basis_map

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

1056 sequences

• basis-map coefficients of A026729 → basis A013609
  1 · 1, 2 · 1, 4, 4 · 1, 6, 12, 8 … row sums 1, 3, 9, 27, 81, 243, 729, 2187, …
  (−∞, 0] nonnegative rational roots
• A130534 → basis A013610
  1 · 2, 3 · 6, 15, 9 · 24, 78, 81, 27 … row sums 1, 5, 30, 210, 1680, 15120, 151200, …
  (−∞, 0] nonnegative rational roots
• A008288 → basis A008277
  1 · 2, 1 · 5, 6, 1 · 12, 27, 11, 1 … row sums 1, 3, 12, 51, 237, 1190, 6415, 36899, …
  (−∞, 0] nonnegative
• A007318: Binomial
  1 · 1, 1 · 1, 2, 1 · 1, 3, 3, 1 … row sums 1, 2, 4, 8, 16, 32, 64, 128, …
  A007318 (−∞, −1] nonnegative rational roots
• A130123 → basis A013611
  1 · 2, 8 · 4, 32, 64 · 8, 96, 384, 512 … row sums 1, 10, 100, 1000, 10000, 100000, …
  (−∞, 0] nonnegative rational roots
• A099093 → basis A013610
  1 · 3, 9 · 12, 63, 81 · 45, 351, 891, 729 … row sums 1, 12, 156, 2016, 26064, 336960, …
  (−∞, 0] nonnegative
• A159854 → basis A013610
  1, 6, 9 · 2, 15, 36, 27 · 4, 36, 117, 162, 81 … row sums 16, 80, 400, 2000, 10000, 50000, …
  (−∞, 0] nonnegative rational roots
• basis-map coefficients of A112227 → basis A008277
  1, 3, 1 · 1, 7, 6, 1 · 1, 15, 25, 10, 1 … row sums 5, 15, 52, 203, 877, 4140, 21147, …
  (−∞, 0] nonnegative
• A081580 → basis A013609
  1 · 2, 2 · 9, 18, 4 · 28, 84, 64, 8 … row sums 1, 4, 31, 184, 1201, 7564, 48271, …
  (−∞, 0] nonnegative
• basis-map coefficients of A113214, shifted → basis A013609
  1 · -2, -2 · 4, 8, 4 · -8, -24, -24, -8 … row sums 1, -4, 16, -64, 256, -1024, 4096, …
  (−∞, 0] rational roots
• A100861 → basis A008277
  1 · 1 · 2, 1 · 4, 3 … row sums 1, 1, 3, 7, 28, 96, 481, 2143, …
  (−∞, 0] nonnegative
• A102547 → x ↦ (1/27)x → x ↦ x+1
  1 · 3 · 9 · 28, 1 … row sums 1, 3, 9, 29, 93, 297, 949, 3033, …
  (−∞, −1] nonnegative
• A196347: Triangle T(n, k) read by rows, T(n, k) = n!*binomial(n, k).
