basis_map

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

1056 sequences

• A143683 → basis A008277
  1 · 2, 1 · 12, 13, 1 · 40, 83, 25, 1 … row sums 1, 3, 26, 149, 1119, 8162, 65271, …
  (−∞, 0] nonnegative
• A038284 → basis A007318
  196, 168, 36 · 2744, 3528, 1512, 216 … row sums 400, 8000, 160000, 3200000, 64000000, …
  (−∞, 0] nonnegative rational roots
• A188440 → basis A008277
  1 · 1 · 3, 2 · 3, 2 … row sums 1, 1, 5, 5, 29, 29, 193, 193, …
  (−∞, 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
• A064861 → x ↦ x+1
  6, 7, 2 · 18, 33, 20, 4 · 36, 84, 73, 28, 4 … row sums 15, 75, 225, 1125, 3375, 16875, 50625, …
  (−∞, −1] nonnegative rational roots
• A052553 → basis A013611
  1 · 1 · 2, 4 · 3, 8 … row sums 1, 1, 6, 11, 41, 96, 301, 781, …
  (−∞, 0] nonnegative
• A172431 → basis A007318
  1 · 3, 2 · 8, 10, 3 · 21, 38, 22, 4 … row sums 1, 5, 21, 85, 341, 1365, 5461, 21845, …
  (−∞, −1] nonnegative
• basis-map coefficients of Riordan array (1+2x,x(1+x)). shifted by x -> -x + 0
  1 · -1, -1 · 1, 2, 1 · -1, -3, -3, -1 … row sums 1, -2, 4, -8, 16, -32, 64, -128, …
  (−∞, −1] rational roots
• A154233 → basis A013611
  1 · 2, 4 · 9, 36, 16 · 40, 240, 352, 64 … row sums 1, 6, 61, 696, 9971, 160746, 3008531, …
  (−∞, 0] nonnegative
• A188440 → basis A013610
  1 · 1 · 3, 6 · 3, 6 … row sums 1, 1, 9, 9, 81, 81, 729, 729, …
  (−∞, 0] nonnegative rational roots
• A038323 → basis A013609
  1 · 20, 18 · 400, 720, 324 · 8000, 21600, 19440, 5832 … row sums 1, 38, 1444, 54872, 2085136, 79235168, …
  (−∞, 0] nonnegative rational roots
• A204420 → basis A013610
  1 · 1, 3 · 9, 36, 27 · 225, 1035, 1215, 405 … row sums 1, 4, 72, 2880, 201600, 21772800, …
  (−∞, 0] nonnegative rational roots
• A178820 → basis A013611
  1 · 8, 16 · 40, 160, 160 · 160, 960, 1920, 1280 … row sums 1, 24, 360, 4320, 45360, 435456, …
  (−∞, 0] nonnegative rational roots
• A038277 → basis A007318
  1 · 18, 11 · 324, 396, 121 · 5832, 10692, 6534, 1331 … row sums 1, 29, 841, 24389, 707281, 20511149, …
  (−∞, 0] nonnegative rational roots
• A001263 → basis A008277
  1 · 2, 1 · 5, 6, 1 · 14, 31, 12, 1 … row sums 1, 3, 12, 58, 323, 2014, 13793, 102351, …
  (−∞, 0] nonnegative
• A318772 → basis A013611
  1 · 1 · 1 · 1 … row sums 1, 1, 1, 1, 16, 31, 46, 61, …
  (−∞, 0] nonnegative
• A304236 → basis A013611
  1 · 1 · 4, 12 · 7, 24 … row sums 1, 1, 16, 31, 271, 736, 4801, 15841, …
  (−∞, 0] nonnegative
• A011973 → basis A013609
  1 · 1 · 2, 2 · 3, 4 … row sums 1, 1, 4, 7, 19, 40, 97, 217, …
  (−∞, 0] nonnegative
• A054142 → basis A008277
  1 · 2, 1 · 5, 6, 1 · 13, 30, 12, 1 … row sums 1, 3, 12, 56, 292, 1667, 10288, 68026, …
  (−∞, 0] nonnegative
• A317496 → basis A013611
  1 · 1 · 1 · 4, 12 … row sums 1, 1, 1, 16, 31, 46, 286, 751, …
  (−∞, 0] nonnegative
• basis-map coefficients of A026729, shifted → basis A013611
  1 · -1, -4 · 1, 8, 16 · -1, -12, -48, -64 … row sums 1, -5, 25, -125, 625, -3125, 15625, …
  (−∞, 0] rational roots
• A137320 → x ↦ x+1
  1 · 2, 2 · 6, 10, 4 · 24, 52, 36, 8 … row sums 1, 4, 20, 120, 840, 6720, 60480, …
  (−∞, −1] nonnegative rational roots
• A038279 → basis A013610
  1 · 9, 3 · 81, 54, 9 · 729, 729, 243, 27 … row sums 1, 12, 144, 1728, 20736, 248832, …
  (−∞, 0] nonnegative rational roots
• A038327 → basis A007318
  1 · 13, 1 · 169, 26, 1 · 2197, 507, 39, 1 … row sums 1, 14, 196, 2744, 38416, 537824, …
  (−∞, 0] nonnegative rational roots
• A304236 → basis A008277
  1 · 1 · 4, 3 · 7, 6 … row sums 1, 1, 7, 13, 64, 160, 706, 2107, …
  (−∞, 0] nonnegative
• A013620 → basis A013611
  1 · 5, 12 · 25, 120, 144 · 125, 900, 2160, 1728 … row sums 1, 17, 289, 4913, 83521, 1419857, …
  (−∞, 0] nonnegative rational roots
• A103633 → basis A008277
