basis_map

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

1056 sequences

• A033282 → basis A013610
  1 · 3, 6 · 11, 45, 45 · 45, 279, 567, 378 … row sums 1, 9, 101, 1269, 17081, 240849, …
  (−∞, 0] nonnegative
• A100862 → basis A008277
  1 · 2, 1 · 5, 6, 1 · 14, 31, 12, 1 … row sums 1, 3, 12, 58, 328, 2114, 15248, 121356, …
  (−∞, 0] nonnegative
• A081578 → basis A008277
  1 · 2, 1 · 7, 8, 1 · 20, 43, 15, 1 … row sums 1, 3, 16, 79, 439, 2582, 16211, 107655, …
  (−∞, 0] nonnegative
• A027466 → basis A013611
  1 · 8, 4 · 64, 64, 16 · 512, 768, 384, 64 … row sums 1, 12, 144, 1728, 20736, 248832, …
  (−∞, 0] nonnegative rational roots
• A013613 → basis A007318
  1 · 7, 6 · 49, 84, 36 · 343, 882, 756, 216 … row sums 1, 13, 169, 2197, 28561, 371293, …
  (−∞, 0] nonnegative rational roots
• A013610 → basis A008288
  1 · 4, 3 · 16, 33, 9 · 64, 225, 162, 27 … row sums 1, 7, 58, 478, 3940, 32476, 267688, …
  [−3−2√2, −3+2√2] nonnegative
• A137597: Triangle read by rows: A008277 * A007318.
  A007318 → basis A049020
  1 · 2, 1 · 5, 5, 1 · 15, 22, 9, 1 … row sums 1, 3, 11, 47, 227, 1215, 7107, 44959, …
  A137597 (−∞, −1] nonnegative
• A091042 → basis A008277
  1 · 4, 3 · 16, 25, 5 · 64, 175, 77, 7 … row sums 1, 7, 46, 323, 2431, 19504, 165855, …
  (−∞, 0] nonnegative
• A161198 → basis A007318
  1 · 3, 2 · 15, 16, 4 · 105, 142, 60, 8 … row sums 1, 5, 35, 315, 3465, 45045, 675675, …
  (−∞, 0] nonnegative rational roots
• A059364 → basis A013611
  1 · 3, 4 · 15, 44, 32 · 105, 488, 752, 384 … row sums 1, 7, 91, 1729, 43225, 1339975, …
  (−∞, 0] nonnegative rational roots
• A038325 → basis A013609
  1 · 22, 22 · 484, 968, 484 … row sums 1, 44, 1936, 85184, 3748096, 164916224, …
  (−∞, 0] nonnegative rational roots
• A367270 → basis A013610
  1 · 1 · 3, 6 · 10, 36, 27 … row sums 1, 1, 9, 73, 593, 4881, 40665, 342105, …
  (−∞, 0] nonnegative
• A225471 → basis A013609
  1 · 4, 2 · 32, 24, 4 · 384, 352, 96, 8 … row sums 1, 6, 60, 840, 15120, 332640, 8648640, …
  (−∞, 0] nonnegative rational roots
• A081579 → basis A013609
  1 · 2, 2 · 8, 16, 4 · 24, 72, 56, 8 … row sums 1, 4, 28, 160, 976, 5824, 35008, …
  (−∞, 0] nonnegative
• A133214 → basis A008277
  13, 20, 4 · 63, 182, 84, 8 · 321, 1600, 1312, 288, 16 … row sums 37, 337, 3537, 41397, 529829, 7320145, …
  (−∞, 0] nonnegative
• A081578 → x ↦ x+1
  1 · 2, 1 · 7, 7, 1 · 20, 30, 12, 1 … row sums 1, 3, 15, 63, 279, 1215, 5319, 23247, …
  (−∞, −1] nonnegative
• A038301 → basis A007318
  400, 440, 121 · 8000, 13200, 7260, 1331 … row sums 961, 29791, 923521, 28629151, …
  (−∞, 0] nonnegative rational roots
• A178822 → basis A008277
  1 · 12, 6 · 84, 105, 21 · 448, 1064, 504, 56 … row sums 1, 18, 210, 2072, 19026, 169848, …
  (−∞, 0] nonnegative
• A011973 → basis A008277
  1 · 1 · 2, 1 · 3, 2 … row sums 1, 1, 3, 5, 12, 24, 56, 123, …
  (−∞, 0] nonnegative
• A049020: Triangle of numbers a(n,k), 0 <= k <= n: number of set partitions of {1,2,...,n} in which exactly k of the blocks have been distinguished.
