basis_map

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

1056 sequences

• A038330 → basis A013611
  256, 512, 256 · 4096, 12288, 12288, 4096 … row sums 1024, 32768, 1048576, 33554432, …
  (−∞, 0] nonnegative rational roots
• basis-map coefficients of A371080, shifted → basis A013610
  1 · 1, 3 · 4, 15, 9 · 28, 117, 108, 27 … row sums 1, 4, 28, 280, 3640, 58240, 1106560, …
  (−∞, 0] nonnegative rational roots
• A269947 → basis A007318
  1 · 1, 1 · 2, 3, 1 · 18, 29, 12, 1 … row sums 1, 2, 6, 60, 1740, 114840, 14584680, …
  (−∞, 0] nonnegative rational roots
• A066325: Hermite he
  1 · 0, 1 · -1, 0, 1 · 0, -3, 0, 1 … row sums 1, 1, 0, -2, -2, 6, 16, -20, …
  A066325 (−∞, ∞)
• A172431 → basis A013610
  1 · 3, 6 · 8, 30, 27 · 21, 114, 198, 108 … row sums 1, 9, 65, 441, 2929, 19305, 126881, …
  (−∞, 0] nonnegative
• A094816 → basis A013609
  1 · 2, 2 · 5, 10, 4 · 16, 46, 36, 8 … row sums 1, 4, 19, 106, 685, 5056, 42079, …
  (−∞, 0] nonnegative
• A069466 → basis A013610
  1 · 4, 6 · 36, 108, 54 · 400, 1800, 2160, 540 … row sums 1, 10, 198, 4900, 134470, 3912300, …
  (−∞, 0] nonnegative
• A118931 → basis A007318
  1 · 1 · 1 · 3, 2 … row sums 1, 1, 1, 5, 17, 41, 241, 1261, …
  (−∞, −1] nonnegative
• A356546 → basis A008277
  1 · 4, 2 · 24, 30, 6 · 160, 380, 180, 20 … row sums 1, 6, 60, 740, 10570, 169848, 3015012, …
  (−∞, 0] nonnegative
• A038259 → basis A013611
  1 · 11, 20 · 121, 440, 400 · 1331, 7260, 13200, 8000 … row sums 1, 31, 961, 29791, 923521, 28629151, …
  (−∞, 0] nonnegative rational roots
• A030528 → basis A008277
  1 · 2, 1 · 3, 5, 1 · 5, 17, 9, 1 … row sums 1, 3, 9, 32, 127, 558, 2675, 13859, …
  (−∞, 0] nonnegative
• A038277 → basis A013609
  1 · 18, 22 · 324, 792, 484 … row sums 1, 40, 1600, 64000, 2560000, 102400000, …
  (−∞, 0] nonnegative rational roots
• A059344 → basis A013610
  1 · 1 · 3, 6 · 7, 18 … row sums 1, 1, 9, 25, 241, 1041, 10681, 60649, …
  (−∞, 0] nonnegative
• A207607 → basis A013611
  1 · 3, 8 · 8, 36, 32 · 21, 132, 240, 128 … row sums 1, 11, 76, 521, 3571, 24476, 167761, …
  (−∞, 0] nonnegative
• A038324 → basis A013610
  1 · 21, 30 · 441, 1260, 900 … row sums 1, 51, 2601, 132651, 6765201, …
  (−∞, 0] nonnegative rational roots
• A111125 → basis A013610
  1 · 4, 3 · 11, 21, 9 · 29, 93, 90, 27 … row sums 1, 7, 41, 239, 1393, 8119, 47321, …
  (−∞, 0] nonnegative
• A317496 → x ↦ x+1
  1 · 1 · 1 · 4, 3 … row sums 1, 1, 1, 7, 13, 19, 61, 139, …
  (−∞, −1] nonnegative
• A145597 → basis A013610
  1 · 6, 9 · 27, 81, 54 · 110, 495, 675, 270 … row sums 1, 15, 162, 1550, 14019, 123165, …
  (−∞, 0] nonnegative
• A207607 → basis A013609
  1 · 3, 4 · 8, 18, 8 · 21, 66, 60, 16 … row sums 1, 7, 34, 163, 781, 3742, 17929, 85903, …
  (−∞, 0] nonnegative
• A103633 → basis A007318
  1 · 1, 1 · 2, 3, 1 · 2, 5, 4, 1 … row sums 1, 2, 6, 12, 36, 72, 216, 432, …
  (−∞, −1] nonnegative rational roots
• A085881 → basis A013611
  1 · 2, 4 · 12, 48, 48 · 120, 720, 1440, 960 … row sums 1, 6, 108, 3240, 136080, 7348320, …
  (−∞, 0] nonnegative rational roots
• A013613 → basis A013610
  1 · 7, 18 · 49, 252, 324 · 343, 2646, 6804, 5832 … row sums 1, 25, 625, 15625, 390625, 9765625, …
  (−∞, 0] nonnegative rational roots
• A038314 → basis A007318
  484, 528, 144 · 10648, 17424, 9504, 1728 … row sums 1156, 39304, 1336336, 45435424, …
  (−∞, 0] nonnegative rational roots
• delannoy → basis A013609
  1 · 2, 2 · 5, 10, 4 · 12, 36, 32, 8 … row sums 1, 4, 19, 88, 409, 1900, 8827, 41008, …
  (−∞, 0] nonnegative
• A011973 → basis A007318 → basis A013610
  1 · 1 · 3, 3 · 5, 6 … row sums 1, 1, 6, 11, 41, 96, 301, 781, …
