basis_map

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

1056 sequences

• A225471 → basis A008277
  1 · 4, 1 · 32, 13, 1 · 384, 201, 27, 1 … row sums 1, 5, 46, 613, 10679, 229576, 5868715, …
  (−∞, 0] nonnegative
• A225471 → basis A013611
  1 · 4, 4 · 32, 48, 16 · 384, 704, 384, 64 … row sums 1, 8, 96, 1536, 30720, 737280, …
  (−∞, 0] nonnegative rational roots
• A099040 → basis A008277
  1 · 2, 2 · 6, 14, 4 · 16, 80, 56, 8 … row sums 1, 4, 24, 160, 1212, 10184, 93720, …
  (−∞, 0] nonnegative
• A161198 → basis A013611
  1 · 3, 8 · 15, 64, 64 · 105, 568, 960, 512 … row sums 1, 11, 143, 2145, 36465, 692835, …
  (−∞, 0] nonnegative rational roots
• A027465 → basis A013611
  1 · 4, 4 · 16, 32, 16 · 64, 192, 192, 64 … row sums 1, 8, 64, 512, 4096, 32768, 262144, …
  (−∞, 0] nonnegative rational roots
• A123519 → basis A013610
  11, 42, 36 · 41, 228, 396, 216 … row sums 89, 881, 8721, 86329, 854569, 8459361, …
  (−∞, 0] nonnegative
• A038281 → basis A013611
  121, 264, 144 · 1331, 4356, 4752, 1728 … row sums 529, 12167, 279841, 6436343, 148035889, …
  (−∞, 0] nonnegative rational roots
• A038259 → basis A013610
  1 · 11, 15 · 121, 330, 225 · 1331, 5445, 7425, 3375 … row sums 1, 26, 676, 17576, 456976, 11881376, …
  (−∞, 0] nonnegative rational roots
• A013620 → basis A008288
  1 · 5, 3 · 25, 39, 9 · 125, 333, 189, 27 … row sums 1, 8, 73, 674, 6229, 57572, 532117, …
  [−3−2√2, −3+2√2] nonnegative
• A102547 → reverse → basis A008277
  1, 1 · 1, 3, 1 · 1, 7, 6, 1 · 2, 22, 31, 11, 1 … row sums 2, 5, 15, 67, 307, 1486, 7851, 44478, …
  (−∞, 0] nonnegative
• A099040: Riordan array (1, 2+2x).
  1 · 0, 2 · 0, 2, 4 · 0, 0, 8, 8 … row sums 1, 2, 6, 16, 44, 120, 328, 896, …
  A099040 (−2, 0] nonnegative
• A136124 → basis A013610
  1 · 3, 3 · 12, 21, 9 · 60, 141, 108, 27 … row sums 1, 6, 42, 336, 3024, 30240, 332640, …
  (−∞, 0] nonnegative rational roots
• A120910 → basis A013609
  3 · 9, 6 · 27, 36, 12 · 81, 162, 108, 24 … row sums 3, 15, 75, 375, 1875, 9375, 46875, …
  (−∞, −1] nonnegative rational roots
• A099093 → basis A013611
  1 · 3, 12 · 12, 84, 144 · 45, 468, 1584, 1728 … row sums 1, 15, 240, 3825, 60975, 972000, …
  (−∞, 0] nonnegative
• A054142 → basis A013611
  1 · 2, 4 · 5, 20, 16 · 13, 80, 144, 64 … row sums 1, 6, 41, 301, 2286, 17621, 136681, …
