basis_map

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

1056 sequences

• A038321 → basis A008277
  324, 301, 49 · 5832, 9793, 3675, 343 … row sums 674, 19643, 618279, 20951002, …
  (−∞, 0] nonnegative
• A099040 → basis A007318
  1 · 2, 2 · 6, 10, 4 · 16, 40, 32, 8 … row sums 1, 4, 20, 96, 464, 2240, 10816, 52224, …
  (−∞, −1] nonnegative
• A059344 → basis A013611
  1 · 1 · 3, 8 · 7, 24 … row sums 1, 1, 11, 31, 361, 1601, 19651, 115711, …
  (−∞, 0] nonnegative
• A028326 → basis A008277
  2 · 4, 2 · 8, 10, 2 · 16, 38, 18, 2 … row sums 2, 6, 20, 74, 302, 1348, 6526, 34014, …
  (−∞, 0] nonnegative
• A085841 → basis A013610
  1 · 7, 12 · 61, 216, 144 · 547, 3012, 4752, 1728 … row sums 1, 19, 421, 10039, 246601, 6125659, …
  (−∞, 0] nonnegative
• A038327 → basis A013611
  1 · 13, 4 · 169, 104, 16 · 2197, 2028, 624, 64 … row sums 1, 17, 289, 4913, 83521, 1419857, …
  (−∞, 0] nonnegative rational roots
• A143683 → basis A013609
  1 · 2, 2 · 12, 24, 4 · 40, 120, 88, 8 … row sums 1, 4, 40, 256, 1984, 14080, 103936, …
  (−∞, 0] nonnegative
• A081579 → basis A008277
  1 · 2, 1 · 8, 9, 1 · 24, 51, 17, 1 … row sums 1, 3, 18, 93, 555, 3458, 23035, 161735, …
  (−∞, 0] nonnegative
• A109692 → basis A013610
  1 · 2, 3 · 8, 30, 27 · 48, 300, 612, 405 … row sums 1, 5, 65, 1365, 39585, 1464645, …
  (−∞, 0] nonnegative rational roots
• A130534 → basis A008277
  1 · 2, 1 · 6, 6, 1 · 24, 36, 12, 1 … row sums 1, 3, 13, 73, 501, 4051, 37633, 394353, …
  (−∞, 0] nonnegative
• A082985 → x ↦ x+1
  1 · 4, 3 · 11, 15, 5 · 29, 56, 35, 7 … row sums 1, 7, 31, 127, 511, 2047, 8191, 32767, …
  (−∞, −1] nonnegative
• A367270 → basis A008277
  1 · 1 · 3, 2 · 10, 15, 3 … row sums 1, 1, 5, 28, 175, 1201, 8929, 71177, …
  (−∞, 0] nonnegative
• A099093: Riordan array (1, 3+3x).
  1 · 0, 3 · 0, 3, 9 · 0, 0, 18, 27 … row sums 1, 3, 12, 45, 171, 648, 2457, 9315, …
  A099093 (−4/3, 0] nonnegative
• A133214 → basis A013610
  13, 48, 36 · 63, 342, 540, 216 … row sums 97, 1161, 14721, 192969, 2582881, …
  (−∞, 0] nonnegative
• A038259 → basis A007318
  1 · 11, 5 · 121, 110, 25 · 1331, 1815, 825, 125 … row sums 1, 16, 256, 4096, 65536, 1048576, …
  (−∞, 0] nonnegative rational roots
• A145324 → basis A008277
  1 · 3, 2 · 12, 23, 6 · 60, 255, 170, 24 … row sums 1, 5, 41, 509, 8934, 209964, 6341677, …
  (−∞, 0] nonnegative
• A038220: Triangle whose (i,j)-th entry is binomial(i,j)*3^(i-j)*2^j.
  1 · 3, 2 · 9, 12, 4 · 27, 54, 36, 8 … row sums 1, 5, 25, 125, 625, 3125, 15625, 78125, …
  A038220 (−∞, −1] nonnegative rational roots
• A008459 → basis A013611
  1 · 2, 4 · 6, 24, 16 · 20, 120, 192, 64 … row sums 1, 6, 46, 396, 3606, 33876, 324556, …
  (−∞, 0] nonnegative
• A013609 → basis A013609
  1 · 3, 4 · 9, 24, 16 · 27, 108, 144, 64 … row sums 1, 7, 49, 343, 2401, 16807, 117649, …
  (−∞, 0] nonnegative rational roots
• A200536 → basis A013611
  1 · 6, 28, 32 · 36, 336, 1168, 1792, 1024 … row sums 1, 66, 4356, 287496, 18974736, …
  (−∞, 0] nonnegative rational roots
• A081581 → basis A013611
  1 · 2, 4 · 10, 40, 16 · 32, 192, 288, 64 … row sums 1, 6, 66, 576, 5436, 49896, 462456, …
  (−∞, 0] nonnegative
• A078812 → basis A013611
  1 · 3, 4 · 8, 24, 16 · 21, 100, 144, 64 … row sums 1, 7, 48, 329, 2255, 15456, 105937, …
  (−∞, 0] nonnegative
• A013622 → basis A008277
  1 · 8, 5 · 64, 105, 25 · 512, 1685, 975, 125 … row sums 1, 13, 194, 3297, 62911, 1328668, …
  (−∞, 0] nonnegative
• A085881 → basis A007318
  1 · 2, 1 · 12, 12, 3 · 120, 180, 90, 15 … row sums 1, 3, 27, 405, 8505, 229635, 7577955, …
  (−∞, 0] nonnegative rational roots
• A109692 → basis A013611
