basis_map

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

1056 sequences

• A038271 → basis A013611
  1 · 12, 20 · 144, 480, 400 · 1728, 8640, 14400, 8000 … row sums 1, 32, 1024, 32768, 1048576, 33554432, …
  (−∞, 0] nonnegative rational roots
• A038243 → basis A008277
  1 · 6, 1 · 36, 13, 1 · 216, 127, 21, 1 … row sums 1, 7, 50, 365, 2727, 20878, 163967, …
  (−∞, 0] nonnegative
• A367270 → basis A013609
  1 · 1 · 3, 4 · 10, 24, 12 … row sums 1, 1, 7, 46, 307, 2086, 14374, 100108, …
  (−∞, 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
• A026729: Square array of binomial coefficients T(n,k) = binomial(n,k), n >= 0, k >= 0, read by downward antidiagonals.
  1 · 0, 1 · 0, 1, 1 · 0, 0, 2, 1 … row sums 1, 1, 2, 3, 5, 8, 13, 21, …
  A026729 (−4, 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
• A085841 → basis A013609
  1 · 7, 8 · 61, 144, 64 · 547, 2008, 2112, 512 … row sums 1, 15, 269, 5179, 102105, 2028071, …
  (−∞, 0] nonnegative
• A391533 → x ↦ x+1
  9, 6, 1 · 18, 21, 8, 1 · 36, 60, 37, 10, 1 … row sums 16, 48, 144, 432, 1296, 3888, 11664, …
  (−∞, −1] nonnegative rational roots
• A207824 → basis A013609
  1 · 6, 2 · 35, 24, 4 · 204, 212, 72, 8 … row sums 1, 8, 63, 496, 3905, 30744, 242047, …
  (−∞, 0] nonnegative
• A081577 → basis A013610
  1 · 2, 3 · 6, 18, 9 · 16, 72, 90, 27 … row sums 1, 5, 33, 205, 1289, 8085, 50737, …
  (−∞, 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
• A327997 → basis A013610
  1 · 4, 3 · 17, 27, 9 · 78, 195, 135, 27 … row sums 1, 7, 53, 435, 3873, 37383, 390501, …
  (−∞, 0] nonnegative
• narayana → basis A013611
  1 · 2, 4 · 5, 20, 16 · 14, 84, 144, 64 … row sums 1, 6, 41, 306, 2426, 20076, 171481, …
  (−∞, 0] nonnegative
• A038326 → basis A013609
  1 · 23, 24 · 529, 1104, 576 … row sums 1, 47, 2209, 103823, 4879681, …
  (−∞, 0] nonnegative rational roots
• A038333 → basis A013611
  361, 1064, 784 · 6859, 30324, 44688, 21952 … row sums 2209, 103823, 4879681, 229345007, …
  (−∞, 0] nonnegative rational roots
• A232535 → basis A008277
  1 · 3, 2 · 12, 17, 3 · 48, 121, 49, 4 … row sums 1, 5, 32, 222, 1655, 13169, 111169, …
  (−∞, 0] nonnegative
• A114687 → basis A013610
  1 · 3, 6 · 11, 42, 36 · 45, 252, 432, 216 … row sums 1, 9, 89, 945, 10577, 123129, 1476841, …
  (−∞, 0] nonnegative
• A108838 → x ↦ x+1
  2 · 5, 2 · 14, 12, 2 · 42, 56, 21, 2 … row sums 2, 7, 28, 121, 550, 2591, 12536, 61921, …
  (−∞, −1] nonnegative
• A081577 → x ↦ x+1
  1 · 2, 1 · 6, 6, 1 · 16, 24, 10, 1 … row sums 1, 3, 13, 51, 205, 819, 3277, 13107, …
  (−∞, −1] 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
• A113413 → basis A007318
  1 · 3, 1 · 7, 6, 1 · 17, 23, 9, 1 … row sums 1, 4, 14, 50, 178, 634, 2258, 8042, …
  (−∞, −1] nonnegative
• A038303 → basis A013610
  1 · 11, 3 · 121, 66, 9 · 1331, 1089, 297, 27 … row sums 1, 14, 196, 2744, 38416, 537824, …
  (−∞, 0] nonnegative rational roots
• A081581 → basis A007318
  1 · 2, 1 · 10, 10, 1 · 32, 48, 18, 1 … row sums 1, 3, 21, 99, 549, 2835, 15093, 79299, …
  (−∞, −1] nonnegative
• A026374 → x ↦ x+1
  1 · 2, 1 · 5, 5, 1 · 10, 15, 7, 1 … row sums 1, 3, 11, 33, 121, 363, 1331, 3993, …
  (−∞, −1] nonnegative
• A038326 → basis A013611
  1 · 23, 48 · 529, 2208, 2304 … row sums 1, 71, 5041, 357911, 25411681, …
  (−∞, 0] nonnegative rational roots
• A154986 → basis A007318
