basis_map / A008277

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

212 sequences

• A038243 → basis A008277
  1 · 6, 1 · 36, 13, 1 · 216, 127, 21, 1 … row sums 1, 7, 50, 365, 2727, 20878, 163967, …
  (−∞, 0] nonnegative
• A010054: a(n) = 1 if n is a triangular number, otherwise 0.
  1 · 1 · 1 · 1 … row sums 1, 1, 1, 1, 1, 1, 1, 1, …
  A010054 (−∞, −1] [−1, 0] [−3−2√2, −3+2√2] nonnegative rational roots
• A122542 → basis A008277
  1 · 1, 1 · 3, 5, 1 · 7, 21, 10, 1 … row sums 1, 2, 9, 39, 186, 953, 5225, 30484, …
  (−∞, 0] nonnegative
• A269947 → basis A008277
  1 · 1, 1 · 2, 4, 1 · 18, 42, 15, 1 … row sums 1, 2, 7, 76, 2279, 152776, 19564357, …
  (−∞, 0] nonnegative
• A136124 → basis A008277
  1 · 3, 1 · 12, 8, 1 · 60, 60, 15, 1 … row sums 1, 4, 21, 136, 1045, 9276, 93289, …
  (−∞, 0] nonnegative
• A232535 → basis A008277
  1 · 3, 2 · 12, 17, 3 · 48, 121, 49, 4 … row sums 1, 5, 32, 222, 1655, 13169, 111169, …
  (−∞, 0] nonnegative
• A154228 → basis A008277
  1 · 2, 1 · 18, 19, 1 · 96, 195, 53, 1 … row sums 1, 3, 38, 345, 6674, 117814, 3414011, …
  (−∞, 0] nonnegative
• A008277: Triangle of Stirling numbers of the second kind, S2(n,k), n >= 1, 1 <= k <= n.
  1 · 1, 1 · 1, 3, 1 · 1, 7, 6, 1 … row sums 1, 2, 5, 15, 52, 203, 877, 4140, …
  A008277 (−∞, 0) nonnegative
• A013612 → basis A008277
  36, 85, 25 · 216, 1115, 825, 125 … row sums 146, 2281, 40791, 816926, 18036311, …
  (−∞, 0] nonnegative
• A038328 → basis A008277
  196, 60, 4 · 2744, 1352, 192, 8 … row sums 260, 4296, 72256, 1238368, 21646912, …
  (−∞, 0] nonnegative
• A038207 → basis A008277
  1 · 3, 1 · 9, 7, 1 · 27, 37, 12, 1 … row sums 1, 4, 17, 77, 372, 1915, 10481, 60814, …
  (−∞, 0] nonnegative
• A027465 → basis A008277
  1 · 4, 1 · 16, 9, 1 · 64, 61, 15, 1 … row sums 1, 5, 26, 141, 799, 4736, 29371, …
  (−∞, 0] nonnegative
• A118394 → basis A008277
  1 · 1 · 1 · 7, 6 … row sums 1, 1, 1, 13, 49, 121, 2041, 13021, …
  (−∞, 0] nonnegative
• A081580 → basis A008277
  1 · 2, 1 · 9, 10, 1 · 28, 59, 19, 1 … row sums 1, 3, 20, 107, 681, 4454, 31263, …
  (−∞, 0] nonnegative
• A026729 → basis A008277
  1 · 1, 1 · 2, 4, 1 · 3, 13, 8, 1 … row sums 1, 2, 7, 25, 102, 456, 2219, 11640, …
  (−∞, 0] nonnegative
• A099097 → basis A008277
  1 · 3, 3 · 10, 28, 9 · 33, 207, 168, 27 … row sums 1, 6, 47, 435, 4622, 55080, 724371, …
  (−∞, 0] nonnegative
• A120910 → basis A008277
  3 · 9, 3 · 27, 21, 3 · 81, 111, 36, 3 … row sums 3, 12, 51, 231, 1116, 5745, 31443, …
  (−∞, 0] nonnegative
• A038255 → basis A008277
  1 · 7, 1 · 49, 15, 1 · 343, 169, 24, 1 … row sums 1, 8, 65, 537, 4516, 38699, 338233, …
  (−∞, 0] nonnegative
• A100861 → reverse → basis A008277
  1 · 1, 1 · 2, 4, 1 · 4, 16, 9, 1 … row sums 1, 2, 7, 30, 157, 948, 6487, 49332, …
  (−∞, 0] nonnegative
• A111125 → basis A008277
  1 · 4, 1 · 11, 8, 1 · 29, 42, 13, 1 … row sums 1, 5, 20, 85, 391, 1941, 10341, 58800, …
  (−∞, 0] nonnegative
• A011973 → basis A007318 → basis A008277
  1 · 1 · 3, 1 · 5, 2 … row sums 1, 1, 4, 7, 20, 43, 113, 267, …
  (−∞, 0] nonnegative
• A081581 → basis A008277
  1 · 2, 1 · 10, 11, 1 · 32, 67, 21, 1 … row sums 1, 3, 22, 121, 817, 5570, 40985, …
  (−∞, 0] nonnegative
• A114656 → basis A008277
  1 · 3, 1 · 11, 9, 1 · 45, 67, 18, 1 … row sums 1, 4, 21, 131, 928, 7275, 62051, …
  (−∞, 0] nonnegative
• A156992 → basis A008277
  1 · 4, 2 · 24, 30, 6 · 192, 456, 216, 24 … row sums 1, 6, 60, 888, 18120, 485280, 16445520, …
  (−∞, 0] nonnegative
• A038284 → basis A008277
  196, 204, 36 · 2744, 5256, 2160, 216 … row sums 436, 10376, 268864, 7547936, 228241216, …