  1 · 1, 1 · 2, 4, 1 · 2, 10, 7, 1 … row sums 1, 2, 7, 20, 87, 322, 1657, 7432, …
  (−∞, 0] nonnegative
• A152828 → basis A013610
  1 · 1 · 1 · 2, 3 … row sums 1, 1, 1, 5, 5, 5, 25, 25, …
  (−∞, 0] nonnegative rational roots
• A038243: Triangle whose (i,j)-th entry is 5^(i-j)*binomial(i,j).
  1 · 5, 1 · 25, 10, 1 · 125, 75, 15, 1 … row sums 1, 6, 36, 216, 1296, 7776, 46656, …
  A038243 (−∞, −1] nonnegative rational roots
• A225470 → basis A013611
  1 · 3, 4 · 18, 36, 16 · 162, 396, 288, 64 … row sums 1, 7, 70, 910, 14560, 276640, 6086080, …
  (−∞, 0] nonnegative rational roots
• A172431 → basis A013609
  1 · 3, 4 · 8, 20, 12 · 21, 76, 88, 32 … row sums 1, 7, 40, 217, 1159, 6160, 32689, …
  (−∞, 0] nonnegative
• A286718 → basis A013611
  1 · 2, 4 · 10, 28, 16 · 80, 264, 240, 64 … row sums 1, 6, 54, 648, 9720, 174960, 3674160, …
  (−∞, 0] nonnegative rational roots
• A145324 → basis A013609
  1 · 3, 4 · 12, 34, 24 · 60, 266, 392, 192 … row sums 1, 7, 70, 910, 14560, 276640, 6086080, …
  (−∞, 0] nonnegative rational roots
• A269947 → basis A013609
  1 · 1, 2 · 2, 6, 4 · 18, 58, 48, 8 … row sums 1, 3, 12, 132, 3960, 265320, 33960960, …
  (−∞, 0] nonnegative rational roots
• A038271 → basis A007318
  1 · 12, 5 · 144, 120, 25 · 1728, 2160, 900, 125 … row sums 1, 17, 289, 4913, 83521, 1419857, …
  (−∞, 0] nonnegative rational roots
• A038301 → basis A013609
  400, 880, 484 · 8000, 26400, 29040, 10648 … row sums 1764, 74088, 3111696, 130691232, …
  (−∞, 0] nonnegative rational roots
• A128100: Triangle read by rows: T(n,k) is the number of ways to tile a 2 X n rectangle with k pieces of 2 X 2 tiles and n-2k pieces of 1 X 2 tiles (0 <= k <= floor(n/2)).
  A011973 → basis A007318
  1 · 1 · 2, 1 · 3, 2 … row sums 1, 1, 3, 5, 11, 21, 43, 85, …
  A128100 (−∞, −1] nonnegative
• A123519 → basis A008277
  11, 18, 4 · 41, 128, 68, 8 · 153, 832, 796, 216, 16 … row sums 33, 245, 2013, 18105, 176589, 1853433, …
  (−∞, 0] nonnegative
• A125662 → basis A013609
  1 · 4, 2 · 15, 16, 4 · 56, 92, 48, 8 … row sums 1, 6, 35, 204, 1189, 6930, 40391, …
  (−∞, 0] nonnegative
• A272867 → basis A013611
  1 · 6, 24, 16 · 36, 288, 768, 768, 256 … row sums 1, 46, 2116, 97336, 4477456, 205962976, …
  (−∞, 0] nonnegative
• A113214 → basis A013611
  1 · 3, 4 · 4, 20, 16 · 7, 52, 112, 64 … row sums 1, 7, 40, 235, 1375, 8050, 47125, …
  (−∞, 0] nonnegative
• A038334 → basis A013609
  400, 640, 256 · 8000, 19200, 15360, 4096 … row sums 1296, 46656, 1679616, 60466176, …
  (−∞, 0] nonnegative rational roots
• A038305 → basis A013610
  169, 234, 81 · 2197, 4563, 3159, 729 … row sums 484, 10648, 234256, 5153632, 113379904, …
  (−∞, 0] nonnegative rational roots
• A038243 → basis A013610
  1 · 6, 3 · 36, 36, 9 · 216, 324, 162, 27 … row sums 1, 9, 81, 729, 6561, 59049, 531441, …
  (−∞, 0] nonnegative rational roots
• A026729 → basis A013610
  1 · 1, 3 · 2, 9, 9 · 3, 21, 45, 27 … row sums 1, 4, 20, 96, 464, 2240, 10816, 52224, …
  (−∞, 0] nonnegative
• A085841 → basis A008277
  1 · 7, 4 · 61, 88, 16 · 547, 1596, 720, 64 … row sums 1, 11, 165, 2927, 58633, 1295123, …
  (−∞, 0] nonnegative
• A118931 → basis A008277
  1 · 1 · 1 · 3, 2 … row sums 1, 1, 1, 5, 17, 41, 281, 1541, …
  (−∞, 0] nonnegative
• A249250 → basis A013610
  1 · 4, 9 · 10, 36, 27 · 28, 144, 216, 81 … row sums 1, 13, 73, 469, 2929, 18397, 115417, …
  (−∞, 0] nonnegative
• A059364: Triangle T(n,k)=Sum_{i=0..n} |stirling1(n,n-i)|*binomial(i,k), k=0..n-1.
  1 · 2, 1 · 6, 7, 2 · 24, 46, 29, 6 … row sums 1, 3, 15, 105, 945, 10395, 135135, …
  A059364 (−∞, −1] nonnegative rational roots
• A086645 → basis A013611
  1 · 2, 4 · 8, 32, 16 · 32, 192, 288, 64 … row sums 1, 6, 56, 576, 6016, 62976, 659456, …
  (−∞, 0] nonnegative