 → basis A013610
  1 · 4, 9 · 9, 33, 27 · 22, 114, 180, 81 … row sums 1, 13, 69, 397, 2261, 12893, 73509, …
  (−∞, 0] nonnegative
• A272867 → basis A013609
  1 · 6, 12, 4 · 36, 144, 192, 96, 16 … row sums 1, 22, 484, 10648, 234256, 5153632, …
  (−∞, 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
• A132393 → Veronese 2
  1 · 0, 1 · 0, 3 · 0, 11, 1 … row sums 1, 0, 1, 3, 12, 60, 360, 2520, …
  (−∞, 0] nonnegative
• A023531 → basis A341287 → Pₙ + Pₙ₊₁
  1, 1 · -1, 2, 1 · -2, -1, 4, 1 · 1, -11, 4, 7, 1 … row sums 2, 2, 2, 2, 2, 2, 2, 2, …
  (−∞, ∞)
• 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
• A102547 → x ↦ (1/27)x → basis A013609
  1 · 3 · 9 · 28, 2 … row sums 1, 3, 9, 30, 99, 324, 1062, 3483, …
  (−∞, 0] nonnegative
• A081577 → basis A008277
  1 · 2, 1 · 6, 7, 1 · 16, 35, 13, 1 … row sums 1, 3, 14, 65, 333, 1826, 10701, 66579, …
  (−∞, 0] 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
• A257609 → γ
  1 · 2 · 4, 8 · 8, 64 … row sums 1, 2, 12, 72, 624, 6048, 70848, 931968, …
  (−∞, 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
• A035469 → Pₙ + Pₙ₊₁
  5, 1 · 32, 13, 1 · 308, 172, 25, 1 … row sums 6, 46, 506, 7186, 124662, 2551086, …
  (−∞, ∞) 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
• A286718: Triangle read by rows: T(n, k) is the Sheffer triangle ((1 - 3*x)^(-1/3), (-1/3)*log(1 - 3*x)). A generalized Stirling1 triangle.
  1 · 1, 1 · 4, 5, 1 · 28, 39, 12, 1 … row sums 1, 2, 10, 80, 880, 12320, 209440, …
  A286718 (−∞, 0) nonnegative rational roots
• A109692 → basis A007318
  1 · 2, 1 · 8, 10, 3 · 48, 100, 68, 15 … row sums 1, 3, 21, 231, 3465, 65835, 1514205, …
  (−∞, 0] nonnegative rational roots
• A102547 → reverse → basis A013610
  1, 3 · 1, 6, 9 · 1, 9, 27, 27 · 2, 21, 81, 135, 81 … row sums 4, 16, 64, 320, 1536, 7168, 33792, …
  (−∞, 0] nonnegative
• A257610 → γ
  1 · 2 · 4, 12 · 8, 108 … row sums 1, 2, 16, 116, 1348, 17228, 276004, …
  (−∞, 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
• Triangle read by rows: (i,j)-th entry is binomial(i,j)*3^(i-j)*8^j.
  9, 48, 64 · 27, 216, 576, 512 … row sums 121, 1331, 14641, 161051, 1771561, …
  (−∞, 0) nonnegative rational roots
• A102662 → reverse
  1 · 3, 1 · 3, 5, 1 · 3, 11, 7, 1 … row sums 1, 4, 9, 22, 53, 128, 309, 746, …
  (−∞, 0] nonnegative
• A269944 → basis A013610
  1 · 1, 3 · 2, 9, 9 · 10, 51, 72, 27 … row sums 1, 4, 20, 160, 2080, 41600, 1206400, …
  (−∞, 0] nonnegative rational roots
• A069466 → basis A013611
  1 · 4, 8 · 36, 144, 96 · 400, 2400, 3840, 1280 … row sums 1, 12, 276, 7920, 252420, 8536752, …
  (−∞, 0] nonnegative
• A144698 → Pₙ + Pₙ₊₁
  2, 4 · 2, 17, 16 · 2, 45, 129, 64 … row sums 6, 35, 240, 1890, 16800, 166320, …
  (−∞, ∞) nonnegative
• A143491 → basis A008277
  12, 8, 1 · 60, 60, 15, 1 · 360, 480, 180, 24, 1 … row sums 21, 136, 1045, 9276, 93289, 1047376, …
  (−∞, 0] nonnegative
• A344565 → basis A008277
  3 · 30, 15 · 180, 225, 45 · 840, 1995, 945, 105 … row sums 3, 45, 450, 3885, 31710, 254772, …
  (−∞, 0] nonnegative
• A256890 → Pₙ + Pₙ₊₁
  12, 64, 56, 8 · 24, 248, 468, 204, 16 … row sums 140, 960, 7560, 67200, 665280, 7257600, …
  (−∞, ∞) nonnegative
• A144441 → γ
  1 · 1 · 1, 12 · 1, 80 … row sums 1, 1, 13, 81, 1117, 15537, 294733, …
  (−∞, 0] nonnegative
• A026729 → basis A013609
  1 · 1, 2 · 2, 6, 4 · 3, 14, 20, 8 … row sums 1, 3, 12, 45, 171, 648, 2457, 9315, …
  (−∞, 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