basis_map

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

1056 sequences

• A011973 → basis A007318 → basis A008277
  1 · 1 · 3, 1 · 5, 2 … row sums 1, 1, 4, 7, 20, 43, 113, 267, …
  (−∞, 0] nonnegative
• A038329 → basis A013609
  225, 180, 36 · 3375, 4050, 1620, 216 … row sums 441, 9261, 194481, 4084101, 85766121, …
  (−∞, 0] nonnegative rational roots
• A207823 → basis A013609
  1 · 5, 2 · 24, 20, 4 · 115, 146, 60, 8 … row sums 1, 7, 48, 329, 2255, 15456, 105937, …
  (−∞, 0] nonnegative
• A038208 → basis A013610
  1 · 4, 6 · 16, 48, 36 · 64, 288, 432, 216 … row sums 1, 10, 100, 1000, 10000, 100000, …
  (−∞, 0] nonnegative rational roots
• A038271 → basis A013609
  1 · 12, 10 · 144, 240, 100 · 1728, 4320, 3600, 1000 … row sums 1, 22, 484, 10648, 234256, 5153632, …
  (−∞, 0] nonnegative rational roots
• A081581 → basis A008277
  1 · 2, 1 · 10, 11, 1 · 32, 67, 21, 1 … row sums 1, 3, 22, 121, 817, 5570, 40985, …
  (−∞, 0] nonnegative
• A081580 → basis A007318
  1 · 2, 1 · 9, 9, 1 · 28, 42, 16, 1 … row sums 1, 3, 19, 87, 451, 2223, 11179, 55767, …
  (−∞, −1] nonnegative
• A091042 → basis A013609
  1 · 4, 6 · 16, 40, 20 · 64, 224, 224, 56 … row sums 1, 10, 76, 568, 4240, 31648, 236224, …
  (−∞, 0] nonnegative
• A038335 → basis A013610
  1 · 21, 27 · 441, 1134, 729 … row sums 1, 48, 2304, 110592, 5308416, …
  (−∞, 0] nonnegative rational roots
• A114656 → basis A008277
  1 · 3, 1 · 11, 9, 1 · 45, 67, 18, 1 … row sums 1, 4, 21, 131, 928, 7275, 62051, …
  (−∞, 0] nonnegative
• A156992 → basis A008277
  1 · 4, 2 · 24, 30, 6 · 192, 456, 216, 24 … row sums 1, 6, 60, 888, 18120, 485280, 16445520, …
  (−∞, 0] nonnegative
• A178821 → basis A013609
  1 · 10, 10 · 60, 120, 60 · 280, 840, 840, 280 … row sums 1, 20, 240, 2240, 17920, 129024, …
  (−∞, 0] nonnegative rational roots
• A290319 → basis A013610
  1 · 2, 3 · 12, 24, 9 · 120, 276, 162, 27 … row sums 1, 5, 45, 585, 9945, 208845, 5221125, …
  (−∞, 0] nonnegative rational roots
• A030528 → basis A007318
  1 · 2, 1 · 3, 4, 1 · 5, 10, 6, 1 … row sums 1, 3, 8, 22, 60, 164, 448, 1224, …
  (−∞, −1] nonnegative
• A038323 → basis A013611
  1 · 20, 36 · 400, 1440, 1296 … row sums 1, 56, 3136, 175616, 9834496, …
  (−∞, 0] nonnegative rational roots
• A063967 → basis A013610
  1 · 2, 3 · 6, 15, 9 · 16, 60, 72, 27 … row sums 1, 5, 30, 175, 1025, 6000, 35125, …
  (−∞, 0] nonnegative
• A038284 → basis A008277
  196, 204, 36 · 2744, 5256, 2160, 216 … row sums 436, 10376, 268864, 7547936, 228241216, …
  (−∞, 0] nonnegative
• A130534 → basis A013611
  1 · 2, 4 · 6, 20, 16 · 24, 104, 144, 64 … row sums 1, 6, 42, 336, 3024, 30240, 332640, …
  (−∞, 0] nonnegative rational roots
• A344565 → basis A013611
  3 · 30, 60 · 180, 720, 720 · 840, 5040, 10080, 6720 … row sums 3, 90, 1620, 22680, 272160, 2939328, …
  (−∞, 0] nonnegative rational roots
• A038335 → basis A013611
  1 · 21, 36 · 441, 1512, 1296 … row sums 1, 57, 3249, 185193, 10556001, …
  (−∞, 0] nonnegative rational roots
• A013609 → basis A013610
  1 · 3, 6 · 9, 36, 36 · 27, 162, 324, 216 … row sums 1, 9, 81, 729, 6561, 59049, 531441, …
  (−∞, 0] nonnegative rational roots
• A038321 → basis A013609
  324, 504, 196 · 5832, 13608, 10584, 2744 … row sums 1024, 32768, 1048576, 33554432, …
  (−∞, 0] nonnegative rational roots
• A178821 → basis A013610
  1 · 10, 15 · 60, 180, 135 · 280, 1260, 1890, 945 … row sums 1, 25, 375, 4375, 43750, 393750, …
  (−∞, 0] nonnegative rational roots
• A027466 → basis A008277
  1 · 8, 1 · 64, 17, 1 · 512, 217, 27, 1 … row sums 1, 9, 82, 757, 7087, 67340, 649931, …
  (−∞, 0] nonnegative
• A318772 → x ↦ (1/243)x → basis A008277
  1 · 3 · 9 · 27 … row sums 1, 3, 9, 27, 83, 255, 783, 2403, …
  (−∞, 0] nonnegative
• A135838 → basis A013610
