Sequences

3,043 sequences

• A027467 → basis A013610
  1 · 16, 3 · 256, 96, 9 · 4096, 2304, 432, 27 … row sums 1, 19, 361, 6859, 130321, 2476099, …
  (−∞, 0] nonnegative rational roots
• A145597 → basis A008277
  1 · 6, 3 · 27, 33, 6 · 110, 250, 105, 10 … row sums 1, 9, 66, 475, 3525, 27384, 223538, …
  (−∞, 0] nonnegative
• A001263 → θ+1
  1 · 1, 2 · 1, 6, 3 · 1, 12, 18, 4 … row sums 1, 3, 10, 35, 126, 462, 1716, 6435, …
  (−∞, 0] nonnegative
• A225472: Triangle read by rows, k!*S_3(n, k) where S_m(n, k) are the Stirling-Frobenius subset numbers of order m; n >= 0, k >= 0.
  1 · 2, 3 · 4, 21, 18 · 8, 117, 270, 162 … row sums 1, 5, 43, 557, 9643, 208685, 5419243, …
  A225472 (−1, 0) nonnegative
• A113413 → reverse
  1 · 1, 2 · 1, 4, 2 · 1, 6, 8, 2 … row sums 1, 3, 7, 17, 41, 99, 239, 577, …
  (−∞, 0] nonnegative
• A196347 → basis A007318
  1 · 2, 1 · 8, 8, 2 · 48, 72, 36, 6 … row sums 1, 3, 18, 162, 1944, 29160, 524880, …
  (−∞, 0] nonnegative rational roots
• A054142 → basis A013610
  1 · 2, 3 · 5, 15, 9 · 13, 60, 81, 27 … row sums 1, 5, 29, 181, 1165, 7589, 49661, …
  (−∞, 0] nonnegative
• A257617 → γ
  1 · 2 · 4, 28 · 8, 364 … row sums 1, 2, 32, 372, 8724, 216108, 7186068, …
  (−∞, 0] nonnegative
• A166343 → γ
  1, 10 · 1, 24 · 1, 54, 48 · 1, 116, 360 … row sums 11, 25, 103, 477, 2739, 17745, 131247, …
  (−∞, 0] nonnegative
• A039757: Triangle of coefficients in expansion of (x-1)*(x-3)*(x-5)*...*(x-(2*n-1)).
  A028338 → x ↦ −x (shift -1)
  1 · -1, 1 · 3, -4, 1 · -15, 23, -9, 1 … row sums 1, 0, 0, 0, 0, 0, 0, 0, …
  A039757 [0, ∞) rational roots
• A008292 → γ (scale 1/2) (shift +1) → x ↦ x+1
  1 · 1 · 2, 1 · 5, 4 … row sums 1, 1, 3, 9, 39, 189, 1107, 7281, …
  (−∞, −1] nonnegative
• A106246: Number triangle T(n,k)=C(n,k)C(2,n-k).
  A023531 → (1/2)D²+2D+1
  1 · 2, 1 · 1, 4, 1 · 0, 3, 6, 1 … row sums 1, 3, 6, 10, 15, 21, 28, 36, …
  A106246 (−∞, 0] nonnegative
• A075498: Stirling2 triangle with scaled diagonals (powers of 3).
