basis_map / A013609

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

210 sequences

• A059344 → basis A013609
  1 · 1 · 3, 4 · 7, 12 … row sums 1, 1, 7, 19, 145, 601, 4951, 26587, …
  (−∞, 0] nonnegative
• A038337 → basis A013609
  529, 1012, 484 · 12167, 34914, 33396, 10648 … row sums 2025, 91125, 4100625, 184528125, …
  (−∞, 0] nonnegative rational roots
• A013609: Triangle of coefficients in expansion of (1+2*x)^n.
  1 · 1, 2 · 1, 4, 4 · 1, 6, 12, 8 … row sums 1, 3, 9, 27, 81, 243, 729, 2187, …
  A013609 (−∞, 0) [−1, 0] nonnegative rational roots
• A063967 → basis A013609
  1 · 2, 2 · 6, 10, 4 · 16, 40, 32, 8 … row sums 1, 4, 20, 96, 464, 2240, 10816, 52224, …
  (−∞, 0] nonnegative
• A178820 → basis A013609
  1 · 8, 8 · 40, 80, 40 · 160, 480, 480, 160 … row sums 1, 16, 160, 1280, 8960, 57344, 344064, …
  (−∞, 0] nonnegative rational roots
• A038323 → basis A013609
  1 · 20, 18 · 400, 720, 324 · 8000, 21600, 19440, 5832 … row sums 1, 38, 1444, 54872, 2085136, 79235168, …
  (−∞, 0] nonnegative rational roots
• A011973 → basis A013609
  1 · 1 · 2, 2 · 3, 4 … row sums 1, 1, 4, 7, 19, 40, 97, 217, …
  (−∞, 0] nonnegative
• A137320 → x ↦ x+1
  1 · 2, 2 · 6, 10, 4 · 24, 52, 36, 8 … row sums 1, 4, 20, 120, 840, 6720, 60480, …
  (−∞, −1] nonnegative rational roots
• A172431 → basis A013609
  1 · 3, 4 · 8, 20, 12 · 21, 76, 88, 32 … row sums 1, 7, 40, 217, 1159, 6160, 32689, …
  (−∞, 0] nonnegative
• A145324 → basis A013609
  1 · 3, 4 · 12, 34, 24 · 60, 266, 392, 192 … row sums 1, 7, 70, 910, 14560, 276640, 6086080, …
  (−∞, 0] nonnegative rational roots
• A269947 → basis A013609
  1 · 1, 2 · 2, 6, 4 · 18, 58, 48, 8 … row sums 1, 3, 12, 132, 3960, 265320, 33960960, …
  (−∞, 0] nonnegative rational roots
• A038301 → basis A013609
  400, 880, 484 · 8000, 26400, 29040, 10648 … row sums 1764, 74088, 3111696, 130691232, …
  (−∞, 0] nonnegative rational roots
• A125662 → basis A013609
  1 · 4, 2 · 15, 16, 4 · 56, 92, 48, 8 … row sums 1, 6, 35, 204, 1189, 6930, 40391, …
  (−∞, 0] nonnegative
• A038334 → basis A013609
  400, 640, 256 · 8000, 19200, 15360, 4096 … row sums 1296, 46656, 1679616, 60466176, …
  (−∞, 0] nonnegative rational roots
• A116414 → basis A013609
  1 · 5, 2 · 22, 20, 4 · 95, 138, 60, 8 … row sums 1, 7, 46, 301, 1969, 12880, 84253, …
  (−∞, 0] nonnegative
• A116412 → basis A013609
  1 · 4, 2 · 13, 16, 4 · 43, 84, 48, 8 … row sums 1, 6, 33, 183, 1014, 5619, 31137, …
  (−∞, 0] nonnegative
• A033282 → basis A013609
  1 · 3, 4 · 11, 30, 20 · 45, 186, 252, 112 … row sums 1, 7, 61, 595, 6217, 68047, 770149, …
  (−∞, 0] nonnegative
• A118394 → basis A013609
  1 · 1 · 1 · 7, 12 … row sums 1, 1, 1, 19, 73, 181, 3601, 23311, …
  (−∞, 0] nonnegative
• A200536 → basis A013609
  1 · 6, 14, 8 · 36, 168, 292, 224, 64 … row sums 1, 28, 784, 21952, 614656, 17210368, …
  (−∞, 0] nonnegative rational roots
• A059364 → basis A013609
  1 · 3, 2 · 15, 22, 8 · 105, 244, 188, 48 … row sums 1, 5, 45, 585, 9945, 208845, 5221125, …
  (−∞, 0] nonnegative rational roots
• A318772 → x ↦ (1/243)x → basis A013609
  1 · 3 · 9 · 27 … row sums 1, 3, 9, 27, 84, 261, 810, 2511, …
  (−∞, 0] nonnegative
• A122542 → basis A013609
  1 · 1, 2 · 3, 8, 4 · 7, 26, 28, 8 … row sums 1, 3, 15, 69, 321, 1491, 6927, 32181, …
  (−∞, 0] nonnegative
• A026374 → basis A013609
  1 · 2, 2 · 5, 10, 4 · 10, 30, 28, 8 … row sums 1, 4, 19, 76, 361, 1444, 6859, 27436, …
  (−∞, 0] nonnegative
• A103327 → basis A013609
  1 · 4, 2 · 16, 24, 4 · 64, 160, 96, 8 … row sums 1, 6, 44, 328, 2448, 18272, 136384, …
  (−∞, 0] nonnegative
• A078812 → basis A013609
  1 · 3, 2 · 8, 12, 4 · 21, 50, 36, 8 … row sums 1, 5, 24, 115, 551, 2640, 12649, 60605, …
  (−∞, 0] nonnegative
