basis_map

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

1056 sequences

• 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
• A358735 → basis A013609
  1 · 2, 2 · 7, 16, 8 · 33, 120, 136, 48 … row sums 1, 4, 31, 337, 4687, 79342, 1582153, …
  (−∞, 0] nonnegative
• A038324 → basis A007318
  1 · 21, 10 · 441, 420, 100 · 9261, 13230, 6300, 1000 … row sums 1, 31, 961, 29791, 923521, 28629151, …
  (−∞, 0] nonnegative rational roots
• A136572 → basis A008277
  1 · 1, 1 · 2, 6, 2 · 6, 42, 36, 6 … row sums 1, 2, 10, 90, 1248, 24360, 631440, …
  (−∞, 0] nonnegative
• A161198 → basis A013609
  1 · 3, 4 · 15, 32, 16 · 105, 284, 240, 64 … row sums 1, 7, 63, 693, 9009, 135135, 2297295, …
  (−∞, 0] nonnegative rational roots
• A088996 → basis A007318
  1 · 1, 1 · 3, 5, 2 · 15, 34, 25, 6 … row sums 1, 2, 10, 80, 880, 12320, 209440, …
  (−∞, 0] nonnegative rational roots
• A111125 → x ↦ x+1
  1 · 4, 1 · 11, 7, 1 · 29, 31, 10, 1 … row sums 1, 5, 19, 71, 265, 989, 3691, 13775, …
  (−5, −1) nonnegative
• A152842 → x ↦ x+1
  1 · 4, 3 · 8, 10, 3 · 32, 64, 42, 9 … row sums 1, 7, 21, 147, 441, 3087, 9261, 64827, …
  (−∞, −1] nonnegative rational roots
• A038255 → basis A013610
  1 · 7, 3 · 49, 42, 9 · 343, 441, 189, 27 … row sums 1, 10, 100, 1000, 10000, 100000, …
  (−∞, 0] nonnegative rational roots
• A038338 → basis A013610
  576, 1728, 1296 · 13824, 62208, 93312, 46656 … row sums 3600, 216000, 12960000, 777600000, …
  (−∞, 0] nonnegative rational roots
• A038331 → basis A013609
  289, 340, 100 · 4913, 8670, 5100, 1000 … row sums 729, 19683, 531441, 14348907, …
  (−∞, 0] nonnegative rational roots
• A133087 → basis A013609
  1 · 3, 2 · 4, 8, 4 · 12, 32, 28, 8 … row sums 1, 5, 16, 80, 256, 1280, 4096, 20480, …
  (−∞, 0] nonnegative rational roots
• A133214 → basis A007318
  13, 16, 4 · 63, 114, 60, 8 · 321, 768, 624, 192, 16 … row sums 33, 245, 1921, 15525, 127905, 1067925, …
  (−∞, 0] nonnegative
• A118933 → basis A013610
  1 · 1 · 1 · 1 … row sums 1, 1, 1, 1, 25, 121, 361, 841, …
  (−∞, 0] nonnegative
• A008955 → basis A007318
  1 · 2, 1 · 10, 13, 4 · 100, 220, 157, 36 … row sums 1, 3, 27, 513, 16929, 863379, 63026667, …
  (−∞, 0] nonnegative rational roots
• A038255 → basis A013609
  1 · 7, 2 · 49, 28, 4 · 343, 294, 84, 8 … row sums 1, 9, 81, 729, 6561, 59049, 531441, …
  (−∞, 0] nonnegative rational roots
• A013610: Triangle of coefficients in expansion of (1+3*x)^n.
  1 · 1, 3 · 1, 6, 9 · 1, 9, 27, 27 … row sums 1, 4, 16, 64, 256, 1024, 4096, 16384, …
  A013610 (−∞, 0) [−1, 0] nonnegative rational roots
• A100861 → basis A013609
  1 · 1 · 2, 2 · 4, 6 … row sums 1, 1, 4, 10, 46, 166, 856, 3844, …
  (−∞, 0] nonnegative
• A232535 → basis A013610
  1 · 3, 6 · 12, 42, 27 · 48, 240, 333, 108 … row sums 1, 9, 81, 729, 6561, 59049, 531441, …
  (−∞, 0] nonnegative
• A114656 → basis A007318
  1 · 3, 1 · 11, 8, 1 · 45, 51, 15, 1 … row sums 1, 4, 20, 112, 672, 4224, 27456, …
  (−∞, −1] nonnegative
• A154227 → basis A013609
  1 · 2, 2 · 10, 20, 4 · 40, 120, 88, 8 … row sums 1, 4, 34, 256, 2554, 26344, 319912, …
  (−∞, 0] nonnegative
• A152198 → basis A013610
  1 · 1 · 2, 3 · 2, 3 … row sums 1, 1, 5, 5, 25, 25, 125, 125, …
  (−∞, 0] nonnegative rational roots
• A128813 → basis A007318
  1 · 2, 1 · 8, 10, 3 · 56, 118, 81, 18 … row sums 1, 3, 21, 273, 5733, 177723, 7642089, …
  (−∞, 0] nonnegative rational roots
• A100862 → x ↦ x+1
  1 · 2, 1 · 5, 5, 1 · 14, 21, 9, 1 … row sums 1, 3, 11, 45, 201, 963, 4899, 26253, …