  A023531 → basis A049020
  1 · 1, 1 · 2, 3, 1 · 5, 10, 6, 1 … row sums 1, 2, 6, 22, 94, 454, 2430, 14214, …
  A049020 (−∞, −1] nonnegative
• A152830 → basis A013610
  1 · 1 · 1 · 1 … row sums 1, 1, 1, 1, 5, 5, 5, 5, …
  (−∞, 0] nonnegative rational roots
• A116412 → basis A013610
  1 · 4, 3 · 13, 24, 9 · 43, 126, 108, 27 … row sums 1, 7, 46, 304, 2008, 13264, 87616, …
  (−∞, 0] nonnegative
• A086645 → x ↦ x+1
  1 · 2, 1 · 8, 8, 1 · 32, 48, 18, 1 … row sums 1, 3, 17, 99, 577, 3363, 19601, 114243, …
  (−∞, −1] nonnegative
• A038220 → basis A013610
  1 · 5, 6 · 25, 60, 36 · 125, 450, 540, 216 … row sums 1, 11, 121, 1331, 14641, 161051, …
  (−∞, 0] nonnegative rational roots
• A081578 → basis A013609
  1 · 2, 2 · 7, 14, 4 · 20, 60, 48, 8 … row sums 1, 4, 25, 136, 769, 4300, 24121, …
  (−∞, 0] nonnegative
• A038338 → basis A013611
  576, 2304, 2304 · 13824, 82944, 165888, 110592 … row sums 5184, 373248, 26873856, 1934917632, …
  (−∞, 0] nonnegative rational roots
• A027467 → basis A007318
  1 · 16, 1 · 256, 32, 1 · 4096, 768, 48, 1 … row sums 1, 17, 289, 4913, 83521, 1419857, …
  (−∞, 0] nonnegative rational roots
• A196347 → basis A013610
  1 · 2, 3 · 8, 24, 18 · 48, 216, 324, 162 … row sums 1, 5, 50, 750, 15000, 375000, 11250000, …
  (−∞, 0] nonnegative rational roots
• A038320 → basis A013610
  289, 612, 324 · 4913, 15606, 16524, 5832 … row sums 1225, 42875, 1500625, 52521875, …
  (−∞, 0] nonnegative rational roots
• A207607 → basis A007318
  1 · 3, 2 · 8, 9, 2 · 21, 33, 15, 2 … row sums 1, 5, 19, 71, 265, 989, 3691, 13775, …
  (−5, −1) nonnegative
• A113214: Riordan array (1+2x,x(1+x)).
  1 · 2, 1 · 0, 3, 1 · 0, 2, 4, 1 … row sums 1, 3, 4, 7, 11, 18, 29, 47, …
  A113214 (−4, 0] nonnegative
• A367270 → x ↦ x+1
  1 · 1 · 3, 2 · 10, 12, 3 … row sums 1, 1, 5, 25, 129, 681, 3653, 19825, …
  (−∞, −1] nonnegative
• A207824: Triangle of coefficients of Chebyshev's S(n,x+5) polynomials (exponents of x in increasing order).
