basis_map

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

1056 sequences

• A136572 → basis A013610
  1 · 1, 3 · 2, 12, 18 · 6, 54, 162, 162 … row sums 1, 4, 32, 384, 6144, 122880, 2949120, …
  (−∞, 0] nonnegative rational roots
• A027465 → basis A008277
  1 · 4, 1 · 16, 9, 1 · 64, 61, 15, 1 … row sums 1, 5, 26, 141, 799, 4736, 29371, …
  (−∞, 0] nonnegative
• A028326 → basis A007318
  2 · 4, 2 · 8, 8, 2 · 16, 24, 12, 2 … row sums 2, 6, 18, 54, 162, 486, 1458, 4374, …
  (−∞, −1] nonnegative rational roots
• A266213 → basis A013610
  1 · 1 · 3, 6 · 7, 24, 18 … row sums 1, 1, 9, 49, 281, 1601, 9129, 52049, …
  (−∞, 0] nonnegative
• A118394 → basis A008277
  1 · 1 · 1 · 7, 6 … row sums 1, 1, 1, 13, 49, 121, 2041, 13021, …
  (−∞, 0] nonnegative
• A100862 → basis A013610
  1 · 2, 3 · 5, 15, 9 · 14, 63, 81, 27 … row sums 1, 5, 29, 185, 1273, 9325, 72085, …
  (−∞, 0] nonnegative
• A145597 → basis A007318
  1 · 6, 3 · 27, 27, 6 · 110, 165, 75, 10 … row sums 1, 9, 60, 360, 2061, 11529, 63728, …
  (−∞, −1] nonnegative
• A103633 → basis A013611
  1 · 1, 4 · 2, 12, 16 · 2, 20, 64, 64 … row sums 1, 5, 30, 150, 900, 4500, 27000, …
  (−∞, 0] nonnegative rational roots
• A059473 → x ↦ x+1
  1 · 4, 2 · 18, 18, 4 · 80, 120, 56, 8 … row sums 1, 6, 40, 264, 1744, 11520, 76096, …
  (−∞, −1] nonnegative
• A152830 → basis A013609
  1 · 1 · 1 · 1 … row sums 1, 1, 1, 1, 4, 4, 4, 4, …
  (−∞, 0] nonnegative rational roots
• A136572 → basis A013609
  1 · 1, 2 · 2, 8, 8 · 6, 36, 72, 48 … row sums 1, 3, 18, 162, 1944, 29160, 524880, …
  (−∞, 0] nonnegative rational roots
• A013618 → basis A013609
  144, 528, 484 · 1728, 9504, 17424, 10648 … row sums 1156, 39304, 1336336, 45435424, …
  (−∞, 0] nonnegative rational roots
• A159854 → basis A013609
  1, 4, 4 · 2, 10, 16, 8 · 4, 24, 52, 48, 16 … row sums 9, 36, 144, 576, 2304, 9216, 36864, …
  (−∞, 0] nonnegative rational roots
• A113413 → basis A013610
  1 · 3, 3 · 7, 18, 9 · 17, 69, 81, 27 … row sums 1, 6, 34, 194, 1106, 6306, 35954, …
  (−∞, 0] nonnegative
• A081580 → basis A008277
  1 · 2, 1 · 9, 10, 1 · 28, 59, 19, 1 … row sums 1, 3, 20, 107, 681, 4454, 31263, …
  (−∞, 0] nonnegative
• A121574 → basis A013611
  1 · 3, 4 · 10, 28, 16 · 33, 140, 176, 64 … row sums 1, 7, 54, 413, 3161, 24192, 185149, …
  (−∞, 0] nonnegative
• A013612 → basis A007318
  36, 60, 25 · 216, 540, 450, 125 … row sums 121, 1331, 14641, 161051, 1771561, …
  (−∞, 0] nonnegative rational roots
• A172431 → basis A013611
  1 · 3, 8 · 8, 40, 48 · 21, 152, 352, 256 … row sums 1, 11, 96, 781, 6191, 48576, 379561, …
  (−∞, 0] nonnegative
• A111125 → basis A013609
  1 · 4, 2 · 11, 14, 4 · 29, 62, 40, 8 … row sums 1, 6, 29, 139, 666, 3191, 15289, 73254, …
  (−∞, 0] nonnegative
• A035607 → basis A013609
  1 · 1 · 3, 4 · 7, 16, 8 … row sums 1, 1, 7, 31, 145, 673, 3127, 14527, …
  (−∞, 0] nonnegative
• A026729 → basis A008277
  1 · 1, 1 · 2, 4, 1 · 3, 13, 8, 1 … row sums 1, 2, 7, 25, 102, 456, 2219, 11640, …
  (−∞, 0] nonnegative
• A099097 → basis A008277
  1 · 3, 3 · 10, 28, 9 · 33, 207, 168, 27 … row sums 1, 6, 47, 435, 4622, 55080, 724371, …
  (−∞, 0] nonnegative
• A130123 → basis A013609
  1 · 2, 4 · 4, 16, 16 · 8, 48, 96, 64 … row sums 1, 6, 36, 216, 1296, 7776, 46656, …
  (−∞, 0] nonnegative rational roots
• A120910 → basis A008277
  3 · 9, 3 · 27, 21, 3 · 81, 111, 36, 3 … row sums 3, 12, 51, 231, 1116, 5745, 31443, …
  (−∞, 0] nonnegative
• A156992 → basis A013611
  1 · 4, 8 · 24, 96, 96 · 192, 1152, 2304, 1536 … row sums 1, 12, 216, 5184, 155520, 5598720, …
  (−∞, 0] nonnegative rational roots