• A008955 → basis A013609
  1 · 2, 2 · 10, 26, 16 · 100, 440, 628, 288 … row sums 1, 4, 52, 1456, 71344, 5422144, …
  (−∞, 0] nonnegative rational roots
• A086645 → basis A013609
  1 · 2, 2 · 8, 16, 4 · 32, 96, 72, 8 … row sums 1, 4, 28, 208, 1552, 11584, 86464, …
  (−∞, 0] nonnegative
• basis-map coefficients of A030528, shifted → basis A013609
  1 · -1, -2 · 1, 4, 4 · -1, -6, -12, -8 … row sums 1, -3, 9, -27, 81, -243, 729, -2187, …
  (−∞, 0] rational roots
• A046716 → basis A013609
  1 · 2, 2 · 5, 10, 4 · 16, 50, 44, 8 … row sums 1, 4, 19, 118, 1021, 12088, 183727, …
  (−∞, 0] nonnegative
• A013613 → basis A013609
  1 · 7, 12 · 49, 168, 144 · 343, 1764, 3024, 1728 … row sums 1, 19, 361, 6859, 130321, 2476099, …
  (−∞, 0] nonnegative rational roots
• basis-map coefficients of A021012 → basis A013609
  1 · -1, -2 · 2, 8, 8 · -6, -36, -72, -48 … row sums 1, -3, 18, -162, 1944, -29160, 524880, …
  (−∞, 0] rational roots
• A178822 → basis A013609
  1 · 12, 12 · 84, 168, 84 · 448, 1344, 1344, 448 … row sums 1, 24, 336, 3584, 32256, 258048, …
  (−∞, 0] nonnegative rational roots
• A064861 → basis A013609
  6, 14, 8 · 18, 66, 80, 32 · 36, 168, 292, 224, 64 … row sums 28, 196, 784, 5488, 21952, 153664, …
  (−∞, 0] nonnegative rational roots
• A079638 → basis A013609
  1 · 4, 2 · 24, 22, 4 · 192, 244, 84, 8 … row sums 1, 6, 50, 528, 6720, 99840, 1693440, …
  (−∞, 0] nonnegative
• A118931 → basis A013609
  1 · 1 · 1 · 3, 4 … row sums 1, 1, 1, 7, 25, 61, 481, 2731, …
  (−∞, 0] nonnegative
• A128099 → basis A013609
  1 · 1 · 3, 4 · 5, 8 … row sums 1, 1, 7, 13, 55, 133, 463, 1261, …
  (−∞, 0] nonnegative
• A225470 → basis A013609
  1 · 3, 2 · 18, 18, 4 · 162, 198, 72, 8 … row sums 1, 5, 40, 440, 6160, 104720, 2094400, …
  (−∞, 0] nonnegative rational roots
• A038284 → basis A013609
  196, 336, 144 · 2744, 7056, 6048, 1728 … row sums 676, 17576, 456976, 11881376, …
  (−∞, 0] nonnegative rational roots
• A027466 → basis A013609
  1 · 8, 2 · 64, 32, 4 · 512, 384, 96, 8 … row sums 1, 10, 100, 1000, 10000, 100000, …
  (−∞, 0] nonnegative rational roots
• A152842 → basis A013609
  1 · 4, 6 · 8, 20, 12 · 32, 128, 168, 72 … row sums 1, 10, 40, 400, 1600, 16000, 64000, …
  (−∞, 0] nonnegative rational roots
• A356546 → basis A013609
  1 · 4, 4 · 24, 48, 24 · 160, 480, 480, 160 … row sums 1, 8, 96, 1280, 17920, 258048, 3784704, …
  (−∞, 0] nonnegative rational roots
• A109692 → basis A013609
  1 · 2, 2 · 8, 20, 12 · 48, 200, 272, 120 … row sums 1, 4, 40, 640, 14080, 394240, 13404160, …
  (−∞, 0] nonnegative rational roots
• A038322 → basis A013609
  1 · 19, 16 · 361, 608, 256 · 6859, 17328, 14592, 4096 … row sums 1, 35, 1225, 42875, 1500625, 52521875, …
  (−∞, 0] nonnegative rational roots
• A094816 → basis A013609
  1 · 2, 2 · 5, 10, 4 · 16, 46, 36, 8 … row sums 1, 4, 19, 106, 685, 5056, 42079, …
  (−∞, 0] nonnegative
• A038277 → basis A013609
  1 · 18, 22 · 324, 792, 484 … row sums 1, 40, 1600, 64000, 2560000, 102400000, …
  (−∞, 0] nonnegative rational roots
• A207607 → basis A013609
  1 · 3, 4 · 8, 18, 8 · 21, 66, 60, 16 … row sums 1, 7, 34, 163, 781, 3742, 17929, 85903, …
  (−∞, 0] nonnegative
• delannoy → basis A013609
  1 · 2, 2 · 5, 10, 4 · 12, 36, 32, 8 … row sums 1, 4, 19, 88, 409, 1900, 8827, 41008, …
  (−∞, 0] nonnegative
• A038320 → basis A013609
  289, 408, 144 · 4913, 10404, 7344, 1728 … row sums 841, 24389, 707281, 20511149, …
  (−∞, 0] nonnegative rational roots
• A114687 → basis A007318
  1 · 3, 2 · 11, 14, 4 · 45, 84, 48, 8 … row sums 1, 5, 29, 185, 1257, 8925, 65445, …
  (−∞, −1] nonnegative
• A152198 → basis A013609
  1 · 1 · 2, 2 · 2, 2 … row sums 1, 1, 4, 4, 16, 16, 64, 64, …
  (−∞, 0] nonnegative rational roots