  (−∞, 0] nonnegative
• A143683 → x ↦ x+1
  1 · 2, 1 · 12, 12, 1 · 40, 60, 22, 1 … row sums 1, 3, 25, 123, 769, 4275, 25129, …
  (−∞, −1] nonnegative
• A038320 → basis A013609
  289, 408, 144 · 4913, 10404, 7344, 1728 … row sums 841, 24389, 707281, 20511149, …
  (−∞, 0] nonnegative rational roots
• A116412 → basis A008277
  1 · 4, 1 · 13, 9, 1 · 43, 55, 15, 1 … row sums 1, 5, 23, 114, 601, 3368, 20005, …
  (−∞, 0] nonnegative
• A225470 → basis A007318
  1 · 3, 1 · 18, 9, 1 · 162, 99, 18, 1 … row sums 1, 4, 28, 280, 3640, 58240, 1106560, …
  (−∞, 0] nonnegative rational roots
• A114687 → basis A007318
  1 · 3, 2 · 11, 14, 4 · 45, 84, 48, 8 … row sums 1, 5, 29, 185, 1257, 8925, 65445, …
  (−∞, −1] nonnegative
• A169803 → basis A013610
  1 · 2, 3 · 3, 6 · 5, 15, 9 … row sums 1, 5, 9, 29, 65, 181, 441, 1165, …
  (−∞, 0] nonnegative
• A391533 → basis A013610
  9, 18, 9 · 18, 63, 72, 27 · 36, 180, 333, 270, 81 … row sums 36, 180, 900, 4500, 22500, 112500, …
  (−∞, 0] nonnegative rational roots
• A152198 → basis A013609
  1 · 1 · 2, 2 · 2, 2 … row sums 1, 1, 4, 4, 16, 16, 64, 64, …
  (−∞, 0] nonnegative rational roots
• A232535 → basis A013609
  1 · 3, 4 · 12, 28, 12 · 48, 160, 148, 32 … row sums 1, 7, 52, 388, 2896, 21616, 161344, …
  (−∞, 0] nonnegative
• A207606 → basis A013611
  13, 44, 32 · 34, 176, 272, 128 … row sums 89, 610, 4181, 28657, 196418, 1346269, …
  (−∞, 0] nonnegative
• A145324 → basis A007318
  1 · 3, 2 · 12, 17, 6 · 60, 133, 98, 24 … row sums 1, 5, 35, 315, 3465, 45045, 675675, …
  (−∞, 0] nonnegative rational roots
• A038305 → basis A013611
  169, 312, 144 · 2197, 6084, 5616, 1728 … row sums 625, 15625, 390625, 9765625, 244140625, …
  (−∞, 0] nonnegative rational roots
• A038279 → basis A013611
  1 · 9, 4 · 81, 72, 16 · 729, 972, 432, 64 … row sums 1, 13, 169, 2197, 28561, 371293, …
  (−∞, 0] nonnegative rational roots
• basis-map coefficients of A112227 → basis A013610
  1, 6, 9 · 1, 9, 27, 27 · 1, 12, 54, 108, 81 … row sums 16, 64, 256, 1024, 4096, 16384, 65536, …
  (−∞, 0] nonnegative rational roots
• A367270 → basis A013611
  1 · 1 · 3, 8 · 10, 48, 48 … row sums 1, 1, 11, 106, 1011, 9726, 94526, …
  (−∞, 0] nonnegative
• A154233 → basis A013609
  1 · 2, 2 · 9, 18, 4 · 40, 120, 88, 8 … row sums 1, 4, 31, 256, 2791, 33436, 477037, …
  (−∞, 0] nonnegative
• A121574 → basis A007318
  1 · 3, 1 · 10, 7, 1 · 33, 35, 11, 1 … row sums 1, 4, 18, 80, 356, 1584, 7048, 31360, …
  (−∞, −1] nonnegative
• A113953: A Jacobsthal triangle.
  1 · 0, 1 · 0, 2, 1 · 0, 0, 4, 1 … row sums 1, 1, 3, 5, 11, 21, 43, 85, …
  A113953 (−8, 0] nonnegative
• A038331 → basis A008277
  289, 195, 25 · 4913, 5735, 1650, 125 … row sums 509, 12423, 320356, 8730007, 251174029, …
  (−∞, 0] nonnegative
• A193685: 5-Stirling numbers of the second kind.
  1 · 5, 1 · 25, 11, 1 · 125, 91, 18, 1 … row sums 1, 6, 37, 235, 1540, 10427, 73013, …
  A193685 (−∞, 0) nonnegative
• A169803 → basis A013609
  1 · 2, 2 · 3, 4 · 5, 10, 4 … row sums 1, 4, 7, 19, 40, 97, 217, 508, …
  (−∞, 0] nonnegative
• A299989 → basis A013609
  1, 2 · 8, 28, 28, 8 · 64, 320, 592, 512, 208, 32 … row sums 3, 72, 1728, 41472, 995328, 23887872, …
  (−∞, 0] nonnegative rational roots
• A102662 → basis A013611
  1 · 4, 12 · 9, 44, 48 · 22, 152, 320, 192 … row sums 1, 16, 101, 686, 4621, 31156, 210041, …
  (−∞, 0] nonnegative
• A118394 → basis A013610
  1 · 1 · 1 · 7, 18 … row sums 1, 1, 1, 25, 97, 241, 6241, 41161, …
  (−∞, 0] nonnegative
• A038301 → basis A008277
  400, 561, 121 · 8000, 21791, 11253, 1331 … row sums 1082, 42375, 1844815, 88316152, …
  (−∞, 0] nonnegative