basis_map

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

1056 sequences

• A028338 → basis A008277
  1 · 2, 1 · 8, 7, 1 · 48, 57, 15, 1 … row sums 1, 3, 16, 121, 1179, 14026, 196783, …
  (−∞, 0] nonnegative
• A038271 → basis A013610
  1 · 12, 15 · 144, 360, 225 · 1728, 6480, 8100, 3375 … row sums 1, 27, 729, 19683, 531441, 14348907, …
  (−∞, 0] nonnegative rational roots
• A113214 → basis A013610
  1 · 3, 3 · 4, 15, 9 · 7, 39, 63, 27 … row sums 1, 6, 28, 136, 656, 3168, 15296, 73856, …
  (−∞, 0] nonnegative
• A196347 → basis A013609
  1 · 2, 2 · 8, 16, 8 · 48, 144, 144, 48 … row sums 1, 4, 32, 384, 6144, 122880, 2949120, …
  (−∞, 0] nonnegative rational roots
• A121574 → basis A013609
  1 · 3, 2 · 10, 14, 4 · 33, 70, 44, 8 … row sums 1, 5, 28, 155, 859, 4760, 26377, …
  (−∞, 0] nonnegative
• A102547 → reverse → basis A013609
  1, 2 · 1, 4, 4 · 1, 6, 12, 8 · 2, 14, 36, 40, 16 … row sums 3, 9, 27, 108, 405, 1458, 5346, 19683, …
  (−∞, 0] nonnegative
• A132393 → basis A013610
  1 · 1, 3 · 2, 9, 9 · 6, 33, 54, 27 … row sums 1, 4, 20, 120, 840, 6720, 60480, …
  (−∞, 0] nonnegative rational roots
• A038326 → basis A013610
  1 · 23, 36 · 529, 1656, 1296 … row sums 1, 59, 3481, 205379, 12117361, …
  (−∞, 0] nonnegative rational roots
• A069466 → basis A013609
  1 · 4, 4 · 36, 72, 24 · 400, 1200, 960, 160 … row sums 1, 8, 132, 2720, 62020, 1497888, …
  (−∞, 0] nonnegative
• A038281 → basis A008277
  121, 75, 9 · 1331, 1413, 378, 27 … row sums 205, 3149, 50836, 863057, 15404437, …
  (−∞, 0] nonnegative
• A038319 → basis A007318
  256, 160, 25 · 4096, 3840, 1200, 125 … row sums 441, 9261, 194481, 4084101, 85766121, …
  (−∞, 0] nonnegative rational roots
• A028338 → basis A013611
  1 · 2, 4 · 8, 24, 16 · 48, 176, 192, 64 … row sums 1, 6, 48, 480, 5760, 80640, 1290240, …
  (−∞, 0] nonnegative rational roots
• A028338 → basis A013610
  1 · 2, 3 · 8, 18, 9 · 48, 132, 108, 27 … row sums 1, 5, 35, 315, 3465, 45045, 675675, …
  (−∞, 0] nonnegative rational roots
• basis-map coefficients of A112227 → x ↦ x+1
  1, 2, 1 · 1, 3, 3, 1 · 1, 4, 6, 4, 1 … row sums 4, 8, 16, 32, 64, 128, 256, 512, …
  (−∞, −1] nonnegative rational roots
• A207606 → basis A007318
  13, 11, 2 · 34, 44, 17, 2 · 89, 155, 93, 23, 2 … row sums 26, 97, 362, 1351, 5042, 18817, 70226, …
