basis_map

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

1056 sequences

• A178822 → x ↦ x+1
  1 · 12, 6 · 84, 84, 21 · 448, 672, 336, 56 … row sums 1, 18, 189, 1512, 10206, 61236, 336798, …
  (−∞, −1] nonnegative rational roots
• A133080 → basis A008277
  1 · 2, 1 · 1, 3, 1 · 2, 10, 7, 1 … row sums 1, 3, 5, 20, 52, 255, 877, 5017, …
  (−∞, 0] nonnegative
• A358735 → basis A008277
  1 · 2, 1 · 7, 10, 2 · 33, 100, 52, 6 … row sums 1, 3, 19, 191, 2779, 55247, 1436433, …
  (−∞, 0] nonnegative
• A125662 → basis A013610
  1 · 4, 3 · 15, 24, 9 · 56, 138, 108, 27 … row sums 1, 7, 48, 329, 2255, 15456, 105937, …
  (−∞, 0] nonnegative
• A152830 → basis A008277
  1 · 1 · 1 · 1 … row sums 1, 1, 1, 1, 3, 3, 3, 3, …
  (−∞, 0] nonnegative
• A113413 → basis A008277
  1 · 3, 1 · 7, 7, 1 · 17, 33, 12, 1 … row sums 1, 4, 15, 63, 288, 1427, 7605, 43314, …
  (−∞, 0] nonnegative
• A114656 → basis A013610
  1 · 3, 3 · 11, 24, 9 · 45, 153, 135, 27 … row sums 1, 6, 44, 360, 3152, 28896, 273856, …
  (−∞, 0] nonnegative
• A225470 → basis A013610
  1 · 3, 3 · 18, 27, 9 · 162, 297, 162, 27 … row sums 1, 6, 54, 648, 9720, 174960, 3674160, …
  (−∞, 0] nonnegative rational roots
• A249248 → x ↦ x+1
  1 · 4, 3 · 11, 13, 3 · 38, 65, 31, 3 … row sums 1, 7, 27, 137, 681, 3687, 20595, …
  (−∞, −1] nonnegative
• A172431 → basis A008277
  1 · 3, 2 · 8, 13, 3 · 21, 64, 34, 4 … row sums 1, 5, 24, 123, 682, 4079, 26159, …
  (−∞, 0] nonnegative
• A249251 → basis A013610
  1 · 4, 9 · 13, 54, 54 · 43, 261, 513, 324 … row sums 1, 13, 121, 1141, 10753, 101341, …
  (−∞, 0] nonnegative
• basis-map coefficients of A297191, shifted → basis A013609
  1 · 1, 4, 4 · 1, 8, 24, 32, 16 … row sums 1, 9, 81, 729, 6561, 59049, 531441, …
  (−∞, 0] nonnegative rational roots
• A085478 → basis A008277
  1 · 1 · 2, 1 · 5, 6, 1 … row sums 1, 1, 3, 12, 53, 253, 1297, 7103, …
  (−∞, 0] nonnegative
• A099097: Riordan array (1, 3+x).
  1 · 0, 3 · 0, 1, 9 · 0, 0, 6, 27 … row sums 1, 3, 10, 33, 109, 360, 1189, 3927, …
  A099097 (−4/9, 0] nonnegative
• A109692 → basis A008277
  1 · 2, 1 · 8, 13, 3 · 48, 183, 113, 15 … row sums 1, 3, 24, 359, 8563, 295114, 13765813, …
  (−∞, 0] nonnegative
• A249248 → basis A013609
  1 · 4, 6 · 11, 26, 12 · 38, 130, 124, 24 … row sums 1, 10, 49, 316, 1999, 13684, 96715, …
  (−∞, 0] nonnegative
• A178820 → basis A007318
  1 · 8, 4 · 40, 40, 10 · 160, 240, 120, 20 … row sums 1, 12, 90, 540, 2835, 13608, 61236, …
  (−∞, −1] nonnegative rational roots
• A108838 → basis A013611
  2 · 5, 8 · 14, 48, 32 · 42, 224, 336, 128 … row sums 2, 13, 94, 730, 5956, 50357, 437318, …
  (−∞, 0] nonnegative
• A110441 → basis A008277
  1 · 4, 1 · 14, 9, 1 · 48, 57, 15, 1 … row sums 1, 5, 24, 121, 647, 3668, 21997, …
  (−∞, 0] nonnegative
• A038327 → basis A008277
  1 · 13, 1 · 169, 27, 1 · 2197, 547, 42, 1 … row sums 1, 14, 197, 2787, 39652, 567515, …
  (−∞, 0] nonnegative
• A008955 → basis A013610
  1 · 2, 3 · 10, 39, 36 · 100, 660, 1413, 972 … row sums 1, 5, 85, 3145, 204425, 20646925, …
  (−∞, 0] nonnegative rational roots
• A147716 → basis A013611
  1 · 15, 4 · 225, 120, 16 · 3375, 2700, 720, 64 … row sums 1, 19, 361, 6859, 130321, 2476099, …
  (−∞, 0] nonnegative rational roots
• A038334 → basis A013610
  400, 960, 576 · 8000, 28800, 34560, 13824 … row sums 1936, 85184, 3748096, 164916224, …
  (−∞, 0] nonnegative rational roots
• A104684 → basis A013609
  1 · 3, 2 · 13, 16, 4 · 63, 114, 60, 8 … row sums 1, 5, 33, 245, 1921, 15525, 127905, …
  (−∞, 0] nonnegative
• A274498 → basis A013609
  1 · 3 · 9, 12 · 27, 36 … row sums 1, 3, 21, 63, 441, 1323, 9261, 27783, …
  (−∞, 0] nonnegative rational roots