  (−∞, 0] nonnegative
• A046716 → basis A007318
  1 · 2, 1 · 5, 5, 1 · 16, 25, 11, 1 … row sums 1, 3, 11, 53, 345, 2947, 31411, 400437, …
  (−∞, −1] nonnegative
• A118933 → basis A013609
  1 · 1 · 1 · 1 … row sums 1, 1, 1, 1, 19, 91, 271, 631, …
  (−∞, 0] nonnegative
• A100861 → reverse → basis A013609
  1 · 1, 2 · 2, 6, 4 · 4, 18, 24, 8 … row sums 1, 3, 12, 54, 270, 1458, 8424, 51516, …
  (−∞, 0] nonnegative
• A207823 → basis A013611
  1 · 5, 4 · 24, 40, 16 · 115, 292, 240, 64 … row sums 1, 9, 80, 711, 6319, 56160, 499121, …
  (−∞, 0] nonnegative
• A081582 → basis A008277
  1 · 2, 1 · 11, 12, 1 · 36, 75, 23, 1 … row sums 1, 3, 24, 135, 963, 6806, 52291, …
  (−∞, 0] nonnegative
• A128099 → basis A013610
  1 · 1 · 3, 6 · 5, 12 … row sums 1, 1, 9, 17, 89, 225, 937, 2737, …
  (−∞, 0] nonnegative
• A085841 → basis A013611
  1 · 7, 16 · 61, 288, 256 · 547, 4016, 8448, 4096 … row sums 1, 23, 605, 17107, 500089, 14828111, …
  (−∞, 0] nonnegative
• A099093 → basis A013609
  1 · 3, 6 · 12, 42, 36 · 45, 234, 396, 216 … row sums 1, 9, 90, 891, 8829, 87480, 866781, …
  (−∞, 0] nonnegative
• basis-map coefficients of A113214, shifted → x ↦ x+1
  1 · -2, -1 · 4, 4, 1 · -8, -12, -6, -1 … row sums 1, -3, 9, -27, 81, -243, 729, -2187, …
  (−∞, −1] rational roots
• A139548 → basis A013611
  1 · 8, 32, 32 · 64, 512, 1536, 2048, 1024 … row sums 1, 72, 5184, 373248, 26873856, …
  (−∞, 0] nonnegative rational roots
• A034870 → basis A008277
  1 · 4, 5, 1 · 16, 65, 55, 14, 1 … row sums 1, 10, 151, 3263, 94828, 3535027, …
  (−∞, 0] nonnegative
• A266213 → basis A013611
  1 · 1 · 3, 8 · 7, 32, 32 … row sums 1, 1, 11, 71, 481, 3241, 21851, 147311, …
  (−∞, 0] nonnegative
• A038333 → basis A013610
  361, 798, 441 · 6859, 22743, 25137, 9261 … row sums 1600, 64000, 2560000, 102400000, …
  (−∞, 0] nonnegative rational roots
• narayana → basis A013609
  1 · 2, 2 · 5, 10, 4 · 14, 42, 36, 8 … row sums 1, 4, 19, 100, 562, 3304, 20071, …
  (−∞, 0] nonnegative
• A063967 → basis A008277
  1 · 2, 1 · 6, 6, 1 · 16, 29, 11, 1 … row sums 1, 3, 13, 57, 272, 1389, 7576, 43929, …
  (−∞, 0] nonnegative
• A060920: Bisection of Fibonacci triangle A037027: even-indexed members of column sequences of A037027 (not counting leading zeros).