  1 · 5, 1 · 24, 10, 1 · 115, 73, 15, 1 … row sums 1, 6, 35, 204, 1189, 6930, 40391, …
  A207824 (−7, −3) nonnegative
• A269947 → basis A013610
  1 · 1, 3 · 2, 9, 9 · 18, 87, 108, 27 … row sums 1, 4, 20, 240, 7440, 505920, 65263680, …
  (−∞, 0] nonnegative rational roots
• A028338 → basis A013609
  1 · 2, 2 · 8, 12, 4 · 48, 88, 48, 8 … row sums 1, 4, 24, 192, 1920, 23040, 322560, …
  (−∞, 0] nonnegative rational roots
• A133080 → basis A013611
  1 · 2, 4 · 1, 8, 16 · 2, 20, 64, 64 … row sums 1, 6, 25, 150, 625, 3750, 15625, 93750, …
  (−∞, 0] nonnegative rational roots
• A038336 → basis A013609
  484, 880, 400 · 10648, 29040, 26400, 8000 … row sums 1764, 74088, 3111696, 130691232, …
  (−∞, 0] nonnegative rational roots
• A272867 → basis A013610
  1 · 6, 18, 9 · 36, 216, 432, 324, 81 … row sums 1, 33, 1089, 35937, 1185921, 39135393, …
  (−∞, 0] nonnegative
• A126351 → reverse
  1 · 2, 1 · 4, 5, 1 · 8, 19, 9, 1 … row sums 1, 3, 10, 37, 151, 674, 3263, 17007, …
  (−∞, 0] nonnegative
• A269944 → basis A007318
  1 · 1, 1 · 2, 3, 1 · 10, 17, 8, 1 … row sums 1, 2, 6, 36, 396, 7128, 192456, …
  (−∞, 0] nonnegative rational roots
• A038279 → basis A008277
  1 · 9, 1 · 81, 19, 1 · 729, 271, 30, 1 … row sums 1, 10, 101, 1031, 10644, 111211, …
  (−∞, 0] nonnegative
• A063967 → basis A007318
  1 · 2, 1 · 6, 5, 1 · 16, 20, 8, 1 … row sums 1, 3, 12, 45, 171, 648, 2457, 9315, …
  (−∞, −1] nonnegative
• A154233 → basis A013610
  1 · 2, 3 · 9, 27, 9 · 40, 180, 198, 27 … row sums 1, 5, 45, 445, 5645, 79845, 1325005, …
  (−∞, 0] nonnegative
• A038277 → basis A008277
  1 · 18, 11 · 324, 517, 121 · 5832, 18557, 10527, 1331 … row sums 1, 29, 962, 36247, 1530807, 71478890, …
  (−∞, 0] nonnegative
• A063967: Triangle read by rows, T(n,k) = T(n-1,k) + T(n-2,k) + T(n-1,k-1) + T(n-2,k-1) and T(0,0) = 1.
  1 · 1, 1 · 2, 3, 1 · 3, 7, 5, 1 … row sums 1, 2, 6, 16, 44, 120, 328, 896, …
  A063967 (−5, −1] nonnegative
• A038335 → basis A013609
  1 · 21, 18 · 441, 756, 324 · 9261, 23814, 20412, 5832 … row sums 1, 39, 1521, 59319, 2313441, 90224199, …
  (−∞, 0] nonnegative rational roots
• A122431 → basis A013611
  8, 48, 96, 64 · 8, 80, 288, 448, 256 … row sums 216, 1080, 5400, 27000, 135000, 675000, …
  (−∞, 0] nonnegative rational roots
• A152842 → basis A013610
  1 · 4, 9 · 8, 30, 27 · 32, 192, 378, 243 … row sums 1, 13, 65, 845, 4225, 54925, 274625, …
  (−∞, 0] nonnegative rational roots
• A102547 → basis A013610
  1 · 1 · 1 · 2, 3 … row sums 1, 1, 1, 5, 9, 13, 33, 69, …
  (−∞, 0] nonnegative
• A178821 → basis A008277
  1 · 10, 5 · 60, 75, 15 · 280, 665, 315, 35 … row sums 1, 15, 150, 1295, 10570, 84924, 685230, …
  (−∞, 0] nonnegative