Sequences

3,043 sequences

• A038321 → basis A008277
  324, 301, 49 · 5832, 9793, 3675, 343 … row sums 674, 19643, 618279, 20951002, …
  (−∞, 0] nonnegative
• A113953 → Veronese 2 (j=1)
  1 · 2 · 0, 1 · 0, 6 … row sums 0, 1, 2, 1, 6, 13, 18, 41, …
  (−∞, 0] nonnegative
• Stirling2 triangle with scaled diagonals (powers of 9).
  81, 27, 1 · 729, 567, 54, 1 … row sums 109, 1351, 19612, 333451, 6493069, …
  (−∞, 0) nonnegative
• A099040 → basis A007318
  1 · 2, 2 · 6, 10, 4 · 16, 40, 32, 8 … row sums 1, 4, 20, 96, 464, 2240, 10816, 52224, …
  (−∞, −1] nonnegative
• A113953 → x ↦ x−3
  1 · -3, 1 · 3, -4, 1 · 9, 3, -5, 1 … row sums 1, -2, 0, 8, -16, 0, 64, -128, …
  (−5, 3]
• A028326 → θ+1
  2 · 2, 4 · 2, 8, 6 · 2, 12, 18, 8 … row sums 2, 6, 16, 40, 96, 224, 512, 1152, …
  (−∞, 0] nonnegative rational roots
• A059344 → basis A013611
  1 · 1 · 3, 8 · 7, 24 … row sums 1, 1, 11, 31, 361, 1601, 19651, 115711, …
  (−∞, 0] nonnegative
• A063007 → θ+1
  1 · 1, 4 · 1, 12, 18 · 1, 24, 90, 80 … row sums 1, 5, 31, 195, 1221, 7593, 46915, …
  (−∞, 0] nonnegative
• A091042 → x ↦ x/(x+1)
  1 · 1, 4 · 1, 12, 16 · 1, 24, 80, 64 … row sums 1, 5, 29, 169, 985, 5741, 33461, …
  [−1, 0] nonnegative
• A028326 → basis A008277
  2 · 4, 2 · 8, 10, 2 · 16, 38, 18, 2 … row sums 2, 6, 20, 74, 302, 1348, 6526, 34014, …
  (−∞, 0] nonnegative
• A085841 → basis A013610
  1 · 7, 12 · 61, 216, 144 · 547, 3012, 4752, 1728 … row sums 1, 19, 421, 10039, 246601, 6125659, …
  (−∞, 0] nonnegative
• A038327 → basis A013611
  1 · 13, 4 · 169, 104, 16 · 2197, 2028, 624, 64 … row sums 1, 17, 289, 4913, 83521, 1419857, …
  (−∞, 0] nonnegative rational roots
• A272866 → Veronese 2 (j=1)
  3 · 6, 6 · 9, 45, 9 · 12, 144, 144, 12 … row sums 0, 3, 12, 63, 312, 1563, 7812, 39063, …
  (−∞, 0] nonnegative
• A038326 → Pₙ + Pₙ₊₁
  12, 12 · 132, 276, 144 · 1452, 4620, 4896, 1728 … row sums 24, 552, 12696, 292008, 6716184, …
  (−∞, ∞) nonnegative rational roots
• A178820 → θ+1
  1 · 4, 8 · 10, 40, 30 · 20, 120, 180, 80 … row sums 1, 12, 80, 400, 1680, 6272, 21504, …
  (−∞, 0] nonnegative rational roots
• A144699 → Pₙ + Pₙ₊₁
  2, 5 · 2, 21, 25 · 2, 55, 196, 125 … row sums 7, 48, 378, 3360, 33264, 362880, …
  (−∞, ∞) nonnegative
• A143683 → basis A013609
  1 · 2, 2 · 12, 24, 4 · 40, 120, 88, 8 … row sums 1, 4, 40, 256, 1984, 14080, 103936, …
  (−∞, 0] nonnegative
• A132812 → x ↦ x+1
  1 · 4, 2 · 15, 15, 3 · 56, 84, 36, 4 … row sums 1, 6, 33, 180, 985, 5418, 29953, …
