basis_map

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

1056 sequences

• A103327 → basis A013610
  1 · 4, 3 · 16, 36, 9 · 64, 240, 216, 27 … row sums 1, 7, 61, 547, 4921, 44287, 398581, …
  (−∞, 0] nonnegative
• A038322 → basis A013611
  1 · 19, 32 · 361, 1216, 1024 … row sums 1, 51, 2601, 132651, 6765201, …
  (−∞, 0] nonnegative rational roots
• A152830 → basis A013611
  1 · 1 · 1 · 1 … row sums 1, 1, 1, 1, 6, 6, 6, 6, …
  (−∞, 0] nonnegative rational roots
• basis-map coefficients of A030528, shifted → basis A013610
  1 · -1, -3 · 1, 6, 9 · -1, -9, -27, -27 … row sums 1, -4, 16, -64, 256, -1024, 4096, …
  (−∞, 0] rational roots
• A169803 → basis A008277
  1 · 2, 1 · 3, 2 · 5, 6, 1 … row sums 1, 3, 5, 12, 24, 56, 123, 292, …
  (−∞, 0] nonnegative
• A013613 → basis A013609
  1 · 7, 12 · 49, 168, 144 · 343, 1764, 3024, 1728 … row sums 1, 19, 361, 6859, 130321, 2476099, …
  (−∞, 0] nonnegative rational roots
• A286718 → basis A013610
  1 · 2, 3 · 10, 21, 9 · 80, 198, 135, 27 … row sums 1, 5, 40, 440, 6160, 104720, 2094400, …
  (−∞, 0] nonnegative rational roots
• A102662 → basis A008277
  1 · 4, 3 · 9, 14, 3 · 22, 61, 29, 3 … row sums 1, 7, 26, 115, 545, 2788, 15267, 89015, …
  (−∞, 0] nonnegative
• A088996 → basis A008277
  1 · 1, 1 · 3, 7, 2 · 15, 65, 43, 6 … row sums 1, 2, 12, 129, 2095, 47025, 1380141, …
  (−∞, 0] nonnegative
• A120910 → basis A013610
  3 · 9, 9 · 27, 54, 27 · 81, 243, 243, 81 … row sums 3, 18, 108, 648, 3888, 23328, 139968, …
  (−∞, 0] nonnegative rational roots
• A038325 → basis A013611
  1 · 22, 44 · 484, 1936, 1936 … row sums 1, 66, 4356, 287496, 18974736, …
  (−∞, 0] nonnegative rational roots
• A081578 → basis A013610
  1 · 2, 3 · 7, 21, 9 · 20, 90, 108, 27 … row sums 1, 5, 37, 245, 1669, 11285, 76453, …
  (−∞, 0] nonnegative
• A132812: Triangle read by rows, n>=1, 1<=k<=n, T(n,k) = k*binomial(n,k)^2/(n-k+1).
  1 · 2, 2 · 3, 9, 3 · 4, 24, 24, 4 … row sums 1, 4, 15, 56, 210, 792, 3003, 11440, …
  A132812 (−∞, 0) nonnegative
• A038335 → basis A008277
  1 · 21, 9 · 441, 459, 81 · 9261, 17739, 7290, 729 … row sums 1, 30, 981, 35019, 1361124, 57317139, …
  (−∞, 0] nonnegative
• basis-map coefficients of A021012 → basis A013609
  1 · -1, -2 · 2, 8, 8 · -6, -36, -72, -48 … row sums 1, -3, 18, -162, 1944, -29160, 524880, …
  (−∞, 0] rational roots
• A178822 → basis A013609
  1 · 12, 12 · 84, 168, 84 · 448, 1344, 1344, 448 … row sums 1, 24, 336, 3584, 32256, 258048, …
  (−∞, 0] nonnegative rational roots
• A104684 → basis A008277
  1 · 3, 1 · 13, 9, 1 · 63, 73, 18, 1 … row sums 1, 4, 23, 155, 1152, 9225, 78661, …
  (−∞, 0] nonnegative
• A207606 → basis A013610
  13, 33, 18 · 34, 132, 153, 54 … row sums 64, 373, 2174, 12671, 73852, 430441, …
  (−∞, 0] nonnegative
• A274496 → basis A013611
  1 · 2 · 4, 8 · 8, 16 … row sums 1, 2, 12, 24, 144, 288, 1728, 3456, …
  (−∞, 0] nonnegative rational roots
• A143685 → basis A008277
  1 · 2, 1 · 13, 14, 1 · 44, 91, 27, 1 … row sums 1, 3, 28, 163, 1285, 9638, 80015, …
  (−∞, 0] nonnegative
• A064861 → basis A013609
  6, 14, 8 · 18, 66, 80, 32 · 36, 168, 292, 224, 64 … row sums 28, 196, 784, 5488, 21952, 153664, …
  (−∞, 0] nonnegative rational roots
• A159854 → basis A008277
  1, 3, 1 · 2, 10, 7, 1 · 4, 32, 38, 12, 1 … row sums 5, 20, 87, 409, 2066, 11155, 64077, …
  (−∞, 0] nonnegative
• A391533 → Pₙ + Pₙ₊₁
  8, 12, 6, 1 · 8, 20, 18, 7, 1 · 8, 28, 38, 25, 8, 1 … row sums 27, 54, 108, 216, 432, 864, 1728, 3456, …
  (−∞, −1] nonnegative rational roots
• A035607 → basis A007318
  1 · 1 · 3, 2 · 7, 8, 2 … row sums 1, 1, 5, 17, 61, 217, 773, 2753, …
