basis_map

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

1056 sequences

• A154227 → basis A013610
  1 · 2, 3 · 10, 30, 9 · 40, 180, 198, 27 … row sums 1, 5, 49, 445, 5165, 63205, 894505, …
  (−∞, 0] nonnegative
• A078812 → basis A007318
  1 · 3, 1 · 8, 6, 1 · 21, 25, 9, 1 … row sums 1, 4, 15, 56, 209, 780, 2911, 10864, …
  (−5, −1) nonnegative
• A038303 → basis A008277
  1 · 11, 1 · 121, 23, 1 · 1331, 397, 36, 1 … row sums 1, 12, 145, 1765, 21652, 267803, …
  (−∞, 0] nonnegative
• A038327 → basis A013609
  1 · 13, 2 · 169, 52, 4 · 2197, 1014, 156, 8 … row sums 1, 15, 225, 3375, 50625, 759375, …
  (−∞, 0] nonnegative rational roots
• A013610 → basis A007318
  1 · 4, 3 · 16, 24, 9 · 64, 144, 108, 27 … row sums 1, 7, 49, 343, 2401, 16807, 117649, …
  (−∞, −1] nonnegative rational roots
• A085880 → basis A013609
  1 · 2, 2 · 8, 16, 8 · 40, 120, 120, 40 … row sums 1, 4, 32, 320, 3584, 43008, 540672, …
  (−∞, 0] nonnegative rational roots
• A147716 → basis A013609
  1 · 15, 2 · 225, 60, 4 · 3375, 1350, 180, 8 … row sums 1, 17, 289, 4913, 83521, 1419857, …
  (−∞, 0] nonnegative rational roots
• A344565 → basis A007318
  3 · 30, 15 · 180, 180, 45 · 840, 1260, 630, 105 … row sums 3, 45, 405, 2835, 17010, 91854, 459270, …
  (−∞, −1] nonnegative rational roots
• A038324 → basis A013611
  1 · 21, 40 · 441, 1680, 1600 … row sums 1, 61, 3721, 226981, 13845841, …
  (−∞, 0] nonnegative rational roots
• A013610 → basis A008277
  1 · 4, 3 · 16, 33, 9 · 64, 279, 189, 27 … row sums 1, 7, 58, 559, 6127, 74920, 1007299, …
  (−∞, 0] nonnegative
• A013618 → basis A013610
  144, 792, 1089 · 1728, 14256, 39204, 35937 … row sums 2025, 91125, 4100625, 184528125, …
  (−∞, 0] nonnegative rational roots
• A100862 → basis A013609
  1 · 2, 2 · 5, 10, 4 · 14, 42, 36, 8 … row sums 1, 4, 19, 100, 571, 3484, 22501, …
  (−∞, 0] nonnegative
• basis-map coefficients of A297191, shifted → basis A013610
  1 · 1, 6, 9 · 1, 12, 54, 108, 81 … row sums 1, 16, 256, 4096, 65536, 1048576, …
  (−∞, 0] nonnegative rational roots
• A143685 → basis A013609
  1 · 2, 2 · 13, 26, 4 · 44, 132, 96, 8 … row sums 1, 4, 43, 280, 2281, 16684, 128323, …
  (−∞, 0] nonnegative
• A232535 → basis A013611
  1 · 3, 8 · 12, 56, 48 · 48, 320, 592, 256 … row sums 1, 11, 116, 1216, 12736, 133376, …
  (−∞, 0] nonnegative
• A122542 → x ↦ x+1
  1 · 1, 1 · 3, 4, 1 · 7, 13, 7, 1 … row sums 1, 2, 8, 28, 100, 356, 1268, 4516, …
