basis_map / A013610

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

210 sequences

• A085841 → basis A013610
  1 · 7, 12 · 61, 216, 144 · 547, 3012, 4752, 1728 … row sums 1, 19, 421, 10039, 246601, 6125659, …
  (−∞, 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
• A133214 → basis A013610
  13, 48, 36 · 63, 342, 540, 216 … row sums 97, 1161, 14721, 192969, 2582881, …
  (−∞, 0] nonnegative
• A122431 → basis A013610
  8, 36, 54, 27 · 8, 60, 162, 189, 81 … row sums 125, 500, 2000, 8000, 32000, 128000, …
  (−∞, 0] nonnegative rational roots
• A011973 → basis A013610
  1 · 1 · 2, 3 · 3, 6 … row sums 1, 1, 5, 9, 29, 65, 181, 441, …
  (−∞, 0] nonnegative
• A038336 → basis A013610
  484, 1320, 900 · 10648, 43560, 59400, 27000 … row sums 2704, 140608, 7311616, 380204032, …
  (−∞, 0] nonnegative rational roots
• A013620 → basis A007318
  1 · 5, 3 · 25, 30, 9 · 125, 225, 135, 27 … row sums 1, 8, 64, 512, 4096, 32768, 262144, …
  (−∞, −1] nonnegative rational roots
• A249248 → basis A013610
  1 · 4, 9 · 11, 39, 27 · 38, 195, 279, 81 … row sums 1, 13, 77, 593, 4505, 36757, 309925, …
  (−∞, 0] nonnegative
• A207823 → basis A013610
  1 · 5, 3 · 24, 30, 9 · 115, 219, 135, 27 … row sums 1, 8, 63, 496, 3905, 30744, 242047, …
  (−∞, 0] nonnegative
• A082985 → basis A013610
  1 · 4, 9 · 11, 45, 45 · 29, 168, 315, 189 … row sums 1, 13, 101, 701, 4693, 31021, 204101, …
  (−∞, 0] nonnegative
• A052553 → basis A013610
  1 · 1 · 2, 3 · 3, 6 … row sums 1, 1, 5, 9, 29, 65, 181, 441, …
  (−∞, 0] nonnegative
• A099040 → basis A013610
  1 · 2, 6 · 6, 30, 36 · 16, 120, 288, 216 … row sums 1, 8, 72, 640, 5696, 50688, 451072, …
  (−∞, 0] nonnegative
• A133087 → basis A013610
  1 · 3, 3 · 4, 12, 9 · 12, 48, 63, 27 … row sums 1, 6, 25, 150, 625, 3750, 15625, 93750, …
  (−∞, 0] nonnegative rational roots
• A091044 → basis A013610
  1 · 4, 6 · 16, 48, 27 · 64, 288, 360, 108 … row sums 1, 10, 91, 820, 7381, 66430, 597871, …
  (−∞, 0] nonnegative
• A143491 → basis A013610
  12, 21, 9 · 60, 141, 108, 27 … row sums 42, 336, 3024, 30240, 332640, 3991680, …
  (−∞, 0] nonnegative rational roots
• A064861 → basis A013610
  6, 21, 18 · 18, 99, 180, 108 · 36, 252, 657, 756, 324 … row sums 45, 405, 2025, 18225, 91125, 820125, …
  (−∞, 0] nonnegative rational roots
• A143683 → basis A013610
  1 · 2, 3 · 12, 36, 9 · 40, 180, 198, 27 … row sums 1, 5, 57, 445, 4049, 34485, 301993, …
  (−∞, 0] nonnegative
• A318772 → basis A013610
  1 · 1 · 1 · 1 … row sums 1, 1, 1, 1, 13, 25, 37, 49, …
  (−∞, 0] nonnegative
• A028326 → basis A013610
  2 · 4, 6 · 8, 24, 18 · 16, 72, 108, 54 … row sums 2, 10, 50, 250, 1250, 6250, 31250, …
  (−∞, 0] nonnegative rational roots
• A008459 → basis A013610
  1 · 2, 3 · 6, 18, 9 · 20, 90, 108, 27 … row sums 1, 5, 33, 245, 1921, 15525, 127905, …
  (−∞, 0] 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
• A001263 → basis A013610
  1 · 2, 3 · 5, 15, 9 · 14, 63, 81, 27 … row sums 1, 5, 29, 185, 1257, 8925, 65445, …
  (−∞, 0] nonnegative
• 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
• A054142 → basis A013610
  1 · 2, 3 · 5, 15, 9 · 13, 60, 81, 27 … row sums 1, 5, 29, 181, 1165, 7589, 49661, …
