basis_map / A013611

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

210 sequences

• A013618 → basis A013611
  144, 1056, 1936 · 1728, 19008, 69696, 85184 … row sums 3136, 175616, 9834496, 550731776, …
  (−∞, 0] nonnegative rational roots
• A113953 → basis A013611
  1 · 1, 4 · 3, 16, 16 · 5, 44, 112, 64 … row sums 1, 5, 35, 225, 1475, 9625, 62875, …
  (−∞, 0] nonnegative
• A001263 → basis A013611
  1 · 2, 4 · 5, 20, 16 · 14, 84, 144, 64 … row sums 1, 6, 41, 306, 2426, 20076, 171481, …
  (−∞, 0] nonnegative
• A110441 → basis A013611
  1 · 4, 4 · 14, 32, 16 · 48, 176, 192, 64 … row sums 1, 8, 62, 480, 3716, 28768, 222712, …
  (−∞, 0] nonnegative
• A100861 → basis A013611
  1 · 1 · 2, 4 · 4, 12 … row sums 1, 1, 6, 16, 106, 426, 3076, 15856, …
  (−∞, 0] nonnegative
• A038271 → basis A013611
  1 · 12, 20 · 144, 480, 400 · 1728, 8640, 14400, 8000 … row sums 1, 32, 1024, 32768, 1048576, 33554432, …
  (−∞, 0] nonnegative rational roots
• A010054: a(n) = 1 if n is a triangular number, otherwise 0.
  1 · 1 · 1 · 1 … row sums 1, 1, 1, 1, 1, 1, 1, 1, …
  A010054 (−∞, −1] [−1, 0] [−3−2√2, −3+2√2] nonnegative rational roots
• narayana → basis A013611
  1 · 2, 4 · 5, 20, 16 · 14, 84, 144, 64 … row sums 1, 6, 41, 306, 2426, 20076, 171481, …
  (−∞, 0] nonnegative
• A038333 → basis A013611
  361, 1064, 784 · 6859, 30324, 44688, 21952 … row sums 2209, 103823, 4879681, 229345007, …
  (−∞, 0] nonnegative rational roots
• A038326 → basis A013611
  1 · 23, 48 · 529, 2208, 2304 … row sums 1, 71, 5041, 357911, 25411681, …
  (−∞, 0] nonnegative rational roots
• A114656 → basis A013611
  1 · 3, 4 · 11, 32, 16 · 45, 204, 240, 64 … row sums 1, 7, 59, 553, 5541, 58107, 629799, …
  (−∞, 0] nonnegative
• A013611 → basis A013611
  1 · 5, 16 · 25, 160, 256 · 125, 1200, 3840, 4096 … row sums 1, 21, 441, 9261, 194481, 4084101, …
  (−∞, 0] nonnegative rational roots
• A169803 → basis A013611
  1 · 2, 4 · 3, 8 · 5, 20, 16 … row sums 1, 6, 11, 41, 96, 301, 781, 2286, …
  (−∞, 0] nonnegative
• A038243 → basis A013611
  1 · 6, 4 · 36, 48, 16 · 216, 432, 288, 64 … row sums 1, 10, 100, 1000, 10000, 100000, …
  (−∞, 0] nonnegative rational roots
• A103633 → basis A013611
  1 · 1, 4 · 2, 12, 16 · 2, 20, 64, 64 … row sums 1, 5, 30, 150, 900, 4500, 27000, …
  (−∞, 0] nonnegative rational roots
• A121574 → basis A013611
  1 · 3, 4 · 10, 28, 16 · 33, 140, 176, 64 … row sums 1, 7, 54, 413, 3161, 24192, 185149, …
  (−∞, 0] nonnegative
• A172431 → basis A013611
  1 · 3, 8 · 8, 40, 48 · 21, 152, 352, 256 … row sums 1, 11, 96, 781, 6191, 48576, 379561, …
  (−∞, 0] nonnegative
• A130123 → basis A013609
  1 · 2, 4 · 4, 16, 16 · 8, 48, 96, 64 … row sums 1, 6, 36, 216, 1296, 7776, 46656, …
  (−∞, 0] nonnegative rational roots
• A156992 → basis A013611
  1 · 4, 8 · 24, 96, 96 · 192, 1152, 2304, 1536 … row sums 1, 12, 216, 5184, 155520, 5598720, …
  (−∞, 0] nonnegative rational roots
• A145597 → basis A013611
  1 · 6, 12 · 27, 108, 96 · 110, 660, 1200, 640 … row sums 1, 18, 231, 2610, 27765, 286146, …
