basis_map

Image under a basis map u^k -> P_k. All operations

1056 sequences

• A038334 → basis A013611
  400, 1280, 1024 · 8000, 38400, 61440, 32768 … row sums 2704, 140608, 7311616, 380204032, …
  (−∞, 0] nonnegative rational roots
• A038320 → basis A008277
  289, 240, 36 · 4913, 7254, 2484, 216 … row sums 565, 14867, 419161, 12640799, …
  (−∞, 0] nonnegative
• A091042 → basis A013611
  1 · 4, 12 · 16, 80, 80 · 64, 448, 896, 448 … row sums 1, 16, 176, 1856, 19456, 203776, …
  (−∞, 0] nonnegative
• A297191: Irregular triangle read by rows formed by taking every other row of the Delannoy array (A008288) regarded as a triangle.
  basis-map coefficients of A297191, shifted → basis A008288
  1 · 1, 3, 1 · 1, 7, 13, 7, 1 … row sums 1, 5, 29, 169, 985, 5741, 33461, …
  A297191 [−3−2√2, −3+2√2] nonnegative
• A026374 → basis A013610
  1 · 2, 3 · 5, 15, 9 · 10, 45, 63, 27 … row sums 1, 5, 29, 145, 841, 4205, 24389, …
  (−∞, 0] nonnegative
• A038226 → basis A013609
  121, 352, 256 · 1331, 5808, 8448, 4096 … row sums 729, 19683, 531441, 14348907, …
  (−∞, 0] nonnegative rational roots
• A249251 → basis A013609
  1 · 4, 6 · 13, 36, 24 · 43, 174, 228, 96 … row sums 1, 10, 73, 541, 4006, 29665, 219673, …
  (−∞, 0] nonnegative
• A038226 → basis A008277
  121, 240, 64 · 1331, 5528, 3648, 512 … row sums 425, 11019, 324241, 10631107, …
  (−∞, 0] nonnegative
• A001263 → basis A013610
  1 · 2, 3 · 5, 15, 9 · 14, 63, 81, 27 … row sums 1, 5, 29, 185, 1257, 8925, 65445, …
  (−∞, 0] nonnegative
• A038277 → basis A013611
  1 · 18, 44 · 324, 1584, 1936 … row sums 1, 62, 3844, 238328, 14776336, …
  (−∞, 0] nonnegative rational roots
• A038329 → basis A013611
  225, 360, 144 · 3375, 8100, 6480, 1728 … row sums 729, 19683, 531441, 14348907, …
  (−∞, 0] nonnegative rational roots
• 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
• 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
• 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
• 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
• A038337 → basis A007318
  529, 506, 121 · 12167, 17457, 8349, 1331 … row sums 1156, 39304, 1336336, 45435424, …
  (−∞, 0] nonnegative rational roots
• A091042 → basis A013610
  1 · 4, 9 · 16, 60, 45 · 64, 336, 504, 189 … row sums 1, 13, 121, 1093, 9841, 88573, 797161, …
  (−∞, 0] nonnegative
• A038277 → basis A013610
  1 · 18, 33 · 324, 1188, 1089 … row sums 1, 51, 2601, 132651, 6765201, …
  (−∞, 0] nonnegative rational roots
• 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
• 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
• 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
• A274498 → x ↦ x+1
  1 · 3 · 9, 6 · 27, 18 … row sums 1, 3, 15, 45, 225, 675, 3375, 10125, …
  (−∞, −1] nonnegative rational roots
• A038305 → basis A013609
  169, 156, 36 · 2197, 3042, 1404, 216 … row sums 361, 6859, 130321, 2476099, 47045881, …
  (−∞, 0] nonnegative rational roots
• A318772 → basis A013609
  1 · 1 · 1 · 1 … row sums 1, 1, 1, 1, 10, 19, 28, 37, …
