basis_map

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

1056 sequences

• A120910 → basis A007318
  3 · 9, 3 · 27, 18, 3 · 81, 81, 27, 3 … row sums 3, 12, 48, 192, 768, 3072, 12288, …
  (−∞, −1] nonnegative rational roots
• A013612 → basis A013611
  36, 240, 400 · 216, 2160, 7200, 8000 … row sums 676, 17576, 456976, 11881376, …
  (−∞, 0] nonnegative rational roots
• A013610 → basis A013610
  1 · 4, 9 · 16, 72, 81 · 64, 432, 972, 729 … row sums 1, 13, 169, 2197, 28561, 371293, …
  (−∞, 0] nonnegative rational roots
• A225470 → basis A013609
  1 · 3, 2 · 18, 18, 4 · 162, 198, 72, 8 … row sums 1, 5, 40, 440, 6160, 104720, 2094400, …
  (−∞, 0] nonnegative rational roots
• A099097 → basis A013610
  1 · 3, 9 · 10, 57, 81 · 33, 279, 783, 729 … row sums 1, 12, 148, 1824, 22480, 277056, …
  (−∞, 0] nonnegative
• A038284 → basis A013609
  196, 336, 144 · 2744, 7056, 6048, 1728 … row sums 676, 17576, 456976, 11881376, …
  (−∞, 0] nonnegative rational roots
• A154986 → basis A013611
  1 · 2, 4 · 6, 24, 16 · 24, 144, 224, 64 … row sums 1, 6, 46, 456, 5496, 78576, 1295856, …
  (−∞, 0] nonnegative
• A027466 → basis A013609
  1 · 8, 2 · 64, 32, 4 · 512, 384, 96, 8 … row sums 1, 10, 100, 1000, 10000, 100000, …
  (−∞, 0] nonnegative rational roots
• A052553 → basis A008277
  1 · 1 · 2, 1 · 3, 2 … row sums 1, 1, 3, 5, 12, 24, 56, 123, …
  (−∞, 0] nonnegative
• basis-map coefficients of A113214, shifted → basis A008277
  1 · -2, -1 · 4, 5, 1 · -8, -19, -9, -1 … row sums 1, -3, 10, -37, 151, -674, 3263, …
  (−∞, 0]
• A038323 → basis A013610
  1 · 20, 27 · 400, 1080, 729 … row sums 1, 47, 2209, 103823, 4879681, …
  (−∞, 0] nonnegative rational roots
• A225470 → basis A008277
  1 · 3, 1 · 18, 10, 1 · 162, 118, 21, 1 … row sums 1, 4, 29, 302, 4089, 68056, 1342949, …
  (−∞, 0] nonnegative
• A152842 → basis A013609
  1 · 4, 6 · 8, 20, 12 · 32, 128, 168, 72 … row sums 1, 10, 40, 400, 1600, 16000, 64000, …
  (−∞, 0] nonnegative rational roots
• A356546 → basis A013609
  1 · 4, 4 · 24, 48, 24 · 160, 480, 480, 160 … row sums 1, 8, 96, 1280, 17920, 258048, 3784704, …
  (−∞, 0] nonnegative rational roots
• A152828 → basis A007318
  1 · 1 · 1 · 2, 1 … row sums 1, 1, 1, 3, 3, 3, 9, 9, …
  (−∞, −1] nonnegative rational roots
• A249248 → basis A008277
  1 · 4, 3 · 11, 16, 3 · 38, 99, 40, 3 … row sums 1, 7, 30, 180, 1138, 8242, 65012, …
  (−∞, 0] nonnegative
• A109692 → basis A013609
  1 · 2, 2 · 8, 20, 12 · 48, 200, 272, 120 … row sums 1, 4, 40, 640, 14080, 394240, 13404160, …
  (−∞, 0] nonnegative rational roots
• A038336 → basis A008277
  484, 540, 100 · 10648, 22120, 9600, 1000 … row sums 1124, 43368, 1830976, 84062432, …
  (−∞, 0] nonnegative
• A028326 → basis A013611
  2 · 4, 8 · 8, 32, 32 · 16, 96, 192, 128 … row sums 2, 12, 72, 432, 2592, 15552, 93312, …
  (−∞, 0] nonnegative rational roots
• A013622 → basis A013610
  1 · 8, 15 · 64, 240, 225 · 512, 2880, 5400, 3375 … row sums 1, 23, 529, 12167, 279841, 6436343, …
  (−∞, 0] nonnegative rational roots
• A099097 → basis A013611
  1 · 3, 12 · 10, 76, 144 · 33, 372, 1392, 1728 … row sums 1, 15, 230, 3525, 54025, 828000, …
  (−∞, 0] nonnegative
• basis-map coefficients of A026729 → basis A007318
  1 · 1, 1 · 1, 2, 1 · 1, 3, 3, 1 … row sums 1, 2, 4, 8, 16, 32, 64, 128, …
  (−∞, −1] nonnegative rational roots
• A013618 → basis A008277
  144, 385, 121 · 1728, 10439, 8349, 1331 … row sums 650, 21847, 844911, 36705824, …
  (−∞, 0] nonnegative
• basis-map coefficients of A021012 → x ↦ x+1
  1 · -1, -1 · 2, 4, 2 · -6, -18, -18, -6 … row sums 1, -2, 8, -48, 384, -3840, 46080, …
  (−∞, −1] rational roots
• A013609 → basis A008277
  1 · 3, 2 · 9, 16, 4 · 27, 98, 60, 8 … row sums 1, 5, 29, 193, 1449, 12077, 110309, …