  1 · 2, 1 · 5, 5, 1 · 13, 20, 9, 1 … row sums 1, 3, 11, 43, 171, 683, 2731, 10923, …
  A060920 (−∞, −1] nonnegative
• A113214 → basis A007318
  1 · 3, 1 · 4, 5, 1 · 7, 13, 7, 1 … row sums 1, 4, 10, 28, 76, 208, 568, 1552, …
  (−∞, −1] nonnegative
• basis-map coefficients of A030528, shifted → basis A008277
  1 · -1, -1 · 1, 3, 1 · -1, -7, -6, -1 … row sums 1, -2, 5, -15, 52, -203, 877, -4140, …
  (−∞, 0]
• A290319 → basis A013611
  1 · 2, 4 · 12, 32, 16 · 120, 368, 288, 64 … row sums 1, 6, 60, 840, 15120, 332640, 8648640, …
  (−∞, 0] nonnegative rational roots
• A108838 → basis A013610
  2 · 5, 6 · 14, 36, 18 · 42, 168, 189, 54 … row sums 2, 11, 68, 453, 3174, 23055, 172040, …
  (−∞, 0] nonnegative
• A136124 → basis A013609
  1 · 3, 2 · 12, 14, 4 · 60, 94, 48, 8 … row sums 1, 5, 30, 210, 1680, 15120, 151200, …
  (−∞, 0] nonnegative rational roots
• A038324 → basis A013609
  1 · 21, 20 · 441, 840, 400 · 9261, 26460, 25200, 8000 … row sums 1, 41, 1681, 68921, 2825761, 115856201, …
  (−∞, 0] nonnegative rational roots
• A100862 → basis A013611
  1 · 2, 4 · 5, 20, 16 · 14, 84, 144, 64 … row sums 1, 6, 41, 306, 2451, 20826, 186231, …
  (−∞, 0] nonnegative
• A038330 → basis A013610
  256, 384, 144 · 4096, 9216, 6912, 1728 … row sums 784, 21952, 614656, 17210368, …
  (−∞, 0] nonnegative rational roots
• A100861 → reverse → basis A013611
  1 · 1, 4 · 2, 12, 16 · 4, 36, 96, 64 … row sums 1, 5, 30, 200, 1450, 11250, 92500, …
  (−∞, 0] nonnegative
• A028338 → basis A007318
  1 · 2, 1 · 8, 6, 1 · 48, 44, 12, 1 … row sums 1, 3, 15, 105, 945, 10395, 135135, …
  (−∞, 0] nonnegative rational roots
• A161198 → basis A013610
  1 · 3, 6 · 15, 48, 36 · 105, 426, 540, 216 … row sums 1, 9, 99, 1287, 19305, 328185, 6235515, …
  (−∞, 0] nonnegative rational roots
• basis-map coefficients of A112227 → basis A013609
  1, 4, 4 · 1, 6, 12, 8 · 1, 8, 24, 32, 16 … row sums 9, 27, 81, 243, 729, 2187, 6561, 19683, …
  (−∞, 0] nonnegative rational roots
• A038338 → basis A013609
  576, 1152, 576 · 13824, 41472, 41472, 13824 … row sums 2304, 110592, 5308416, 254803968, …
  (−∞, 0] nonnegative rational roots
• A011973 → basis A007318 → x ↦ x+1
  1 · 1 · 3, 1 · 5, 2 … row sums 1, 1, 4, 7, 19, 40, 97, 217, …
  (−∞, −1] nonnegative
• A178821 → basis A007318
  1 · 10, 5 · 60, 60, 15 · 280, 420, 210, 35 … row sums 1, 15, 135, 945, 5670, 30618, 153090, …
  (−∞, −1] nonnegative rational roots
• A008459 → basis A013609
  1 · 2, 2 · 6, 12, 4 · 20, 60, 48, 8 … row sums 1, 4, 22, 136, 886, 5944, 40636, …
  (−∞, 0] nonnegative
• basis-map coefficients of A297191, shifted → basis A013611
  1 · 1, 8, 16 · 1, 16, 96, 256, 256 … row sums 1, 25, 625, 15625, 390625, 9765625, …
  (−∞, 0] nonnegative rational roots
• A272866 → basis A013609
  1 · 5, 10, 4 · 25, 100, 140, 80, 16 … row sums 1, 19, 361, 6859, 130321, 2476099, …
  (−∞, 0] nonnegative
• A038221 → basis A013611
  1 · 6, 12 · 36, 144, 144 · 216, 1296, 2592, 1728 … row sums 1, 18, 324, 5832, 104976, 1889568, …
  (−∞, 0] nonnegative rational roots