  (−∞, 0] nonnegative
• A079638 → basis A013609
  1 · 4, 2 · 24, 22, 4 · 192, 244, 84, 8 … row sums 1, 6, 50, 528, 6720, 99840, 1693440, …
  (−∞, 0] nonnegative
• A059344 → basis A008277
  1 · 1 · 3, 2 · 7, 6 … row sums 1, 1, 5, 13, 85, 341, 2761, 14785, …
  (−∞, 0] nonnegative
• A038221 → basis A008277
  1 · 6, 3 · 36, 45, 9 · 216, 513, 243, 27 … row sums 1, 9, 90, 999, 12231, 163782, 2378727, …
  (−∞, 0] nonnegative
• A038314 → basis A013611
  484, 2112, 2304 · 10648, 69696, 152064, 110592 … row sums 4900, 343000, 24010000, 1680700000, …
  (−∞, 0] nonnegative rational roots
• A152842 → basis A008277
  1 · 4, 3 · 8, 13, 3 · 32, 115, 69, 9 … row sums 1, 7, 24, 225, 955, 11296, 56845, …
  (−∞, 0] nonnegative
• A156992 → basis A013610
  1 · 4, 6 · 24, 72, 54 · 192, 864, 1296, 648 … row sums 1, 10, 150, 3000, 75000, 2250000, …
  (−∞, 0] nonnegative rational roots
• A122542 → basis A013610
  1 · 1, 3 · 3, 12, 9 · 7, 39, 63, 27 … row sums 1, 4, 24, 136, 776, 4424, 25224, …
  (−∞, 0] nonnegative
• narayana → basis A013610
  1 · 2, 3 · 5, 15, 9 · 14, 63, 81, 27 … row sums 1, 5, 29, 185, 1257, 8925, 65445, …
  (−∞, 0] nonnegative
• A118931 → basis A013609
  1 · 1 · 1 · 3, 4 … row sums 1, 1, 1, 7, 25, 61, 481, 2731, …
  (−∞, 0] nonnegative
• A038221 → basis A013610
  1 · 6, 9 · 36, 108, 81 · 216, 972, 1458, 729 … row sums 1, 15, 225, 3375, 50625, 759375, …
  (−∞, 0] nonnegative rational roots
• A013609 → basis A013611
  1 · 3, 8 · 9, 48, 64 · 27, 216, 576, 512 … row sums 1, 11, 121, 1331, 14641, 161051, …
  (−∞, 0] nonnegative rational roots
• A133087 → basis A008277
  1 · 3, 1 · 4, 5, 1 · 12, 24, 10, 1 … row sums 1, 4, 10, 47, 151, 825, 3263, 20270, …
  (−∞, 0] nonnegative
• A102547 → basis A008277
  1 · 1 · 1 · 2, 1 … row sums 1, 1, 1, 3, 5, 7, 14, 26, …
  (−∞, 0] nonnegative
• A128099 → basis A013609
  1 · 1 · 3, 4 · 5, 8 … row sums 1, 1, 7, 13, 55, 133, 463, 1261, …
  (−∞, 0] nonnegative
• A026374 → basis A013611
  1 · 2, 4 · 5, 20, 16 · 10, 60, 112, 64 … row sums 1, 6, 41, 246, 1681, 10086, 68921, …
  (−∞, 0] nonnegative
• A152828 → basis A008277
  1 · 1 · 1 · 2, 1 … row sums 1, 1, 1, 3, 3, 3, 10, 10, …
  (−∞, 0] nonnegative
• A063007 → basis A013611
  1 · 3, 8 · 13, 72, 96 · 63, 528, 1440, 1280 … row sums 1, 11, 181, 3311, 63601, 1256651, …
  (−∞, 0] nonnegative
• A081582 → x ↦ x+1
  1 · 2, 1 · 11, 11, 1 · 36, 54, 20, 1 … row sums 1, 3, 23, 111, 655, 3519, 19727, …
  (−∞, −1] nonnegative
• A225471 → basis A013610
  1 · 4, 3 · 32, 36, 9 · 384, 528, 216, 27 … row sums 1, 7, 77, 1155, 21945, 504735, …
  (−∞, 0] nonnegative rational roots
• A038336 → basis A007318
  484, 440, 100 · 10648, 14520, 6600, 1000 … row sums 1024, 32768, 1048576, 33554432, …
  (−∞, 0] nonnegative rational roots
• A038259 → basis A008277
  1 · 11, 5 · 121, 135, 25 · 1331, 2765, 1200, 125 … row sums 1, 16, 281, 5421, 114436, 2626951, …
  (−∞, 0] nonnegative
• A013620 → basis A013610
  1 · 5, 9 · 25, 90, 81 · 125, 675, 1215, 729 … row sums 1, 14, 196, 2744, 38416, 537824, …
  (−∞, 0] nonnegative rational roots
• A165253 → basis A013611
  1 · 1 · 2, 4 · 5, 20, 16 … row sums 1, 1, 6, 41, 281, 1926, 13201, 90481, …
  (−∞, 0] nonnegative
• A200536 → basis A007318
  1 · 6, 7, 2 · 36, 84, 73, 28, 4 … row sums 1, 15, 225, 3375, 50625, 759375, …
  (−∞, 0] nonnegative rational roots
• A207824 → basis A013611
  1 · 6, 4 · 35, 48, 16 · 204, 424, 288, 64 … row sums 1, 10, 99, 980, 9701, 96030, 950599, …
  (−∞, 0] nonnegative
• A027466 → basis A013610
  1 · 8, 3 · 64, 48, 9 · 512, 576, 216, 27 … row sums 1, 11, 121, 1331, 14641, 161051, …
  (−∞, 0] nonnegative rational roots