  (−∞, −1] nonnegative
• A110441 → basis A007318
  1 · 4, 1 · 14, 8, 1 · 48, 44, 12, 1 … row sums 1, 5, 23, 105, 479, 2185, 9967, 45465, …
  (−7, −1) nonnegative
• A130595: Triangle read by rows: lower triangular matrix which is inverse to Pascal's triangle (A007318) regarded as a lower triangular matrix.
  basis-map coefficients of A026729 → basis A130595
  1 · -1, 1 · 1, -2, 1 · -1, 3, -3, 1 … row sums 1, 0, 0, 0, 0, 0, 0, 0, …
  A130595 (−∞, ∞) rational roots
• A046716 → basis A013610
  1 · 2, 3 · 5, 15, 9 · 16, 75, 99, 27 … row sums 1, 5, 29, 217, 2297, 34349, 674965, …
  (−∞, 0] nonnegative
• A038291 → basis A013610
  1 · 10, 3 · 100, 60, 9 · 1000, 900, 270, 27 … row sums 1, 13, 169, 2197, 28561, 371293, …
  (−∞, 0] nonnegative rational roots
• A038220 → basis A008277
  1 · 5, 2 · 25, 24, 4 · 125, 218, 84, 8 … row sums 1, 7, 53, 435, 3865, 37039, 381037, …
  (−∞, 0] nonnegative
• A102547 → reverse → basis A013611
  1, 4 · 1, 8, 16 · 1, 12, 48, 64 … row sums 5, 25, 125, 750, 4375, 25000, 143750, …
  (−∞, 0] nonnegative
• A272866 → basis A013610
  1 · 5, 15, 9 · 25, 150, 315, 270, 81 … row sums 1, 29, 841, 24389, 707281, 20511149, …
  (−∞, 0] nonnegative
• A038335 → basis A007318
  1 · 21, 9 · 441, 378, 81 · 9261, 11907, 5103, 729 … row sums 1, 30, 900, 27000, 810000, 24300000, …
  (−∞, 0] nonnegative rational roots
• basis-map coefficients of A371080, shifted → basis A008277
  1 · 1, 1 · 4, 6, 1 · 28, 52, 15, 1 … row sums 1, 2, 11, 96, 1141, 17126, 310207, …
  (−∞, 0] nonnegative
• A108838 → basis A013609
  2 · 5, 4 · 14, 24, 8 · 42, 112, 84, 16 … row sums 2, 9, 46, 254, 1476, 8893, 55046, …
  (−∞, 0] nonnegative
• A102547 → x ↦ x+1
  1 · 1 · 1 · 2, 1 … row sums 1, 1, 1, 3, 5, 7, 13, 23, …
  (−∞, −1] 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
• A059364 → basis A007318
  1 · 3, 1 · 15, 11, 2 · 105, 122, 47, 6 … row sums 1, 4, 28, 280, 3640, 58240, 1106560, …
  (−∞, 0] nonnegative rational roots
• narayana → basis A007318
  1 · 2, 1 · 5, 5, 1 · 14, 21, 9, 1 … row sums 1, 3, 11, 45, 197, 903, 4279, 20793, …
  (−∞, −1] nonnegative
• A207606 → basis A008277
  13, 13, 2 · 34, 63, 23, 2 · 89, 273, 176, 35, 2 … row sums 28, 122, 575, 2916, 15825, 91434, …
  (−∞, 0] nonnegative
• A059344 → basis A013609
  1 · 1 · 3, 4 · 7, 12 … row sums 1, 1, 7, 19, 145, 601, 4951, 26587, …
  (−∞, 0] nonnegative
• A038320 → basis A007318
  289, 204, 36 · 4913, 5202, 1836, 216 … row sums 529, 12167, 279841, 6436343, 148035889, …
  (−∞, 0] nonnegative rational roots
• A145324 → basis A013610
  1 · 3, 6 · 12, 51, 54 · 60, 399, 882, 648 … row sums 1, 9, 117, 1989, 41769, 1044225, …
  (−∞, 0] nonnegative rational roots
• A371080: Triangle read by rows: BellMatrix(Product_{p in P(n)} p), where P(n) = {k : k mod m = 1 and 1 <= k <= m*(n + 1)} and m = 3.
  basis-map coefficients of A371080, shifted → x ↦ x−1 → basis A008277
  1 · 0, 1 · 0, 4, 1 · 0, 28, 12, 1 … row sums 1, 1, 5, 41, 465, 6721, 117941, …
  A371080 (−∞, 0] nonnegative
• A118931 → basis A013611
  1 · 1 · 1 · 3, 8 … row sums 1, 1, 1, 11, 41, 101, 1201, 7351, …
  (−∞, 0] nonnegative
• A152830 → x ↦ x+1
  1 · 1 · 1 · 1 … row sums 1, 1, 1, 1, 3, 3, 3, 3, …
  (−∞, −1] nonnegative rational roots
• 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
• A318772 → x ↦ (1/243)x → basis A013611
  1 · 3 · 9 · 27 … row sums 1, 3, 9, 27, 86, 273, 864, 2727, …
  (−∞, 0] nonnegative
• 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