• A123519 → x ↦ x+1
  11, 14, 4 · 41, 76, 44, 8 · 153, 372, 324, 120, 16 … row sums 29, 169, 985, 5741, 33461, 195025, …
  (−3, −1) nonnegative
• A145597 → basis A013611
  1 · 6, 12 · 27, 108, 96 · 110, 660, 1200, 640 … row sums 1, 18, 231, 2610, 27765, 286146, …
  (−∞, 0] nonnegative
• A038255 → basis A008277
  1 · 7, 1 · 49, 15, 1 · 343, 169, 24, 1 … row sums 1, 8, 65, 537, 4516, 38699, 338233, …
  (−∞, 0] nonnegative
• basis-map coefficients of A113214, shifted → basis A013610
  1 · -2, -3 · 4, 12, 9 · -8, -36, -54, -27 … row sums 1, -5, 25, -125, 625, -3125, 15625, …
  (−∞, 0] rational roots
• A038325 → basis A013610
  1 · 22, 33 · 484, 1452, 1089 … row sums 1, 55, 3025, 166375, 9150625, …
  (−∞, 0] nonnegative rational roots
• A122431 → basis A013609
  8, 24, 24, 8 · 8, 40, 72, 56, 16 … row sums 64, 192, 576, 1728, 5184, 15552, 46656, …
  (−∞, 0] nonnegative rational roots
• A356546 → basis A013610
  1 · 4, 6 · 24, 72, 54 · 160, 720, 1080, 540 … row sums 1, 10, 150, 2500, 43750, 787500, …
  (−∞, 0] nonnegative rational roots
• A100861 → reverse → basis A008277
  1 · 1, 1 · 2, 4, 1 · 4, 16, 9, 1 … row sums 1, 2, 7, 30, 157, 948, 6487, 49332, …
  (−∞, 0] nonnegative
• A317496 → basis A013609
  1 · 1 · 1 · 4, 6 … row sums 1, 1, 1, 10, 19, 28, 118, 289, …
  (−∞, 0] nonnegative
• A358735 → basis A007318
  1 · 2, 1 · 7, 8, 2 · 33, 60, 34, 6 … row sums 1, 3, 17, 133, 1313, 15623, 217409, …
  (−∞, 0] nonnegative
• A120910 → basis A013611
  3 · 9, 12 · 27, 72, 48 · 81, 324, 432, 192 … row sums 3, 21, 147, 1029, 7203, 50421, 352947, …
  (−∞, 0] nonnegative rational roots
• A143683 → basis A013611
  1 · 2, 4 · 12, 48, 16 · 40, 240, 352, 64 … row sums 1, 6, 76, 696, 7216, 71136, 715456, …
  (−∞, 0] nonnegative
• A133214 → basis A013611
  13, 64, 64 · 63, 456, 960, 512 … row sums 141, 1991, 29761, 460251, 7272861, …
  (−∞, 0] nonnegative
• A038331 → basis A007318
  289, 170, 25 · 4913, 4335, 1275, 125 … row sums 484, 10648, 234256, 5153632, 113379904, …
  (−∞, 0] nonnegative rational roots
• A038321 → basis A013611
  324, 1008, 784 · 5832, 27216, 42336, 21952 … row sums 2116, 97336, 4477456, 205962976, …
  (−∞, 0] nonnegative rational roots
• A008288 → basis A013609
  1 · 2, 2 · 5, 10, 4 · 12, 36, 32, 8 … row sums 1, 4, 19, 88, 409, 1900, 8827, 41008, …
  (−∞, 0] nonnegative
• A038305 → basis A007318
  169, 78, 9 · 2197, 1521, 351, 27 … row sums 256, 4096, 65536, 1048576, 16777216, …
  (−∞, 0] nonnegative rational roots
• A111125 → basis A008277
  1 · 4, 1 · 11, 8, 1 · 29, 42, 13, 1 … row sums 1, 5, 20, 85, 391, 1941, 10341, 58800, …
  (−∞, 0] nonnegative
• A139548 → basis A007318
  1 · 8, 8, 2 · 64, 128, 96, 32, 4 … row sums 1, 18, 324, 5832, 104976, 1889568, …
  (−∞, 0] nonnegative rational roots
• A114656 → basis A013609
  1 · 3, 2 · 11, 16, 4 · 45, 102, 60, 8 … row sums 1, 5, 31, 215, 1597, 12425, 99955, …
  (−∞, 0] nonnegative
• A304236 → basis A007318
  1 · 1 · 4, 3 · 7, 6 … row sums 1, 1, 7, 13, 55, 133, 463, 1261, …
  (−∞, −1] nonnegative
• A152198 → basis A013611
  1 · 1 · 2, 4 · 2, 4 … row sums 1, 1, 6, 6, 36, 36, 216, 216, …
  (−∞, 0] nonnegative rational roots
• A128813 → basis A013610
  1 · 2, 3 · 8, 30, 27 · 56, 354, 729, 486 … row sums 1, 5, 65, 1625, 66625, 4064125, …
  (−∞, 0] nonnegative rational roots
• A356546 → basis A013611
  1 · 4, 8 · 24, 96, 96 · 160, 960, 1920, 1280 … row sums 1, 12, 216, 4320, 90720, 1959552, …
  (−∞, 0] nonnegative rational roots
• A188440 → basis A007318
  1 · 1 · 3, 2 · 3, 2 … row sums 1, 1, 5, 5, 25, 25, 125, 125, …
  (−∞, −1] nonnegative rational roots