• A102662 → x ↦ x+1
  1 · 4, 3 · 9, 11, 3 · 22, 38, 20, 3 … row sums 1, 7, 23, 83, 295, 1051, 3743, 13331, …
  (−∞, −1] nonnegative
• A154227 → basis A013611
  1 · 2, 4 · 10, 40, 16 · 40, 240, 352, 64 … row sums 1, 6, 66, 696, 9126, 127836, 2044656, …
  (−∞, 0] nonnegative
• A225471 → basis A007318
  1 · 4, 1 · 32, 12, 1 · 384, 176, 24, 1 … row sums 1, 5, 45, 585, 9945, 208845, 5221125, …
  (−∞, 0] nonnegative rational roots
• A052553 → x ↦ x+1
  1 · 1 · 2, 1 · 3, 2 … row sums 1, 1, 3, 5, 11, 21, 43, 85, …
  (−∞, −1] nonnegative
• A128813 → basis A013609
  1 · 2, 2 · 8, 20, 12 · 56, 236, 324, 144 … row sums 1, 4, 40, 760, 23560, 1083760, …
  (−∞, 0] nonnegative rational roots
• A059364 → basis A013610
  1 · 3, 3 · 15, 33, 18 · 105, 366, 423, 162 … row sums 1, 6, 66, 1056, 22176, 576576, …
  (−∞, 0] nonnegative rational roots
• A099097 → basis A013609
  1 · 3, 6 · 10, 38, 36 · 33, 186, 348, 216 … row sums 1, 9, 84, 783, 7299, 68040, 634257, …
  (−∞, 0] nonnegative
• A038291 → basis A013609
  1 · 10, 2 · 100, 40, 4 · 1000, 600, 120, 8 … row sums 1, 12, 144, 1728, 20736, 248832, …
  (−∞, 0] nonnegative rational roots
• A125662 → basis A008277
  1 · 4, 1 · 15, 9, 1 · 56, 59, 15, 1 … row sums 1, 5, 25, 131, 722, 4187, 25531, …
  (−∞, 0] nonnegative
• A038336 → basis A013611
  484, 1760, 1600 · 10648, 58080, 105600, 64000 … row sums 3844, 238328, 14776336, 916132832, …
  (−∞, 0] nonnegative rational roots
• A249248 → basis A013611
  1 · 4, 12 · 11, 52, 48 · 38, 260, 496, 192 … row sums 1, 16, 111, 986, 8691, 81726, 794541, …
  (−∞, 0] nonnegative
• A136124 → basis A007318
  1 · 3, 1 · 12, 7, 1 · 60, 47, 12, 1 … row sums 1, 4, 20, 120, 840, 6720, 60480, …
  (−∞, 0] nonnegative rational roots
• A102547 → reverse → x ↦ x+1
  1, 1 · 1, 2, 1 · 1, 3, 3, 1 · 2, 7, 9, 5, 1 … row sums 2, 4, 8, 24, 64, 160, 416, 1088, …
  (−∞, −1] nonnegative
• A104684 → basis A013611
  1 · 3, 4 · 13, 32, 16 · 63, 228, 240, 64 … row sums 1, 7, 61, 595, 6145, 65527, 712909, …
  (−∞, 0] nonnegative
• A038321 → basis A013610
  324, 756, 441 · 5832, 20412, 23814, 9261 … row sums 1521, 59319, 2313441, 90224199, …
  (−∞, 0] nonnegative rational roots
• A013610 → basis A013611
  1 · 4, 12 · 16, 96, 144 · 64, 576, 1728, 1728 … row sums 1, 16, 256, 4096, 65536, 1048576, …
  (−∞, 0] nonnegative rational roots
• A038325 → basis A008277
  1 · 22, 11 · 484, 605, 121 … row sums 1, 33, 1210, 49247, 2210791, 108548374, …
  (−∞, 0] nonnegative
• A154986 → basis A008277
  1 · 2, 1 · 6, 7, 1 · 24, 51, 17, 1 … row sums 1, 3, 14, 93, 811, 8914, 118881, …
  (−∞, 0] nonnegative
• A038333 → basis A013609
  361, 532, 196 · 6859, 15162, 11172, 2744 … row sums 1089, 35937, 1185921, 39135393, …
  (−∞, 0] nonnegative rational roots
• A038334 → basis A007318
  400, 320, 64 · 8000, 9600, 3840, 512 … row sums 784, 21952, 614656, 17210368, …
  (−∞, 0] nonnegative rational roots
• basis-map coefficients of A297191, shifted → basis A008277
  1 · 1, 3, 1 · 1, 15, 25, 10, 1 … row sums 1, 5, 52, 877, 21147, 678570, 27644437, …
  (−∞, 0] nonnegative
• A327997 → basis A013609
  1 · 4, 2 · 17, 18, 4 · 78, 130, 60, 8 … row sums 1, 6, 39, 276, 2133, 18018, 166203, …
  (−∞, 0] nonnegative
• A358735 → basis A013610
  1 · 2, 3 · 7, 24, 18 · 33, 180, 306, 162 … row sums 1, 5, 49, 681, 12209, 267917, 6953633, …
  (−∞, 0] nonnegative
• A028326 → basis A013609
  2 · 4, 4 · 8, 16, 8 · 16, 48, 48, 16 … row sums 2, 8, 32, 128, 512, 2048, 8192, 32768, …
  (−∞, 0] nonnegative rational roots
• A094638 → basis A013609
  1 · 2, 2 · 6, 14, 8 · 24, 92, 116, 48 … row sums 1, 4, 28, 280, 3640, 58240, 1106560, …
  (−∞, 0] nonnegative rational roots