  (−∞, 0] nonnegative
• A027466 → basis A008277
  1 · 8, 1 · 64, 17, 1 · 512, 217, 27, 1 … row sums 1, 9, 82, 757, 7087, 67340, 649931, …
  (−∞, 0] nonnegative
• A318772 → x ↦ (1/243)x → basis A008277
  1 · 3 · 9 · 27 … row sums 1, 3, 9, 27, 83, 255, 783, 2403, …
  (−∞, 0] nonnegative
• A113953 → basis A008277
  1 · 1, 1 · 3, 5, 1 · 5, 19, 10, 1 … row sums 1, 2, 9, 35, 162, 799, 4275, 24448, …
  (−∞, 0] nonnegative
• A114687 → basis A008277
  1 · 3, 2 · 11, 18, 4 · 45, 140, 72, 8 … row sums 1, 5, 33, 265, 2473, 26037, 303089, …
  (−∞, 0] nonnegative
• A038326 → basis A008277
  1 · 23, 12 · 529, 696, 144 … row sums 1, 35, 1369, 59723, 2883889, 152682227, …
  (−∞, 0] nonnegative
• A133080 → basis A008277
  1 · 2, 1 · 1, 3, 1 · 2, 10, 7, 1 … row sums 1, 3, 5, 20, 52, 255, 877, 5017, …
  (−∞, 0] nonnegative
• A358735 → basis A008277
  1 · 2, 1 · 7, 10, 2 · 33, 100, 52, 6 … row sums 1, 3, 19, 191, 2779, 55247, 1436433, …
  (−∞, 0] nonnegative
• A152830 → basis A008277
  1 · 1 · 1 · 1 … row sums 1, 1, 1, 1, 3, 3, 3, 3, …
  (−∞, 0] nonnegative
• A113413 → basis A008277
  1 · 3, 1 · 7, 7, 1 · 17, 33, 12, 1 … row sums 1, 4, 15, 63, 288, 1427, 7605, 43314, …
  (−∞, 0] nonnegative
• A172431 → basis A008277
  1 · 3, 2 · 8, 13, 3 · 21, 64, 34, 4 … row sums 1, 5, 24, 123, 682, 4079, 26159, …
  (−∞, 0] nonnegative
• A085478 → basis A008277
  1 · 1 · 2, 1 · 5, 6, 1 … row sums 1, 1, 3, 12, 53, 253, 1297, 7103, …
  (−∞, 0] nonnegative
• A109692 → basis A008277
  1 · 2, 1 · 8, 13, 3 · 48, 183, 113, 15 … row sums 1, 3, 24, 359, 8563, 295114, 13765813, …
  (−∞, 0] nonnegative
• A110441 → basis A008277
  1 · 4, 1 · 14, 9, 1 · 48, 57, 15, 1 … row sums 1, 5, 24, 121, 647, 3668, 21997, …
  (−∞, 0] nonnegative
• A038327 → basis A008277
  1 · 13, 1 · 169, 27, 1 · 2197, 547, 42, 1 … row sums 1, 14, 197, 2787, 39652, 567515, …
  (−∞, 0] nonnegative
• A125662 → basis A008277
  1 · 4, 1 · 15, 9, 1 · 56, 59, 15, 1 … row sums 1, 5, 25, 131, 722, 4187, 25531, …
  (−∞, 0] nonnegative
• A038325 → basis A008277
  1 · 22, 11 · 484, 605, 121 … row sums 1, 33, 1210, 49247, 2210791, 108548374, …
  (−∞, 0] nonnegative
• A154986 → basis A008277
  1 · 2, 1 · 6, 7, 1 · 24, 51, 17, 1 … row sums 1, 3, 14, 93, 811, 8914, 118881, …
  (−∞, 0] nonnegative
• basis-map coefficients of A297191, shifted → basis A008277
  1 · 1, 3, 1 · 1, 15, 25, 10, 1 … row sums 1, 5, 52, 877, 21147, 678570, 27644437, …
  (−∞, 0] nonnegative
• A136572 → basis A008277
  1 · 1, 1 · 2, 6, 2 · 6, 42, 36, 6 … row sums 1, 2, 10, 90, 1248, 24360, 631440, …
  (−∞, 0] nonnegative
• A038220 → basis A008277
  1 · 5, 2 · 25, 24, 4 · 125, 218, 84, 8 … row sums 1, 7, 53, 435, 3865, 37039, 381037, …
  (−∞, 0] nonnegative
• basis-map coefficients of A371080, shifted → basis A008277
  1 · 1, 1 · 4, 6, 1 · 28, 52, 15, 1 … row sums 1, 2, 11, 96, 1141, 17126, 310207, …
  (−∞, 0] nonnegative
• A207606 → basis A008277
  13, 13, 2 · 34, 63, 23, 2 · 89, 273, 176, 35, 2 … row sums 28, 122, 575, 2916, 15825, 91434, …
  (−∞, 0] nonnegative
• A371080: Triangle read by rows: BellMatrix(Product_{p in P(n)} p), where P(n) = {k : k mod m = 1 and 1 <= k <= m*(n + 1)} and m = 3.
  basis-map coefficients of A371080, shifted → x ↦ x−1 → basis A008277
  1 · 0, 1 · 0, 4, 1 · 0, 28, 12, 1 … row sums 1, 1, 5, 41, 465, 6721, 117941, …
  A371080 (−∞, 0] nonnegative
• A143683 → basis A008277
  1 · 2, 1 · 12, 13, 1 · 40, 83, 25, 1 … row sums 1, 3, 26, 149, 1119, 8162, 65271, …
  (−∞, 0] nonnegative
• A188440 → basis A008277
  1 · 1 · 3, 2 · 3, 2 … row sums 1, 1, 5, 5, 29, 29, 193, 193, …
  (−∞, 0] nonnegative