basis_map / A013611

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

210 sequences

• A059344 → basis A013611
  1 · 1 · 3, 8 · 7, 24 … row sums 1, 1, 11, 31, 361, 1601, 19651, 115711, …
  (−∞, 0] nonnegative
• A038327 → basis A013611
  1 · 13, 4 · 169, 104, 16 · 2197, 2028, 624, 64 … row sums 1, 17, 289, 4913, 83521, 1419857, …
  (−∞, 0] nonnegative rational roots
• A008459 → basis A013611
  1 · 2, 4 · 6, 24, 16 · 20, 120, 192, 64 … row sums 1, 6, 46, 396, 3606, 33876, 324556, …
  (−∞, 0] nonnegative
• A013609 → basis A013609
  1 · 3, 4 · 9, 24, 16 · 27, 108, 144, 64 … row sums 1, 7, 49, 343, 2401, 16807, 117649, …
  (−∞, 0] nonnegative rational roots
• A200536 → basis A013611
  1 · 6, 28, 32 · 36, 336, 1168, 1792, 1024 … row sums 1, 66, 4356, 287496, 18974736, …
  (−∞, 0] nonnegative rational roots
• A081581 → basis A013611
  1 · 2, 4 · 10, 40, 16 · 32, 192, 288, 64 … row sums 1, 6, 66, 576, 5436, 49896, 462456, …
  (−∞, 0] nonnegative
• A078812 → basis A013611
  1 · 3, 4 · 8, 24, 16 · 21, 100, 144, 64 … row sums 1, 7, 48, 329, 2255, 15456, 105937, …
  (−∞, 0] nonnegative
• A109692 → basis A013611
  1 · 2, 4 · 8, 40, 48 · 48, 400, 1088, 960 … row sums 1, 6, 96, 2496, 89856, 4133376, …
  (−∞, 0] nonnegative rational roots
• A102547 → basis A013611
  1 · 1 · 1 · 2, 4 … row sums 1, 1, 1, 6, 11, 16, 46, 101, …
  (−∞, 0] nonnegative
• A088996 → basis A013611
  1 · 1, 4 · 3, 20, 32 · 15, 136, 400, 384 … row sums 1, 5, 55, 935, 21505, 623645, 21827575, …
  (−∞, 0] nonnegative rational roots
• A030528 → basis A013611
  1 · 2, 4 · 3, 16, 16 · 5, 40, 96, 64 … row sums 1, 6, 35, 205, 1200, 7025, 41125, …
  (−∞, 0] nonnegative
• A137320 → basis A013611
  1 · 2, 8 · 6, 40, 64 · 24, 208, 576, 512 … row sums 1, 10, 110, 1320, 17160, 240240, …
  (−∞, 0] nonnegative rational roots
• A123519 → basis A013611
  11, 56, 64 · 41, 304, 704, 512 … row sums 131, 1561, 18601, 221651, 2641211, …
  (−∞, 0] nonnegative
• A118933 → basis A013611
  1 · 1 · 1 · 1 … row sums 1, 1, 1, 1, 31, 151, 451, 1051, …
  (−∞, 0] nonnegative
• A272866 → basis A013611
  1 · 5, 20, 16 · 25, 200, 560, 640, 256 … row sums 1, 41, 1681, 68921, 2825761, 115856201, …
  (−∞, 0] nonnegative
• A081578 → basis A013611
  1 · 2, 4 · 7, 28, 16 · 20, 120, 192, 64 … row sums 1, 6, 51, 396, 3141, 24786, 195831, …
  (−∞, 0] nonnegative
• A249251 → basis A013611
  1 · 4, 12 · 13, 72, 96 · 43, 348, 912, 768 … row sums 1, 16, 181, 2071, 23686, 270901, …
  (−∞, 0] nonnegative
• A038284 → basis A013611
  196, 672, 576 · 2744, 14112, 24192, 13824 … row sums 1444, 54872, 2085136, 79235168, …
  (−∞, 0] nonnegative rational roots
• A038208 → basis A013611
  1 · 4, 8 · 16, 64, 64 · 64, 384, 768, 512 … row sums 1, 12, 144, 1728, 20736, 248832, …
  (−∞, 0] nonnegative rational roots
• A034870 → basis A013611
  1 · 4, 16, 16 · 16, 128, 384, 512, 256 … row sums 1, 36, 1296, 46656, 1679616, 60466176, …
  (−∞, 0] nonnegative rational roots
• A111125 → basis A013611
  1 · 4, 4 · 11, 28, 16 · 29, 124, 160, 64 … row sums 1, 8, 55, 377, 2584, 17711, 121393, …
  (−∞, 0] nonnegative
• A102547 → x ↦ (1/27)x → basis A013611
  1 · 3 · 9 · 28, 4 … row sums 1, 3, 9, 32, 111, 378, 1294, 4437, …
  (−∞, 0] nonnegative
• A132393 → basis A013611
  1 · 1, 4 · 2, 12, 16 · 6, 44, 96, 64 … row sums 1, 5, 30, 210, 1680, 15120, 151200, …
  (−∞, 0] nonnegative rational roots
• A128813 → basis A013611
  1 · 2, 4 · 8, 40, 48 · 56, 472, 1296, 1152 … row sums 1, 6, 96, 2976, 151776, 11534976, …
  (−∞, 0] nonnegative rational roots
• A114687 → basis A013609
  1 · 3, 4 · 11, 28, 16 · 45, 168, 192, 64 … row sums 1, 7, 55, 469, 4237, 39907, 387739, …
  (−∞, 0] nonnegative
• basis-map coefficients of A112227 → basis A013611
  1, 8, 16 · 1, 12, 48, 64 · 1, 16, 96, 256, 256 … row sums 25, 125, 625, 3125, 15625, 78125, …