  1 · 4, 6 · 8, 24, 18 · 32, 144, 216, 108 … row sums 1, 10, 50, 500, 2500, 25000, 125000, …
  (−∞, 0] nonnegative rational roots
• A113953 → basis A013609
  1 · 1, 2 · 3, 8, 4 · 5, 22, 28, 8 … row sums 1, 3, 15, 63, 279, 1215, 5319, 23247, …
  (−∞, 0] nonnegative
• A120909 → basis A013611
  3 · 9, 24 · 27, 144, 192 · 81, 648, 1728, 1536 … row sums 3, 33, 363, 3993, 43923, 483153, …
  (−∞, 0] nonnegative rational roots
• A038333 → basis A007318
  361, 266, 49 · 6859, 7581, 2793, 343 … row sums 676, 17576, 456976, 11881376, …
  (−∞, 0] nonnegative rational roots
• A207824 → basis A013610
  1 · 6, 3 · 35, 36, 9 · 204, 318, 162, 27 … row sums 1, 9, 80, 711, 6319, 56160, 499121, …
  (−∞, 0] nonnegative
• A133087 → basis A013611
  1 · 3, 4 · 4, 16, 16 · 12, 64, 112, 64 … row sums 1, 7, 36, 252, 1296, 9072, 46656, …
  (−∞, 0] nonnegative rational roots
• A091044 → basis A013611
  1 · 4, 8 · 16, 64, 48 · 64, 384, 640, 256 … row sums 1, 12, 128, 1344, 14080, 147456, …
  (−∞, 0] nonnegative
• A013622 → basis A008288
  1 · 8, 5 · 64, 105, 25 · 512, 1435, 850, 125 … row sums 1, 13, 194, 2922, 44036, 663668, …
  [−3−2√2, −3+2√2] nonnegative
• A099040 → basis A013609
  1 · 2, 4 · 6, 20, 16 · 16, 80, 128, 64 … row sums 1, 6, 42, 288, 1980, 13608, 93528, …
  (−∞, 0] nonnegative
• A113953 → basis A008277
  1 · 1, 1 · 3, 5, 1 · 5, 19, 10, 1 … row sums 1, 2, 9, 35, 162, 799, 4275, 24448, …
  (−∞, 0] nonnegative
• A154986 → basis A013610
  1 · 2, 3 · 6, 18, 9 · 24, 108, 126, 27 … row sums 1, 5, 33, 285, 3009, 37845, 550305, …
  (−∞, 0] nonnegative
• A013620: Triangle of coefficients in expansion of (2+3x)^n.
  1 · 2, 3 · 4, 12, 9 · 8, 36, 54, 27 … row sums 1, 5, 25, 125, 625, 3125, 15625, 78125, …
  A013620 (−∞, 0) [−1, 0] nonnegative rational roots
• A143491 → basis A013609
  12, 14, 4 · 60, 94, 48, 8 · 360, 684, 476, 144, 16 … row sums 30, 210, 1680, 15120, 151200, 1663200, …
  (−∞, 0] nonnegative rational roots
• A126216: Triangle read by rows: T(n,k) is the number of Schroeder paths of semilength n containing exactly k peaks but no peaks at level one (n >= 1; 0 <= k <= n-1).
  1 · 2, 1 · 5, 5, 1 · 14, 21, 9, 1 … row sums 1, 3, 11, 45, 197, 903, 4279, 20793, …
  A126216 (−∞, −1] nonnegative
• A008459 → x ↦ x+1
  1 · 2, 1 · 6, 6, 1 · 20, 30, 12, 1 … row sums 1, 3, 13, 63, 321, 1683, 8989, 48639, …
  (−∞, −1] nonnegative
• A078812 → basis A013610
  1 · 3, 3 · 8, 18, 9 · 21, 75, 81, 27 … row sums 1, 6, 35, 204, 1189, 6930, 40391, …
  (−∞, 0] nonnegative
• A178821 → basis A013611
  1 · 10, 20 · 60, 240, 240 · 280, 1680, 3360, 2240 … row sums 1, 30, 540, 7560, 90720, 979776, …
  (−∞, 0] nonnegative rational roots
• A001263 → basis A013609
  1 · 2, 2 · 5, 10, 4 · 14, 42, 36, 8 … row sums 1, 4, 19, 100, 562, 3304, 20071, …
  (−∞, 0] nonnegative
• A114687 → basis A008277
  1 · 3, 2 · 11, 18, 4 · 45, 140, 72, 8 … row sums 1, 5, 33, 265, 2473, 26037, 303089, …
  (−∞, 0] nonnegative
• A038301 → basis A013611
  400, 1760, 1936 · 8000, 52800, 116160, 85184 … row sums 4096, 262144, 16777216, 1073741824, …
  (−∞, 0] nonnegative rational roots
• A038322 → basis A013610
  1 · 19, 24 · 361, 912, 576 … row sums 1, 43, 1849, 79507, 3418801, 147008443, …
  (−∞, 0] nonnegative rational roots
• A081580 → basis A013611
  1 · 2, 4 · 9, 36, 16 · 28, 168, 256, 64 … row sums 1, 6, 61, 516, 4621, 40626, 359281, …
  (−∞, 0] nonnegative
• A063007 → basis A008288
  1 · 3, 2 · 13, 24, 6 · 63, 202, 130, 20 … row sums 1, 5, 43, 415, 4201, 43741, 463891, …
  [−3−2√2, −3+2√2] nonnegative
• A121574 → basis A013610
  1 · 3, 3 · 10, 21, 9 · 33, 105, 99, 27 … row sums 1, 6, 40, 264, 1744, 11520, 76096, …
  (−∞, 0] nonnegative
• A038326 → basis A008277
  1 · 23, 12 · 529, 696, 144 … row sums 1, 35, 1369, 59723, 2883889, 152682227, …
  (−∞, 0] nonnegative