  1 · 1, 1 · 2, 4, 2 · 6, 18, 18, 6 … row sums 1, 2, 8, 48, 384, 3840, 46080, 645120, …
  A196347 (−∞, −1] nonnegative rational roots
• A126216 → basis A013610
  1 · 3, 3 · 11, 21, 9 · 45, 126, 108, 27 … row sums 1, 6, 41, 306, 2426, 20076, 171481, …
  (−∞, 0] nonnegative
• basis-map coefficients of A021012 → basis A008277
  1 · -1, -1 · 2, 6, 2 · -6, -42, -36, -6 … row sums 1, -2, 10, -90, 1248, -24360, 631440, …
  (−∞, 0]
• A081579 → basis A013611
  1 · 2, 4 · 8, 32, 16 · 24, 144, 224, 64 … row sums 1, 6, 56, 456, 3856, 32256, 270656, …
  (−∞, 0] nonnegative
• A232535 → x ↦ x+1
  1 · 3, 2 · 12, 14, 3 · 48, 80, 37, 4 … row sums 1, 5, 29, 169, 985, 5741, 33461, …
  (−∞, −1] nonnegative
• A008288 → basis A013611
  1 · 2, 4 · 5, 20, 16 · 12, 72, 128, 64 … row sums 1, 6, 41, 276, 1861, 12546, 84581, …
  (−∞, 0] nonnegative
• A085880 → basis A013610
  1 · 2, 3 · 8, 24, 18 · 40, 180, 270, 135 … row sums 1, 5, 50, 625, 8750, 131250, 2062500, …
  (−∞, 0] nonnegative rational roots
• A196347 → basis A013611
  1 · 2, 4 · 8, 32, 32 · 48, 288, 576, 384 … row sums 1, 6, 72, 1296, 31104, 933120, …
  (−∞, 0] nonnegative rational roots
• A027467 → basis A008277
  1 · 16, 1 · 256, 33, 1 · 4096, 817, 51, 1 … row sums 1, 17, 290, 4965, 85327, 1472228, …
  (−∞, 0] nonnegative
• A038319 → basis A013609
  256, 320, 100 · 4096, 7680, 4800, 1000 … row sums 676, 17576, 456976, 11881376, …
  (−∞, 0] nonnegative rational roots
• A156992 → basis A013609
  1 · 4, 4 · 24, 48, 24 · 192, 576, 576, 192 … row sums 1, 8, 96, 1536, 30720, 737280, …
  (−∞, 0] nonnegative rational roots
• A113413 → basis A013611
  1 · 3, 4 · 7, 24, 16 · 17, 92, 144, 64 … row sums 1, 7, 47, 317, 2137, 14407, 97127, …
  (−∞, 0] nonnegative
• A391533 → basis A013611
  9, 24, 16 · 18, 84, 128, 64 · 36, 240, 592, 640, 256 … row sums 49, 294, 1764, 10584, 63504, 381024, …
  (−∞, 0] nonnegative rational roots
• A013611 → basis A007318
  1 · 5, 4 · 25, 40, 16 · 125, 300, 240, 64 … row sums 1, 9, 81, 729, 6561, 59049, 531441, …
  (−∞, −1] nonnegative rational roots
• A196347 → basis A008277
  1 · 2, 1 · 8, 10, 2 · 48, 114, 54, 6 … row sums 1, 3, 20, 222, 3624, 80880, 2349360, …
  (−∞, 0] nonnegative
• A081579 → basis A013610
  1 · 2, 3 · 8, 24, 9 · 24, 108, 126, 27 … row sums 1, 5, 41, 285, 2081, 14965, 108121, …
  (−∞, 0] nonnegative
• A059473 → basis A013611
  1 · 4, 8 · 18, 72, 64 · 80, 480, 896, 512 … row sums 1, 12, 154, 1968, 25156, 321552, …
  (−∞, 0] nonnegative
• A085478 → x ↦ x+1
  1 · 1 · 2, 1 · 5, 5, 1 … row sums 1, 1, 3, 11, 41, 153, 571, 2131, …
  (−5, −1) nonnegative
• A108838 → basis A008277
  2 · 5, 2 · 14, 14, 2 · 42, 79, 27, 2 … row sums 2, 7, 30, 150, 850, 5348, 36790, …
  (−∞, 0] nonnegative
• A317496 → basis A008277
  1 · 1 · 1 · 4, 3 … row sums 1, 1, 1, 7, 13, 19, 70, 166, …
  (−∞, 0] nonnegative
• A033282 → basis A013611
  1 · 3, 8 · 11, 60, 80 · 45, 372, 1008, 896 … row sums 1, 11, 151, 2321, 38221, 659351, …
  (−∞, 0] nonnegative
• A038314 → basis A013610
  484, 1584, 1296 · 10648, 52272, 85536, 46656 … row sums 3364, 195112, 11316496, 656356768, …
  (−∞, 0] nonnegative rational roots
• A038208: Triangle whose (i,j)-th entry is binomial(i,j)*2^i.