  (−5, −1) nonnegative
• A207607 → basis A013610
  1 · 3, 6 · 8, 27, 18 · 21, 99, 135, 54 … row sums 1, 9, 53, 309, 1801, 10497, 61181, …
  (−∞, 0] nonnegative
• A038330 → basis A013609
  256, 256, 64 · 4096, 6144, 3072, 512 … row sums 576, 13824, 331776, 7962624, 191102976, …
  (−∞, 0] nonnegative rational roots
• A290319 → basis A013609
  1 · 2, 2 · 12, 16, 4 · 120, 184, 72, 8 … row sums 1, 4, 32, 384, 6144, 122880, 2949120, …
  (−∞, 0] nonnegative rational roots
• A207823 → basis A008277
  1 · 5, 1 · 24, 11, 1 · 115, 89, 18, 1 … row sums 1, 6, 36, 223, 1430, 9505, 65534, …
  (−∞, 0] nonnegative
• A033282 → basis A008288
  1 · 3, 2 · 11, 20, 5 · 45, 142, 91, 14 … row sums 1, 5, 36, 292, 2535, 23051, 216736, …
  [−3−2√2, −3+2√2] nonnegative
• A082985 → basis A013611
  1 · 4, 12 · 11, 60, 80 · 29, 224, 560, 448 … row sums 1, 16, 151, 1261, 10096, 79531, 622441, …
  (−∞, 0] nonnegative
• A161198 → basis A008277
  1 · 3, 2 · 15, 20, 4 · 105, 210, 84, 8 … row sums 1, 5, 39, 407, 5281, 81597, 1459015, …
  (−∞, 0] nonnegative
• A272866 → basis A008277
  1 · 5, 6, 1 · 25, 96, 72, 16, 1 … row sums 1, 12, 210, 5108, 163540, 6612400, …
  (−∞, 0] nonnegative
• A156992 → basis A007318
  1 · 4, 2 · 24, 24, 6 · 192, 288, 144, 24 … row sums 1, 6, 54, 648, 9720, 174960, 3674160, …
  (−∞, 0] nonnegative rational roots
• A063007 → basis A013609
  1 · 3, 4 · 13, 36, 24 · 63, 264, 360, 160 … row sums 1, 7, 73, 847, 10321, 129367, 1651609, …
  (−∞, 0] nonnegative
• delannoy
  1 · 1, 1 · 1, 3, 1 · 1, 5, 5, 1 … row sums 1, 2, 5, 12, 29, 70, 169, 408, …
  [−3−2√2, −3+2√2] nonnegative
• A038303 → basis A013611
  1 · 11, 4 · 121, 88, 16 · 1331, 1452, 528, 64 … row sums 1, 15, 225, 3375, 50625, 759375, …
  (−∞, 0] nonnegative rational roots
• A327997 → basis A007318
  1 · 4, 1 · 17, 9, 1 · 78, 65, 15, 1 … row sums 1, 5, 27, 159, 1029, 7353, 58095, …
  (−∞, 0] nonnegative
• A038337 → basis A008277
  529, 627, 121 · 12167, 27137, 12342, 1331 … row sums 1277, 52977, 2415172, 120107065, …
  (−∞, 0] nonnegative
• A133214 → basis A013609
  13, 32, 16 · 63, 228, 240, 64 … row sums 61, 595, 6145, 65527, 712909, 7863667, …
  (−∞, 0] nonnegative
• A038324: Triangle read by rows whose (i,j)-th entry is binomial(i,j)*11^(i-j)*10^j.