  (−∞, −1] nonnegative
• A081582 → basis A013610
  1 · 2, 3 · 11, 33, 9 · 36, 162, 180, 27 … row sums 1, 5, 53, 405, 3509, 28885, 242677, …
  (−∞, 0] nonnegative
• A154233 → basis A008277
  1 · 2, 1 · 9, 10, 1 · 40, 83, 25, 1 … row sums 1, 3, 20, 149, 1571, 19150, 290081, …
  (−∞, 0] nonnegative
• A063007 → basis A013610
  1 · 3, 6 · 13, 54, 54 · 63, 396, 810, 540 … row sums 1, 9, 121, 1809, 28401, 458649, …
  (−∞, 0] nonnegative
• A204420 → basis A008277
  1 · 1, 1 · 9, 15, 3 · 225, 495, 180, 15 … row sums 1, 2, 27, 915, 57540, 5774895, …
  (−∞, 0] nonnegative
• A069466 → basis A007318
  1 · 4, 2 · 36, 36, 6 · 400, 600, 240, 20 … row sums 1, 6, 78, 1260, 22470, 424116, 8305836, …
  (−∞, 0] nonnegative
• A116414 → basis A013611
  1 · 5, 4 · 22, 40, 16 · 95, 276, 240, 64 … row sums 1, 9, 78, 675, 5841, 50544, 437373, …
  (−∞, 0] nonnegative
• A358735 → basis A008288
  1 · 2, 1 · 7, 10, 2 · 33, 88, 46, 6 … row sums 1, 3, 19, 173, 1999, 27955, 458845, …
  [−3−2√2, −3+2√2] nonnegative
• A038330 → basis A007318
  256, 128, 16 · 4096, 3072, 768, 64 … row sums 400, 8000, 160000, 3200000, 64000000, …
  (−∞, 0] nonnegative rational roots
• A085478 → basis A013610
  1 · 1 · 2, 3 · 5, 15, 9 … row sums 1, 1, 5, 29, 169, 985, 5741, 33461, …
  (−∞, 0] nonnegative
• A038328 → basis A007318
  196, 56, 4 · 2744, 1176, 168, 8 … row sums 256, 4096, 65536, 1048576, 16777216, …
  (−∞, 0] nonnegative rational roots
• A130534: Triangle T(n,k), 0 <= k <= n, read by rows, giving coefficients of the polynomial (x+1)(x+2)...(x+n), expanded in increasing powers of x. T(n,k) is also the unsigned Stirling number |s(n+1, …
  1 · 1, 1 · 2, 3, 1 · 6, 11, 6, 1 … row sums 1, 2, 6, 24, 120, 720, 5040, 40320, …
  A130534 (−∞, −1] nonnegative rational roots
• A064861 → basis A008277
  6, 9, 2 · 18, 57, 32, 4 · 36, 189, 185, 52, 4 … row sums 17, 111, 466, 3792, 18885, 182701, …
  (−∞, 0] nonnegative
• A059473 → basis A013609
  1 · 4, 4 · 18, 36, 16 · 80, 240, 224, 64 … row sums 1, 8, 70, 608, 5284, 45920, 399064, …
  (−∞, 0] nonnegative
• A304236 → basis A013609
  1 · 1 · 4, 6 · 7, 12 … row sums 1, 1, 10, 19, 109, 280, 1261, 3781, …
  (−∞, 0] nonnegative
• A038329 → basis A008277
  225, 99, 9 · 3375, 2457, 486, 27 … row sums 333, 6345, 124740, 2533761, 53226477, …
  (−∞, 0] nonnegative
• A159834: Coefficient array of Hermite_H(n, (x-1)/sqrt(2))/(sqrt(2))^n.