  (−∞, 0] nonnegative
• A120910 → basis A013611
  3 · 9, 12 · 27, 72, 48 · 81, 324, 432, 192 … row sums 3, 21, 147, 1029, 7203, 50421, 352947, …
  (−∞, 0] nonnegative rational roots
• A143683 → basis A013611
  1 · 2, 4 · 12, 48, 16 · 40, 240, 352, 64 … row sums 1, 6, 76, 696, 7216, 71136, 715456, …
  (−∞, 0] nonnegative
• A133214 → basis A013611
  13, 64, 64 · 63, 456, 960, 512 … row sums 141, 1991, 29761, 460251, 7272861, …
  (−∞, 0] nonnegative
• A038321 → basis A013611
  324, 1008, 784 · 5832, 27216, 42336, 21952 … row sums 2116, 97336, 4477456, 205962976, …
  (−∞, 0] nonnegative rational roots
• A152198 → basis A013611
  1 · 1 · 2, 4 · 2, 4 … row sums 1, 1, 6, 6, 36, 36, 216, 216, …
  (−∞, 0] nonnegative rational roots
• A356546 → basis A013611
  1 · 4, 8 · 24, 96, 96 · 160, 960, 1920, 1280 … row sums 1, 12, 216, 4320, 90720, 1959552, …
  (−∞, 0] nonnegative rational roots
• A038323 → basis A013611
  1 · 20, 36 · 400, 1440, 1296 … row sums 1, 56, 3136, 175616, 9834496, …
  (−∞, 0] nonnegative rational roots
• 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
• 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
• 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
• 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
• A038301 → basis A013611
  400, 1760, 1936 · 8000, 52800, 116160, 85184 … row sums 4096, 262144, 16777216, 1073741824, …
  (−∞, 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
• A108838 → basis A013611
  2 · 5, 8 · 14, 48, 32 · 42, 224, 336, 128 … row sums 2, 13, 94, 730, 5956, 50357, 437318, …
  (−∞, 0] nonnegative
• 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
• A154227 → basis A013611
  1 · 2, 4 · 10, 40, 16 · 40, 240, 352, 64 … row sums 1, 6, 66, 696, 9126, 127836, 2044656, …
  (−∞, 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
• A104684 → basis A013611
  1 · 3, 4 · 13, 32, 16 · 63, 228, 240, 64 … row sums 1, 7, 61, 595, 6145, 65527, 712909, …
  (−∞, 0] nonnegative
• 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
• A204420 → basis A013611
  1 · 1, 4 · 9, 48, 48 · 225, 1380, 2160, 960 … row sums 1, 5, 105, 4725, 363825, 42567525, …
  (−∞, 0] nonnegative rational roots
• A102547 → reverse → basis A013611
  1, 4 · 1, 8, 16 · 1, 12, 48, 64 … row sums 5, 25, 125, 750, 4375, 25000, 143750, …
  (−∞, 0] nonnegative
• basis-map coefficients of A021012 → basis A013611
  1 · -1, -4 · 2, 16, 32 · -6, -72, -288, -384 … row sums 1, -5, 50, -750, 15000, -375000, …
  (−∞, 0] rational roots
• A118931 → basis A013611
  1 · 1 · 1 · 3, 8 … row sums 1, 1, 1, 11, 41, 101, 1201, 7351, …
  (−∞, 0] nonnegative
• A318772 → x ↦ (1/243)x → basis A013611
  1 · 3 · 9 · 27 … row sums 1, 3, 9, 27, 86, 273, 864, 2727, …
  (−∞, 0] nonnegative
• A094816 → basis A013611
  1 · 2, 4 · 5, 20, 16 · 16, 92, 144, 64 … row sums 1, 6, 41, 316, 2721, 25946, 271801, …
  (−∞, 0] nonnegative
• A052553 → basis A013611
  1 · 1 · 2, 4 · 3, 8 … row sums 1, 1, 6, 11, 41, 96, 301, 781, …
  (−∞, 0] nonnegative