  1 · 2, 1 · 6, 6, 1 · 24, 36, 14, 1 … row sums 1, 3, 13, 75, 537, 4611, 46053, 525483, …
  (−∞, −1] 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
• A038329 → basis A013610
  225, 270, 81 · 3375, 6075, 3645, 729 … row sums 576, 13824, 331776, 7962624, 191102976, …
  (−∞, 0] nonnegative rational roots
• A114656 → basis A013611
  1 · 3, 4 · 11, 32, 16 · 45, 204, 240, 64 … row sums 1, 7, 59, 553, 5541, 58107, 629799, …
  (−∞, 0] nonnegative
• A091044 → basis A013609
  1 · 4, 4 · 16, 32, 12 · 64, 192, 160, 32 … row sums 1, 8, 60, 448, 3344, 24960, 186304, …
  (−∞, 0] nonnegative
• A013612 → basis A008277
  36, 85, 25 · 216, 1115, 825, 125 … row sums 146, 2281, 40791, 816926, 18036311, …
  (−∞, 0] nonnegative
• A091044 → basis A007318
  1 · 4, 2 · 16, 16, 3 · 64, 96, 40, 4 … row sums 1, 6, 35, 204, 1189, 6930, 40391, …
  (−∞, −1] nonnegative
• A154986 → basis A013609
  1 · 2, 2 · 6, 12, 4 · 24, 72, 56, 8 … row sums 1, 4, 22, 160, 1432, 15328, 190192, …
  (−∞, 0] nonnegative
• A038231: Triangle whose (i,j)-th entry is binomial(i,j)*4^(i-j).
  1 · 4, 1 · 16, 8, 1 · 64, 48, 12, 1 … row sums 1, 5, 25, 125, 625, 3125, 15625, 78125, …
  A038231 (−∞, −1] nonnegative rational roots
• A038291: Triangle whose (i,j)-th entry is binomial(i,j)*9^(i-j)*1^j.
  1 · 9, 1 · 81, 18, 1 · 729, 243, 27, 1 … row sums 1, 10, 100, 1000, 10000, 100000, …
  A038291 (−∞, 0) nonnegative rational roots
• A102662 → basis A013609
  1 · 4, 6 · 9, 22, 12 · 22, 76, 80, 24 … row sums 1, 10, 43, 202, 937, 4354, 20227, …
  (−∞, 0] nonnegative
• A013611 → basis A013611
  1 · 5, 16 · 25, 160, 256 · 125, 1200, 3840, 4096 … row sums 1, 21, 441, 9261, 194481, 4084101, …
  (−∞, 0] nonnegative rational roots
• A038328 → basis A008277
  196, 60, 4 · 2744, 1352, 192, 8 … row sums 260, 4296, 72256, 1238368, 21646912, …
  (−∞, 0] nonnegative
• basis-map coefficients of A026729 → basis A013610
  1 · 1, 3 · 1, 6, 9 · 1, 9, 27, 27 … row sums 1, 4, 16, 64, 256, 1024, 4096, 16384, …
  (−∞, 0] nonnegative rational roots
• A102547 → x ↦ (1/27)x → basis A013610
  1 · 3 · 9 · 28, 3 … row sums 1, 3, 9, 31, 105, 351, 1177, 3951, …
  (−∞, 0] nonnegative
• A249252 → basis A013610
  1 · 5, 12 · 17, 72, 72 · 61, 372, 720, 432 … row sums 1, 17, 161, 1585, 15553, 152657, …
  (−∞, 0] nonnegative
• A135838 → x ↦ x+1
  1 · 4, 2 · 8, 8, 2 · 32, 48, 24, 4 … row sums 1, 6, 18, 108, 324, 1944, 5832, 34992, …
  (−∞, −1] nonnegative rational roots
• A038220 → basis A007318
  1 · 5, 2 · 25, 20, 4 · 125, 150, 60, 8 … row sums 1, 7, 49, 343, 2401, 16807, 117649, …
  (−∞, −1] nonnegative rational roots
• A169803 → basis A013611
  1 · 2, 4 · 3, 8 · 5, 20, 16 … row sums 1, 6, 11, 41, 96, 301, 781, 2286, …
  (−∞, 0] nonnegative
• A038243 → basis A013611
  1 · 6, 4 · 36, 48, 16 · 216, 432, 288, 64 … row sums 1, 10, 100, 1000, 10000, 100000, …
  (−∞, 0] nonnegative rational roots
• 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
• A038226 → basis A013610
  121, 528, 576 · 1331, 8712, 19008, 13824 … row sums 1225, 42875, 1500625, 52521875, …
  (−∞, 0] nonnegative rational roots
• A038281 → basis A013610
  121, 198, 81 · 1331, 3267, 2673, 729 … row sums 400, 8000, 160000, 3200000, 64000000, …
  (−∞, 0] nonnegative rational roots
• A318772 → x ↦ (1/243)x → basis A013610
  1 · 3 · 9 · 27 … row sums 1, 3, 9, 27, 85, 267, 837, 2619, …
  (−∞, 0] nonnegative