  1 · 11, 10 · 121, 220, 100 · 1331, 3630, 3300, 1000 … row sums 1, 21, 441, 9261, 194481, 4084101, …
  A038324 (−∞, 0) nonnegative rational roots
• A011973 → basis A013611
  1 · 1 · 2, 4 · 3, 8 … row sums 1, 1, 6, 11, 41, 96, 301, 781, …
  (−∞, 0] nonnegative
• A249252 → basis A013611
  1 · 5, 16 · 17, 96, 128 · 61, 496, 1280, 1024 … row sums 1, 21, 241, 2861, 33881, 401301, …
  (−∞, 0] nonnegative
• A143685 → basis A013610
  1 · 2, 3 · 13, 39, 9 · 44, 198, 216, 27 … row sums 1, 5, 61, 485, 4621, 40565, 369181, …
  (−∞, 0] nonnegative
• A026729 → basis A013611
  1 · 1, 4 · 2, 12, 16 · 3, 28, 80, 64 … row sums 1, 5, 30, 175, 1025, 6000, 35125, …
  (−∞, 0] nonnegative
• A038324 → basis A008277
  1 · 21, 10 · 441, 520, 100 · 9261, 20530, 9300, 1000 … row sums 1, 31, 1061, 40091, 1664121, 75330151, …
  (−∞, 0] nonnegative
• A103633 → basis A013609
  1 · 1, 2 · 2, 6, 4 · 2, 10, 16, 8 … row sums 1, 3, 12, 36, 144, 432, 1728, 5184, …
  (−∞, 0] nonnegative rational roots
• A200536 → basis A008277
  1 · 6, 9, 2 · 36, 189, 185, 52, 4 … row sums 1, 17, 466, 18885, 1046095, 75051180, …
  (−∞, 0] nonnegative
• A100861 → basis A013610
  1 · 1 · 2, 3 · 4, 9 … row sums 1, 1, 5, 13, 73, 281, 1741, 8485, …
  (−∞, 0] nonnegative
• A133087 → x ↦ x+1
  1 · 3, 1 · 4, 4, 1 · 12, 16, 7, 1 … row sums 1, 4, 9, 36, 81, 324, 729, 2916, …
  (−∞, −1] nonnegative rational roots
• A135838 → basis A013609
  1 · 4, 4 · 8, 16, 8 · 32, 96, 96, 32 … row sums 1, 8, 32, 256, 1024, 8192, 32768, …
  (−∞, 0] nonnegative rational roots
• A038327 → basis A013610
  1 · 13, 3 · 169, 78, 9 · 2197, 1521, 351, 27 … row sums 1, 16, 256, 4096, 65536, 1048576, …
  (−∞, 0] nonnegative rational roots
• A094638 → basis A013611
  1 · 2, 4 · 6, 28, 32 · 24, 184, 464, 384 … row sums 1, 6, 66, 1056, 22176, 576576, …
  (−∞, 0] nonnegative rational roots
• A048993: Triangle of Stirling numbers of 2nd kind, S(n,k), n >= 0, 0 <= k <= n.
  A106800 → reverse (shift +1)
  1 · 0, 1 · 0, 1, 1 · 0, 1, 3, 1 … row sums 1, 1, 2, 5, 15, 52, 203, 877, …
  A048993 (−∞, 0] nonnegative
• A085880 → basis A013611
  1 · 2, 4 · 8, 32, 32 · 40, 240, 480, 320 … row sums 1, 6, 72, 1080, 18144, 326592, 6158592, …
  (−∞, 0] nonnegative rational roots
• A013611 → basis A008277
  1 · 5, 4 · 25, 56, 16 · 125, 604, 432, 64 … row sums 1, 9, 97, 1225, 17665, 284873, 5059553, …
  (−∞, 0] nonnegative
• A059473 → basis A013610
  1 · 4, 6 · 18, 54, 36 · 80, 360, 504, 216 … row sums 1, 10, 108, 1160, 12464, 133920, …
  (−∞, 0] nonnegative
• A078812 → basis A008277
  1 · 3, 1 · 8, 7, 1 · 21, 35, 12, 1 … row sums 1, 4, 16, 69, 322, 1619, 8722, 50078, …
  (−∞, 0] nonnegative
• A011973 → x ↦ x+2 (shift +1) → basis A013609
  1 · 4, 2 · 7, 4 · 19, 18, 4 … row sums 1, 6, 11, 41, 96, 301, 781, 2286, …
  (−∞, 0] nonnegative
• A011973 → x ↦ x+2 (shift +1) → basis A007318
  1 · 4, 1 · 7, 2 · 19, 9, 1 … row sums 1, 5, 9, 29, 65, 181, 441, 1165, …
  (−∞, −1] nonnegative