  1 · 2, 2 · 4, 8, 4 · 8, 24, 24, 8 … row sums 1, 4, 16, 64, 256, 1024, 4096, 16384, …
  A038208 (−∞, −1] nonnegative rational roots
• A038323 → basis A007318
  1 · 20, 9 · 400, 360, 81 · 8000, 10800, 4860, 729 … row sums 1, 29, 841, 24389, 707281, 20511149, …
  (−∞, 0] nonnegative rational roots
• A046716 → basis A013611
  1 · 2, 4 · 5, 20, 16 · 16, 100, 176, 64 … row sums 1, 6, 41, 356, 4401, 78826, 1893481, …
  (−∞, 0] nonnegative
• A274496 → x ↦ x+1
  1 · 2 · 4, 2 · 8, 4 … row sums 1, 2, 6, 12, 36, 72, 216, 432, …
  (−∞, −1] nonnegative rational roots
• delannoy → basis A013611
  1 · 2, 4 · 5, 20, 16 · 12, 72, 128, 64 … row sums 1, 6, 41, 276, 1861, 12546, 84581, …
  (−∞, 0] nonnegative
• A154228 → basis A013611
  1 · 2, 4 · 18, 72, 16 · 96, 576, 800, 64 … row sums 1, 6, 106, 1536, 38366, 929076, …
  (−∞, 0] nonnegative
• A094638 → basis A013610
  1 · 2, 3 · 6, 21, 18 · 24, 138, 261, 162 … row sums 1, 5, 45, 585, 9945, 208845, 5221125, …
  (−∞, 0] nonnegative rational roots
• A130123 → basis A013610
  1 · 2, 6 · 4, 24, 36 · 8, 72, 216, 216 … row sums 1, 8, 64, 512, 4096, 32768, 262144, …
  (−∞, 0] nonnegative rational roots
• A013612 → basis A013609
  36, 120, 100 · 216, 1080, 1800, 1000 … row sums 256, 4096, 65536, 1048576, 16777216, …
  (−∞, 0] nonnegative rational roots
• A123519 → basis A013609
  11, 28, 16 · 41, 152, 176, 64 … row sums 55, 433, 3409, 26839, 211303, 1663585, …
  (−∞, 0] nonnegative
• A091044 → basis A008277
  1 · 4, 2 · 16, 19, 3 · 64, 140, 52, 4 … row sums 1, 6, 38, 260, 1915, 15084, 126253, …
  (−∞, 0] nonnegative
• A290319 → basis A008277
  1 · 2, 1 · 12, 9, 1 · 120, 111, 21, 1 … row sums 1, 3, 22, 253, 3951, 77866, 1851943, …
  (−∞, 0] nonnegative
• A113413 → basis A013609
  1 · 3, 2 · 7, 12, 4 · 17, 46, 36, 8 … row sums 1, 5, 23, 107, 497, 2309, 10727, 49835, …
  (−∞, 0] nonnegative
• A085880 → basis A008277
  1 · 2, 1 · 8, 10, 2 · 40, 95, 45, 5 … row sums 1, 3, 20, 185, 2114, 28308, 430716, …
  (−∞, 0] nonnegative
• A122542 → basis A013611
  1 · 1, 4 · 3, 16, 16 · 7, 52, 112, 64 … row sums 1, 5, 35, 235, 1585, 10685, 72035, …
  (−∞, 0] nonnegative
• A133087: A133080 * A007318.
  1 · 2, 1 · 1, 2, 1 · 2, 5, 4, 1 … row sums 1, 3, 4, 12, 16, 48, 64, 192, …
  A133087 (−∞, −1] nonnegative rational roots