  1 · 3, 1 · 9, 9, 1 · 27, 63, 18, 1 … row sums 1, 4, 19, 109, 742, 5815, 51193, …
  A075498 (−∞, 0) nonnegative
• A038226 → Pₙ + Pₙ₊₁
  36, 264, 640, 512 · 108, 1080, 4032, 6656, 4096 … row sums 1452, 15972, 175692, 1932612, 21258732, …
  (−∞, ∞) nonnegative rational roots
• A081581 → basis A013609
  1 · 2, 2 · 10, 20, 4 · 32, 96, 72, 8 … row sums 1, 4, 34, 208, 1444, 9520, 64072, …
  (−∞, 0] nonnegative
• A165253 → basis A013609
  1 · 1 · 2, 2 · 5, 10, 4 … row sums 1, 1, 4, 19, 91, 436, 2089, 10009, …
  (−∞, 0] nonnegative
• A008278 → x ↦ x/(x+1)
  1 · 1, 2 · 1, 5, 5 · 1, 9, 22, 15 … row sums 1, 3, 11, 47, 227, 1215, 7107, 44959, …
  [−1, 0] nonnegative
• A207823 → (θ+1)²
  1 · 4, 4 · 15, 32, 9 · 56, 184, 108, 16 … row sums 1, 8, 56, 364, 2255, 13504, 78841, …
  (−∞, 0] nonnegative
• A013609 → Veronese 2 (j=1)
  2 · 4 · 6, 8 · 8, 32 … row sums 0, 2, 4, 14, 40, 122, 364, 1094, …
  (−∞, 0] nonnegative
• A007318 → 2θ+1 → θ+1
  1 · 1, 6 · 1, 12, 15 · 1, 18, 45, 28 … row sums 1, 7, 28, 92, 272, 752, 1984, 5056, …
  (−∞, 0] nonnegative
• A039755 → D
  1 · 4, 2 · 13, 18, 3 · 40, 116, 48, 4 … row sums 0, 1, 6, 34, 208, 1396, 10232, 81320, …
  (−∞, 0] nonnegative
• A126216 → basis A008277
  1 · 3, 1 · 11, 8, 1 · 45, 55, 15, 1 … row sums 1, 4, 20, 116, 752, 5335, 40861, …
  (−∞, 0] nonnegative
• A118931 → basis A013610
  1 · 1 · 1 · 3, 6 … row sums 1, 1, 1, 9, 33, 81, 801, 4761, …
  (−∞, 0] nonnegative
• A116414 → basis A008277
  1 · 5, 1 · 22, 11, 1 · 95, 85, 18, 1 … row sums 1, 6, 34, 199, 1216, 7769, 51884, …
  (−∞, 0] nonnegative
• A099040 → x ↦ x−9
  1 · -18, 2 · 306, -70, 4 · -5184, 1800, -208, 8 … row sums 1, -16, 240, -3584, 53504, -798720, …
  (7, 9]
• A038337 → basis A007318
  529, 506, 121 · 12167, 17457, 8349, 1331 … row sums 1156, 39304, 1336336, 45435424, …
  (−∞, 0] nonnegative rational roots
• A007318 → 2θ+1 → D
  3 · 6, 10 · 9, 30, 21 · 12, 60, 84, 36 … row sums 0, 3, 16, 60, 192, 560, 1536, 4032, …
  (−∞, 0] nonnegative rational roots
• A249250 → D+1
  1 · 4, 3 · 7, 12, 3 · 10, 39, 24, 3 … row sums 1, 7, 22, 76, 244, 772, 2392, 7312, …
  (−∞, 0] nonnegative
• A091042 → basis A013610
  1 · 4, 9 · 16, 60, 45 · 64, 336, 504, 189 … row sums 1, 13, 121, 1093, 9841, 88573, 797161, …
  (−∞, 0] nonnegative
• A207606 → θ+1
  4, 14, 6 · 5, 32, 33, 8 · 6, 60, 108, 60, 10 … row sums 24, 78, 244, 743, 2218, 6521, 18942, …
  (−∞, 0] nonnegative
• A038277 → basis A013610
  1 · 18, 33 · 324, 1188, 1089 … row sums 1, 51, 2601, 132651, 6765201, …
  (−∞, 0] nonnegative rational roots
• type_b_eulerian → Pₙ + Pₙ₊₁
  2, 1 · 2, 7, 1 · 2, 29, 24, 1 · 2, 99, 253, 77, 1 … row sums 3, 10, 56, 432, 4224, 49920, 691200, …