  (−∞, 0] nonnegative
• A147716 → basis A008277
  1 · 15, 1 · 225, 31, 1 · 3375, 721, 48, 1 … row sums 1, 16, 257, 4145, 67140, 1092427, …
  (−∞, 0] nonnegative
• A318772 → basis A007318
  1 · 1 · 1 · 1 … row sums 1, 1, 1, 1, 7, 13, 19, 25, …
  (−∞, −1] nonnegative
• A088996 → basis A013610
  1 · 1, 3 · 3, 15, 18 · 15, 102, 225, 162 … row sums 1, 4, 36, 504, 9576, 229824, 6664896, …
  (−∞, 0] nonnegative rational roots
• A143491 → basis A007318
  12, 7, 1 · 60, 47, 12, 1 · 360, 342, 119, 18, 1 … row sums 20, 120, 840, 6720, 60480, 604800, …
  (−∞, 0] nonnegative rational roots
• A103327 → basis A008277
  1 · 4, 1 · 16, 13, 1 · 64, 105, 27, 1 … row sums 1, 5, 30, 197, 1399, 10664, 86651, …
  (−∞, 0] nonnegative
• A317496 → basis A013610
  1 · 1 · 1 · 4, 9 … row sums 1, 1, 1, 13, 25, 37, 193, 493, …
  (−∞, 0] nonnegative
• A290319 → basis A007318
  1 · 2, 1 · 12, 8, 1 · 120, 92, 18, 1 … row sums 1, 3, 21, 231, 3465, 65835, 1514205, …
  (−∞, 0] nonnegative rational roots
• A026374 → basis A008277
  1 · 2, 1 · 5, 6, 1 · 10, 23, 10, 1 … row sums 1, 3, 12, 44, 210, 922, 5108, 26068, …
  (−∞, 0] nonnegative
• A123519 → basis A008288
  11, 18, 4 · 41, 112, 60, 8 · 153, 592, 548, 168, 16 … row sums 33, 221, 1477, 9865, 65885, 440025, …
  [−3−2√2, −3+2√2] nonnegative
• A152828 → basis A013609
  1 · 1 · 1 · 2, 2 … row sums 1, 1, 1, 4, 4, 4, 16, 16, …
  (−∞, 0] nonnegative rational roots
• A013613 → basis A013611
  1 · 7, 24 · 49, 336, 576 · 343, 3528, 12096, 13824 … row sums 1, 31, 961, 29791, 923521, 28629151, …
  (−∞, 0] nonnegative rational roots
• basis-map coefficients of A026729, shifted → basis A013610
  1 · -1, -3 · 1, 6, 9 · -1, -9, -27, -27 … row sums 1, -4, 16, -64, 256, -1024, 4096, …
  (−∞, 0] rational roots
• A082985 → basis A008277
  1 · 4, 3 · 11, 20, 5 · 29, 98, 56, 7 … row sums 1, 7, 36, 190, 1072, 6491, 42030, …
  (−∞, 0] nonnegative
• A034870 → basis A013610
  1 · 4, 12, 9 · 16, 96, 216, 216, 81 … row sums 1, 25, 625, 15625, 390625, 9765625, …
  (−∞, 0] nonnegative rational roots
• A088996 → basis A013609
  1 · 1, 2 · 3, 10, 8 · 15, 68, 100, 48 … row sums 1, 3, 21, 231, 3465, 65835, 1514205, …
  (−∞, 0] nonnegative rational roots
• basis-map coefficients of A113214, shifted → basis A013611
  1 · -2, -4 · 4, 16, 16 · -8, -48, -96, -64 … row sums 1, -6, 36, -216, 1296, -7776, 46656, …
  (−∞, 0] rational roots
• basis-map coefficients of A026729 → basis A013611
  1 · 1, 4 · 1, 8, 16 · 1, 12, 48, 64 … row sums 1, 5, 25, 125, 625, 3125, 15625, 78125, …
  (−∞, 0] nonnegative rational roots
• A094816 → basis A013610
  1 · 2, 3 · 5, 15, 9 · 16, 69, 81, 27 … row sums 1, 5, 29, 193, 1457, 12341, 116125, …
  (−∞, 0] nonnegative
• A052553 → basis A013609
  1 · 1 · 2, 2 · 3, 4 … row sums 1, 1, 4, 7, 19, 40, 97, 217, …
  (−∞, 0] nonnegative
• A038271 → basis A008277
  1 · 12, 5 · 144, 145, 25 · 1728, 3185, 1275, 125 … row sums 1, 17, 314, 6313, 137871, 3256232, …
  (−∞, 0] nonnegative