  A066325 → x ↦ x−1 (shift -1)
  1 · -1, 1 · 0, -2, 1 · 2, 0, -3, 1 … row sums 1, 0, -1, 0, 3, 0, -15, 0, …
  A159834 (−∞, ∞)
• A008288 → basis A013610
  1 · 2, 3 · 5, 15, 9 · 12, 54, 72, 27 … row sums 1, 5, 29, 165, 941, 5365, 30589, …
  (−∞, 0] nonnegative
• A133080 → basis A013609
  1 · 2, 2 · 1, 4, 4 · 2, 10, 16, 8 … row sums 1, 4, 9, 36, 81, 324, 729, 2916, …
  (−∞, 0] nonnegative rational roots
• A079638 → basis A008277
  1 · 4, 1 · 24, 12, 1 · 192, 144, 24, 1 … row sums 1, 5, 37, 361, 4361, 62701, 1044205, …
  (−∞, 0] nonnegative
• A286718 → basis A013609
  1 · 2, 2 · 10, 14, 4 · 80, 132, 60, 8 … row sums 1, 4, 28, 280, 3640, 58240, 1106560, …
  (−∞, 0] nonnegative rational roots
• A027466: Triangle whose (i,j)-th entry is binomial(i,j)*7^(i-j).
  1 · 7, 1 · 49, 14, 1 · 343, 147, 21, 1 … row sums 1, 8, 64, 512, 4096, 32768, 262144, …
  A027466 (−∞, 0) nonnegative rational roots
• A116414 → basis A013610
  1 · 5, 3 · 22, 30, 9 · 95, 207, 135, 27 … row sums 1, 8, 61, 464, 3529, 26840, 204133, …
  (−∞, 0] nonnegative
• A118394 → basis A013611
  1 · 1 · 1 · 7, 24 … row sums 1, 1, 1, 31, 121, 301, 9601, 64051, …
  (−∞, 0] nonnegative
• A143491 → basis A013611
  12, 28, 16 · 60, 188, 192, 64 … row sums 56, 504, 5040, 55440, 665280, 8648640, …
  (−∞, 0] nonnegative rational roots
• A154228 → basis A013610
  1 · 2, 3 · 18, 54, 9 · 96, 432, 450, 27 … row sums 1, 5, 81, 1005, 22845, 480045, …
  (−∞, 0] nonnegative
• A139548 → basis A008277
  1 · 8, 10, 2 · 64, 260, 220, 56, 4 … row sums 1, 20, 604, 26104, 1517248, 113120864, …
  (−∞, 0] nonnegative
• A299989 → basis A013611
  1, 4 · 8, 56, 112, 64 … row sums 5, 240, 11520, 552960, 26542080, …
  (−∞, 0] nonnegative rational roots
• A082985 → basis A013609
  1 · 4, 6 · 11, 30, 20 · 29, 112, 140, 56 … row sums 1, 10, 61, 337, 1810, 9637, 51169, …
  (−∞, 0] nonnegative
• A249251 → basis A008277
  1 · 4, 3 · 13, 24, 6 · 43, 156, 93, 12 … row sums 1, 7, 43, 304, 2398, 20842, 197377, …
  (−∞, 0] nonnegative
• A154227 → basis A008277
  1 · 2, 1 · 10, 11, 1 · 40, 83, 25, 1 … row sums 1, 3, 22, 149, 1438, 15122, 195481, …
  (−∞, 0] nonnegative
• A094816 → basis A008277
  1 · 2, 1 · 5, 6, 1 · 16, 33, 12, 1 … row sums 1, 3, 12, 62, 396, 3012, 26536, 265344, …
  (−∞, 0] nonnegative
• A023531 → basis A008277
  1 · 1, 1 · 1, 3, 1 · 1, 7, 6, 1 … row sums 1, 2, 5, 15, 52, 203, 877, 4140, …
  (−∞, 0] nonnegative
• A344565 → basis A013609
  3 · 30, 30 · 180, 360, 180 · 840, 2520, 2520, 840 … row sums 3, 60, 720, 6720, 53760, 387072, …
  (−∞, 0] nonnegative rational roots
• A054142 → basis A013609
  1 · 2, 2 · 5, 10, 4 · 13, 40, 36, 8 … row sums 1, 4, 19, 97, 508, 2683, 14209, 75316, …
  (−∞, 0] nonnegative