  (−∞, 0] nonnegative
• A118931 → basis A013610
  1 · 1 · 1 · 3, 6 … row sums 1, 1, 1, 9, 33, 81, 801, 4761, …
  (−∞, 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
• A038277 → basis A013610
  1 · 18, 33 · 324, 1188, 1089 … row sums 1, 51, 2601, 132651, 6765201, …
  (−∞, 0] nonnegative rational roots
• 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
• A317496 → basis A013610
  1 · 1 · 1 · 4, 9 … row sums 1, 1, 1, 13, 25, 37, 193, 493, …
  (−∞, 0] nonnegative
• 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
• A034870 → basis A013610
  1 · 4, 12, 9 · 16, 96, 216, 216, 81 … row sums 1, 25, 625, 15625, 390625, 9765625, …
  (−∞, 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
• A120909 → basis A013610
  3 · 9, 18 · 27, 108, 108 · 81, 486, 972, 648 … row sums 3, 27, 243, 2187, 19683, 177147, …
  (−∞, 0] nonnegative rational roots
• A030528 → basis A013610
  1 · 2, 3 · 3, 12, 9 · 5, 30, 54, 27 … row sums 1, 5, 24, 116, 560, 2704, 13056, 63040, …
  (−∞, 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
• 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
• 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
• A274498 → basis A013610
  1 · 3 · 9, 18 · 27, 54 … row sums 1, 3, 27, 81, 729, 2187, 19683, 59049, …
  (−∞, 0] nonnegative rational roots
• A081581 → basis A013610
  1 · 2, 3 · 10, 30, 9 · 32, 144, 162, 27 … row sums 1, 5, 49, 365, 3001, 23765, 190849, …
  (−∞, 0] nonnegative
• A079638 → basis A013610
  1 · 4, 3 · 24, 33, 9 · 192, 366, 189, 27 … row sums 1, 7, 66, 774, 10800, 174240, 3185280, …
  (−∞, 0] nonnegative
• A200536 → basis A013610
  1 · 6, 21, 18 · 36, 252, 657, 756, 324 … row sums 1, 45, 2025, 91125, 4100625, 184528125, …
  (−∞, 0] nonnegative rational roots
• A013612 → basis A013610
  36, 180, 225 · 216, 1620, 4050, 3375 … row sums 441, 9261, 194481, 4084101, 85766121, …
  (−∞, 0] nonnegative rational roots
• delannoy → basis A013610
  1 · 2, 3 · 5, 15, 9 · 12, 54, 72, 27 … row sums 1, 5, 29, 165, 941, 5365, 30589, …
  (−∞, 0] nonnegative
• A085881 → basis A013610
  1 · 2, 3 · 12, 36, 27 · 120, 540, 810, 405 … row sums 1, 5, 75, 1875, 65625, 2953125, …
  (−∞, 0] nonnegative rational roots
• A010054: a(n) = 1 if n is a triangular number, otherwise 0.
  1 · 1 · 1 · 1 … row sums 1, 1, 1, 1, 1, 1, 1, 1, …
  A010054 (−∞, −1] [−1, 0] [−3−2√2, −3+2√2] nonnegative rational roots
• A081577 → basis A013610
  1 · 2, 3 · 6, 18, 9 · 16, 72, 90, 27 … row sums 1, 5, 33, 205, 1289, 8085, 50737, …
  (−∞, 0] nonnegative
• A327997 → basis A013610
  1 · 4, 3 · 17, 27, 9 · 78, 195, 135, 27 … row sums 1, 7, 53, 435, 3873, 37383, 390501, …
  (−∞, 0] nonnegative
• A114687 → basis A013610
  1 · 3, 6 · 11, 42, 36 · 45, 252, 432, 216 … row sums 1, 9, 89, 945, 10577, 123129, 1476841, …
  (−∞, 0] nonnegative
• A038303 → basis A013610
  1 · 11, 3 · 121, 66, 9 · 1331, 1089, 297, 27 … row sums 1, 14, 196, 2744, 38416, 537824, …
  (−∞, 0] nonnegative rational roots
• A038329 → basis A013610
  225, 270, 81 · 3375, 6075, 3645, 729 … row sums 576, 13824, 331776, 7962624, 191102976, …
  (−∞, 0] nonnegative rational roots