  (−∞, ∞) nonnegative
• A131689 → Pₙ + Pₙ₊₁
  1, 1 · 0, 2, 2 · 0, 2, 8, 6 · 0, 2, 20, 42, 24 … row sums 2, 4, 16, 88, 616, 5224, 51976, 593128, …
  (−∞, ∞) nonnegative
• A011973 → basis A007318 → D+1
  1 · 1 · 3, 1 · 5, 2 … row sums 1, 1, 4, 7, 18, 37, 84, 179, …
  (−∞, 0] nonnegative
• A272867 → basis A008277
  1 · 6, 7, 1 · 36, 133, 91, 18, 1 … row sums 1, 14, 279, 7565, 265500, 11616193, …
  (−∞, 0] nonnegative
• A008955 → basis A013611
  1 · 2, 4 · 10, 52, 64 · 100, 880, 2512, 2304 … row sums 1, 6, 126, 5796, 469476, 59153976, …
  (−∞, 0] nonnegative rational roots
• A010054 → D∘x → D
  (−∞, 0] nonnegative rational roots
• A007318 → (θ+1)² → reverse
  1 · 4, 1 · 9, 8, 1 · 16, 27, 12, 1 … row sums 1, 5, 18, 56, 160, 432, 1120, 2816, …
  (−∞, 0] nonnegative
• A008288 → Veronese 2 (j=1)
  1 · 3 · 5, 1 · 7, 7 … row sums 0, 1, 3, 6, 14, 35, 85, 204, …
  (−∞, 0] nonnegative
• basis-map coefficients of A371080, shifted → basis A013611
  1 · 1, 4 · 4, 20, 16 · 28, 156, 192, 64 … row sums 1, 5, 40, 440, 6160, 104720, 2094400, …
  (−∞, 0] nonnegative rational roots
• basis-map coefficients of Triangle read by rows: BellMatrix(Product_{p in P(n)} p), where P(n) = {k : k mod m = 1 and 1 <= k <= m*(n + 1)} and m = 3. shifted by x -> x + 1
  1 · 0, 1 · 0, 3, 1 · 0, 18, 9, 1 … row sums 1, 1, 4, 28, 280, 3640, 58240, 1106560, …
  (−∞, 0] nonnegative rational roots
• A085881 → basis A013609
  1 · 2, 2 · 12, 24, 12 · 120, 360, 360, 120 … row sums 1, 4, 48, 960, 26880, 967680, 42577920, …
  (−∞, 0] nonnegative rational roots
• A125662 → Veronese 2
  1 · 3 · 8, 1 · 21, 9 … row sums 1, 3, 9, 30, 107, 393, 1459, 5436, …
  (−∞, 0] nonnegative
• A145597 → x ↦ x/(x+1)
  1 · 3, 6 · 6, 27, 27 · 10, 75, 165, 110 … row sums 1, 9, 60, 360, 2061, 11529, 63728, …
  [−1, 0] nonnegative
• A274498 → x ↦ x+1
  1 · 3 · 9, 6 · 27, 18 … row sums 1, 3, 15, 45, 225, 675, 3375, 10125, …
  (−∞, −1] nonnegative rational roots
• A143494 → x ↦ x/(x+1)
  1 · 2, 3 · 4, 13, 10 · 8, 43, 71, 37 … row sums 1, 5, 27, 159, 1025, 7221, 55307, …
  [−1, 0] nonnegative
• A102662 → (θ+1)²
  1 · 1, 12 · 1, 20, 27 · 1, 28, 99, 48 … row sums 1, 13, 48, 176, 591, 1895, 5858, 17614, …
  (−∞, 0] nonnegative
• A085880 → θ+1
  1 · 1, 2 · 2, 8, 6 · 5, 30, 45, 20 … row sums 1, 3, 16, 100, 672, 4704, 33792, …
  (−∞, 0] nonnegative rational roots
• A081577 → (θ+1)²
  1 · 1, 4 · 1, 16, 9 · 1, 28, 63, 16 … row sums 1, 5, 26, 108, 424, 1564, 5552, 19104, …
  (−∞, 0] nonnegative
• A038305 → basis A013609
  169, 156, 36 · 2197, 3042, 1404, 216 … row sums 361, 6859, 130321, 2476099, 47045881, …
  (−∞, 0] nonnegative rational roots