  (−∞, 0] nonnegative rational roots
• A038334 → basis A013611
  400, 1280, 1024 · 8000, 38400, 61440, 32768 … row sums 2704, 140608, 7311616, 380204032, …
  (−∞, 0] nonnegative rational roots
• A091042 → basis A013611
  1 · 4, 12 · 16, 80, 80 · 64, 448, 896, 448 … row sums 1, 16, 176, 1856, 19456, 203776, …
  (−∞, 0] nonnegative
• A038277 → basis A013611
  1 · 18, 44 · 324, 1584, 1936 … row sums 1, 62, 3844, 238328, 14776336, …
  (−∞, 0] nonnegative rational roots
• A038329 → basis A013611
  225, 360, 144 · 3375, 8100, 6480, 1728 … row sums 729, 19683, 531441, 14348907, …
  (−∞, 0] nonnegative rational roots
• A008955 → basis A013611
  1 · 2, 4 · 10, 52, 64 · 100, 880, 2512, 2304 … row sums 1, 6, 126, 5796, 469476, 59153976, …
  (−∞, 0] nonnegative rational roots
• basis-map coefficients of A371080, shifted → basis A013611
  1 · 1, 4 · 4, 20, 16 · 28, 156, 192, 64 … row sums 1, 5, 40, 440, 6160, 104720, 2094400, …
  (−∞, 0] nonnegative rational roots
• A013613 → basis A013611
  1 · 7, 24 · 49, 336, 576 · 343, 3528, 12096, 13824 … row sums 1, 31, 961, 29791, 923521, 28629151, …
  (−∞, 0] nonnegative rational roots
• basis-map coefficients of A113214, shifted → basis A013611
  1 · -2, -4 · 4, 16, 16 · -8, -48, -96, -64 … row sums 1, -6, 36, -216, 1296, -7776, 46656, …
  (−∞, 0] rational roots
• basis-map coefficients of A026729 → basis A013611
  1 · 1, 4 · 1, 8, 16 · 1, 12, 48, 64 … row sums 1, 5, 25, 125, 625, 3125, 15625, 78125, …
  (−∞, 0] nonnegative rational roots
• A125662 → basis A013611
  1 · 4, 4 · 15, 32, 16 · 56, 184, 192, 64 … row sums 1, 8, 63, 496, 3905, 30744, 242047, …
  (−∞, 0] nonnegative
• A038220 → basis A013611
  1 · 5, 8 · 25, 80, 64 · 125, 600, 960, 512 … row sums 1, 13, 169, 2197, 28561, 371293, …
  (−∞, 0] nonnegative rational roots
• A038337 → basis A013611
  529, 2024, 1936 · 12167, 69828, 133584, 85184 … row sums 4489, 300763, 20151121, 1350125107, …
  (−∞, 0] nonnegative rational roots
• A038320 → basis A013611
  289, 816, 576 · 4913, 20808, 29376, 13824 … row sums 1681, 68921, 2825761, 115856201, …
  (−∞, 0] nonnegative rational roots
• A063967 → basis A013611
  1 · 2, 4 · 6, 20, 16 · 16, 80, 128, 64 … row sums 1, 6, 42, 288, 1980, 13608, 93528, …
  (−∞, 0] nonnegative
• A038331 → basis A013611
  289, 680, 400 · 4913, 17340, 20400, 8000 … row sums 1369, 50653, 1874161, 69343957, …
  (−∞, 0] nonnegative rational roots
• A027467 → basis A013611
  1 · 16, 4 · 256, 128, 16 · 4096, 3072, 768, 64 … row sums 1, 20, 400, 8000, 160000, 3200000, …
  (−∞, 0] nonnegative rational roots
• A069466 → basis A013611
  1 · 4, 8 · 36, 144, 96 · 400, 2400, 3840, 1280 … row sums 1, 12, 276, 7920, 252420, 8536752, …
  (−∞, 0] nonnegative
• A064861 → basis A013611
  6, 28, 32 · 18, 132, 320, 256 … row sums 66, 726, 4356, 47916, 287496, 3162456, …
  (−∞, 0] nonnegative rational roots
• A274498 → basis A013611
  1 · 3 · 9, 24 · 27, 72 … row sums 1, 3, 33, 99, 1089, 3267, 35937, …
  (−∞, 0] nonnegative rational roots
• A116412 → basis A013611
  1 · 4, 4 · 13, 32, 16 · 43, 168, 192, 64 … row sums 1, 8, 61, 467, 3574, 27353, 209341, …
  (−∞, 0] nonnegative
• A079638 → basis A013611
  1 · 4, 4 · 24, 44, 16 · 192, 488, 336, 64 … row sums 1, 8, 84, 1080, 16344, 283680, 5544000, …
  (−∞, 0] nonnegative
• A269947 → basis A013611
  1 · 1, 4 · 2, 12, 16 · 18, 116, 192, 64 … row sums 1, 5, 30, 390, 12480, 861120, …
  (−∞, 0] nonnegative rational roots
• A013611: Triangle of coefficients in expansion of (1+4x)^n.
  1 · 1, 4 · 1, 8, 16 · 1, 12, 48, 64 … row sums 1, 5, 25, 125, 625, 3125, 15625, 78125, …
  A013611 (−∞, 0) [−1, 0] nonnegative rational roots
• A145324 → basis A013611
  1 · 3, 8 · 12, 68, 96 · 60, 532, 1568, 1536 … row sums 1, 11, 176, 3696, 96096, 2978976, …
  (−∞, 0] nonnegative rational roots