  (−∞, −1] nonnegative
• A059473 → θ+1
  1 · 2, 4 · 4, 20, 12 · 8, 64, 96, 32 … row sums 1, 6, 36, 200, 1068, 5544, 28192, …
  (−∞, 0] nonnegative
• A081579 → basis A008277
  1 · 2, 1 · 8, 9, 1 · 24, 51, 17, 1 … row sums 1, 3, 18, 93, 555, 3458, 23035, 161735, …
  (−∞, 0] nonnegative
• A109692 → basis A013610
  1 · 2, 3 · 8, 30, 27 · 48, 300, 612, 405 … row sums 1, 5, 65, 1365, 39585, 1464645, …
  (−∞, 0] nonnegative rational roots
• A128099 → (θ+1)²
  1 · 1 · 1, 8 · 1, 16 … row sums 1, 1, 9, 17, 61, 141, 385, 921, …
  (−∞, 0] nonnegative
• basis-map coefficients of A021012 → D+1
  1 · -1, -1 · 0, 4, 2 · 0, 0, -18, -6 … row sums 1, -2, 6, -24, 120, -720, 5040, -40320, …
  (−∞, 0] rational roots
• A007318 → 2θ+1 → (θ+1)²
  1 · 1, 12 · 1, 24, 45 · 1, 36, 135, 112 … row sums 1, 13, 70, 284, 992, 3152, 9376, 26560, …
  (−∞, 0] nonnegative
• A130534 → basis A008277
  1 · 2, 1 · 6, 6, 1 · 24, 36, 12, 1 … row sums 1, 3, 13, 73, 501, 4051, 37633, 394353, …
  (−∞, 0] nonnegative
• A172431 → ⊙ C(n,k+1) (shift -1) → θ+1
  1 · 1, 2 · 1, 8, 3 · 1, 18, 30, 4 … row sums 1, 3, 12, 53, 244, 1152, 5531, 26875, …
  (−∞, 0] nonnegative
• A082985 → x ↦ x+1
  1 · 4, 3 · 11, 15, 5 · 29, 56, 35, 7 … row sums 1, 7, 31, 127, 511, 2047, 8191, 32767, …
  (−∞, −1] nonnegative
• A367270 → basis A008277
  1 · 1 · 3, 2 · 10, 15, 3 … row sums 1, 1, 5, 28, 175, 1201, 8929, 71177, …
  (−∞, 0] nonnegative
• basis-map coefficients of Triangular array of generalized Narayana numbers: T(n, k) = 2*binomial(n + 1, k + 1)*binomial(n + 1, k - 1)/(n + 1).
  1 · 0, 2 · -2, 2, 3 · 0, -8, 8, 4 … row sums 1, 2, 3, 4, 5, 6, 7, 8, …
  (−∞, 1]
• A178821 → Veronese 2 (j=1)
  5 · 30 · 105, 35 · 280, 280 … row sums 0, 5, 30, 140, 560, 2016, 6720, 21120, …
  (−∞, 0] nonnegative
• A099093: Riordan array (1, 3+3x).
  1 · 0, 3 · 0, 3, 9 · 0, 0, 18, 27 … row sums 1, 3, 12, 45, 171, 648, 2457, 9315, …
  A099093 (−4/3, 0] nonnegative
• A133214 → basis A013610
  13, 48, 36 · 63, 342, 540, 216 … row sums 97, 1161, 14721, 192969, 2582881, …
  (−∞, 0] nonnegative
• A038259 → basis A007318
  1 · 11, 5 · 121, 110, 25 · 1331, 1815, 825, 125 … row sums 1, 16, 256, 4096, 65536, 1048576, …
  (−∞, 0] nonnegative rational roots
• A145324 → basis A008277
  1 · 3, 2 · 12, 23, 6 · 60, 255, 170, 24 … row sums 1, 5, 41, 509, 8934, 209964, 6341677, …
  (−∞, 0] nonnegative
• A038220: Triangle whose (i,j)-th entry is binomial(i,j)*3^(i-j)*2^j.