  1 · 2, 4 · 8, 40, 48 · 48, 400, 1088, 960 … row sums 1, 6, 96, 2496, 89856, 4133376, …
  (−∞, 0] nonnegative rational roots
• A038221 → basis A013609
  1 · 6, 6 · 36, 72, 36 · 216, 648, 648, 216 … row sums 1, 12, 144, 1728, 20736, 248832, …
  (−∞, 0] nonnegative rational roots
• A063007 → x ↦ x+1
  1 · 3, 2 · 13, 18, 6 · 63, 132, 90, 20 … row sums 1, 5, 37, 305, 2641, 23525, 213445, …
  (−2, −1) nonnegative
• A069466 → basis A008277
  1 · 4, 2 · 36, 42, 6 · 400, 860, 300, 20 … row sums 1, 6, 84, 1580, 35350, 895608, …
  (−∞, 0] nonnegative
• A102547 → basis A013611
  1 · 1 · 1 · 2, 4 … row sums 1, 1, 1, 6, 11, 16, 46, 101, …
  (−∞, 0] nonnegative
• A122431 → basis A013610
  8, 36, 54, 27 · 8, 60, 162, 189, 81 … row sums 125, 500, 2000, 8000, 32000, 128000, …
  (−∞, 0] nonnegative rational roots
• A113953 → basis A007318
  1 · 1, 1 · 3, 4, 1 · 5, 11, 7, 1 … row sums 1, 2, 8, 24, 80, 256, 832, 2688, …
  (−∞, −1] nonnegative
• A088996 → basis A013611
  1 · 1, 4 · 3, 20, 32 · 15, 136, 400, 384 … row sums 1, 5, 55, 935, 21505, 623645, 21827575, …
  (−∞, 0] nonnegative rational roots
• A011973 → basis A013610
  1 · 1 · 2, 3 · 3, 6 … row sums 1, 1, 5, 9, 29, 65, 181, 441, …
  (−∞, 0] nonnegative
• A030528 → basis A013611
  1 · 2, 4 · 3, 16, 16 · 5, 40, 96, 64 … row sums 1, 6, 35, 205, 1200, 7025, 41125, …
  (−∞, 0] nonnegative
• A033282 → basis A008277
  1 · 3, 2 · 11, 20, 5 · 45, 170, 105, 14 … row sums 1, 5, 36, 334, 3753, 49097, 728269, …
  (−∞, 0] nonnegative
• A038336 → basis A013610
  484, 1320, 900 · 10648, 43560, 59400, 27000 … row sums 2704, 140608, 7311616, 380204032, …
  (−∞, 0] nonnegative rational roots
• A013620 → basis A007318
  1 · 5, 3 · 25, 30, 9 · 125, 225, 135, 27 … row sums 1, 8, 64, 512, 4096, 32768, 262144, …
  (−∞, −1] nonnegative rational roots
• A249248 → basis A013610
  1 · 4, 9 · 11, 39, 27 · 38, 195, 279, 81 … row sums 1, 13, 77, 593, 4505, 36757, 309925, …
  (−∞, 0] nonnegative
• A059473 → basis A008277
  1 · 4, 2 · 18, 22, 4 · 80, 184, 80, 8 … row sums 1, 6, 44, 352, 3084, 29344, 300984, …
  (−∞, 0] nonnegative
• A207823 → basis A013610
  1 · 5, 3 · 24, 30, 9 · 115, 219, 135, 27 … row sums 1, 8, 63, 496, 3905, 30744, 242047, …
  (−∞, 0] nonnegative
• A082985 → basis A013610
  1 · 4, 9 · 11, 45, 45 · 29, 168, 315, 189 … row sums 1, 13, 101, 701, 4693, 31021, 204101, …
  (−∞, 0] nonnegative
• A137320 → basis A013611
  1 · 2, 8 · 6, 40, 64 · 24, 208, 576, 512 … row sums 1, 10, 110, 1320, 17160, 240240, …
  (−∞, 0] nonnegative rational roots
• basis-map coefficients of A026729, shifted → basis A013609
  1 · -1, -2 · 1, 4, 4 · -1, -6, -12, -8 … row sums 1, -3, 9, -27, 81, -243, 729, -2187, …
  (−∞, 0] rational roots
• A033282 → x ↦ x+1
  1 · 3, 2 · 11, 15, 5 · 45, 93, 63, 14 … row sums 1, 5, 31, 215, 1597, 12425, 99955, …
  (−2, −1) nonnegative
• A123519 → basis A013611
  11, 56, 64 · 41, 304, 704, 512 … row sums 131, 1561, 18601, 221651, 2641211, …
  (−∞, 0] nonnegative
• A121574 → basis A008277
  1 · 3, 1 · 10, 8, 1 · 33, 47, 14, 1 … row sums 1, 4, 19, 95, 506, 2862, 17143, 108398, …
  (−∞, 0] nonnegative
• A030528 → basis A013609
  1 · 2, 2 · 3, 8, 4 · 5, 20, 24, 8 … row sums 1, 4, 15, 57, 216, 819, 3105, 11772, …
  (−∞, 0] nonnegative
• A038319 → basis A008277
  256, 185, 25 · 4096, 5165, 1575, 125 … row sums 466, 10961, 273631, 7247476, 203358371, …
  (−∞, 0] nonnegative
• A038338 → basis A008277
  576, 720, 144 · 13824, 32832, 15552, 1728 … row sums 1440, 63936, 3131136, 167712768, …
  (−∞, 0] nonnegative
• A052553 → basis A013610
  1 · 1 · 2, 3 · 3, 6 … row sums 1, 1, 5, 9, 29, 65, 181, 441, …
  (−∞, 0] nonnegative