  1 · 3, 2 · 9, 12, 4 · 27, 54, 36, 8 … row sums 1, 5, 25, 125, 625, 3125, 15625, 78125, …
  A038220 (−∞, −1] nonnegative rational roots
• A008459 → basis A013611
  1 · 2, 4 · 6, 24, 16 · 20, 120, 192, 64 … row sums 1, 6, 46, 396, 3606, 33876, 324556, …
  (−∞, 0] nonnegative
• A165253: Triangle T(n,k), read by rows given by [1,0,1,0,0,0,0,0,0,...] DELTA [0,1,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938.
  1 · 1 · 1, 1 · 1, 3, 1 … row sums 1, 1, 2, 5, 13, 34, 89, 233, …
  A165253 (−4, 0) nonnegative
• A156366: Triangle of coefficients of p(n, x) where p(n, x) is defined as p(n, x) = (1-3*x)^(n+1)*PolyLog(-n, 3*x)/(3*x), read by rows.
  1, 12, 9 · 1, 33, 99, 27 · 1, 78, 594, 702, 81 … row sums 22, 160, 1456, 15904, 202672, 2951680, …
  A156366 (−∞, 0) nonnegative
• A081578 → D+1
  1 · 2, 1 · 6, 7, 1 · 10, 27, 12, 1 … row sums 1, 3, 14, 50, 183, 637, 2188, 7380, …
  (−∞, 0] nonnegative
• A013609 → basis A013609
  1 · 3, 4 · 9, 24, 16 · 27, 108, 144, 64 … row sums 1, 7, 49, 343, 2401, 16807, 117649, …
  (−∞, 0] nonnegative rational roots
• A123519 → θ+1
  1, 12, 12 · 1, 24, 60, 32 · 1, 40, 180, 224, 80 … row sums 25, 117, 525, 2289, 9773, 41065, …
  (−∞, 0] nonnegative
• A039991 → D
  0, -2 · 0, -6 · 0, -16, 0, 4 · 0, -40, 0, 20 … row sums 0, 0, -2, -6, -12, -20, -30, -42, …
  (−∞, ∞)
• A200536 → basis A013611
  1 · 6, 28, 32 · 36, 336, 1168, 1792, 1024 … row sums 1, 66, 4356, 287496, 18974736, …
  (−∞, 0] nonnegative rational roots
• A081581 → basis A013611
  1 · 2, 4 · 10, 40, 16 · 32, 192, 288, 64 … row sums 1, 6, 66, 576, 5436, 49896, 462456, …
  (−∞, 0] nonnegative
• A078812 → basis A013611
  1 · 3, 4 · 8, 24, 16 · 21, 100, 144, 64 … row sums 1, 7, 48, 329, 2255, 15456, 105937, …
  (−∞, 0] nonnegative
• A135838 → Veronese 2 (j=1)
  2 · 4 · 12, 4 · 16, 16 … row sums 0, 2, 4, 16, 32, 128, 256, 1024, …
  (−∞, 0] nonnegative
• A007318 → θ+1 → Veronese 2 (j=1)
  2 · 4 · 6, 4 · 8, 16 … row sums 0, 2, 4, 10, 24, 56, 128, 288, …
  (−∞, 0] nonnegative
• A013622 → basis A008277
  1 · 8, 5 · 64, 105, 25 · 512, 1685, 975, 125 … row sums 1, 13, 194, 3297, 62911, 1328668, …
  (−∞, 0] nonnegative
• A113953 → x ↦ x/(x+1)
  1 · 0, 1 · 0, 2, 3 · 0, 0, 4, 5 … row sums 1, 1, 5, 9, 29, 65, 181, 441, …
  [−1, 0] nonnegative
• A007318 → D → (θ+1)²
  1 · 2, 8 · 3, 24, 27 · 4, 48, 108, 64 … row sums 0, 1, 10, 54, 224, 800, 2592, 7840, …
  (−∞, 0] nonnegative