  (−∞, 0] nonnegative
• A178822 → basis A013611
  1 · 12, 24 · 84, 336, 336 · 448, 2688, 5376, 3584 … row sums 1, 36, 756, 12096, 163296, 1959552, …
  (−∞, 0] nonnegative rational roots
• A038226 → basis A013611
  121, 704, 1024 · 1331, 11616, 33792, 32768 … row sums 1849, 79507, 3418801, 147008443, …
  (−∞, 0] nonnegative rational roots
• A038319 → basis A013610
  256, 480, 225 · 4096, 11520, 10800, 3375 … row sums 961, 29791, 923521, 28629151, …
  (−∞, 0] nonnegative rational roots
• A081577 → basis A013611
  1 · 2, 4 · 6, 24, 16 · 16, 96, 160, 64 … row sums 1, 6, 46, 336, 2476, 18216, 134056, …
  (−∞, 0] nonnegative
• narayana → basis A008277
  1 · 2, 1 · 5, 6, 1 · 14, 31, 12, 1 … row sums 1, 3, 12, 58, 323, 2014, 13793, 102351, …
  (−∞, 0] nonnegative
• A038303: Triangle whose (i,j)-th entry is binomial(i,j)*10^(i-j)*1^j.
  1 · 10, 1 · 100, 20, 1 · 1000, 300, 30, 1 … row sums 1, 11, 121, 1331, 14641, 161051, …
  A038303 (−∞, 0) nonnegative rational roots
• A099097 → basis A007318
  1 · 3, 3 · 10, 19, 9 · 33, 93, 87, 27 … row sums 1, 6, 38, 240, 1516, 9576, 60488, …
  (−∞, −1] nonnegative
• A154227 → basis A007318
  1 · 2, 1 · 10, 10, 1 · 40, 60, 22, 1 … row sums 1, 3, 21, 123, 999, 8163, 80433, …
  (−∞, 0] nonnegative
• A038322 → basis A013609
  1 · 19, 16 · 361, 608, 256 · 6859, 17328, 14592, 4096 … row sums 1, 35, 1225, 42875, 1500625, 52521875, …
  (−∞, 0] nonnegative rational roots
• A274496 → basis A013610
  1 · 2 · 4, 6 · 8, 12 … row sums 1, 2, 10, 20, 100, 200, 1000, 2000, …
  (−∞, 0] nonnegative rational roots
• A118933 → x ↦ x+1
  1 · 1 · 1 · 1 … row sums 1, 1, 1, 1, 13, 61, 181, 421, …
  (−∞, −1] nonnegative
• A269944 → basis A008277
  1 · 1, 1 · 2, 4, 1 · 10, 26, 11, 1 … row sums 1, 2, 7, 48, 579, 11110, 314093, …
  (−∞, 0] nonnegative
• A391533 → basis A008277
  9, 7, 1 · 18, 30, 11, 1 · 36, 108, 74, 16, 1 … row sums 17, 60, 235, 1013, 4762, 24207, 132105, …
  (−∞, 0] nonnegative
• A327997 → basis A008277
  1 · 4, 1 · 17, 10, 1 · 78, 81, 18, 1 … row sums 1, 5, 28, 178, 1292, 10684, 99880, …
  (−∞, 0] nonnegative
• A113953 → basis A013610
  1 · 1, 3 · 3, 12, 9 · 5, 33, 63, 27 … row sums 1, 4, 24, 128, 704, 3840, 20992, …
  (−∞, 0] nonnegative
• A038255 → basis A013611
  1 · 7, 4 · 49, 56, 16 · 343, 588, 336, 64 … row sums 1, 11, 121, 1331, 14641, 161051, …
  (−∞, 0] nonnegative rational roots
• A008459 → basis A008277
  1 · 2, 1 · 6, 7, 1 · 20, 43, 15, 1 … row sums 1, 3, 14, 79, 505, 3554, 27083, 221015, …
  (−∞, 0] nonnegative
• A152828 → basis A013611
  1 · 1 · 1 · 2, 4 … row sums 1, 1, 1, 6, 6, 6, 36, 36, …
  (−∞, 0] nonnegative rational roots
• A169803 → x ↦ x+1
  1 · 2, 1 · 3, 2 · 5, 5, 1 … row sums 1, 3, 5, 11, 21, 43, 85, 171, …
  (−∞, −1] nonnegative
• basis-map coefficients of A021012 → basis A013610
  1 · -1, -3 · 2, 12, 18 · -6, -54, -162, -162 … row sums 1, -4, 32, -384, 6144, -122880, …
  (−∞, 0] rational roots
• A094645: Triangle of generalized Stirling numbers of the first kind read by rows: T(n, k) = (-1)^(n+k)*Sum_{m=0..n} Stirling1(n, m) * binomial(m, k), where Stirling1 is A048994.
  A028338 → x ↦ 2x−3
  1 · -1, 1 · 0, -1, 1 · 0, -1, 0, 1 … row sums 1, 0, 0, 0, 0, 0, 0, 0, …
  A094645 (−∞, 3/2] rational roots
• A038207: Triangle whose (i,j)-th entry is binomial(i,j)*2^(i-j).
  1 · 2, 1 · 4, 4, 1 · 8, 12, 6, 1 … row sums 1, 3, 9, 27, 81, 243, 729, 2187, …
  A038207 (−∞, −1] nonnegative rational roots
• A128099 → basis A013611
  1 · 1 · 3, 8 · 5, 16 … row sums 1, 1, 11, 21, 131, 341, 1651, 5061, …
  (−∞, 0] nonnegative
• basis-map coefficients of A026729, shifted → basis A008277
  1 · -1, -1 · 1, 3, 1 · -1, -7, -6, -1 … row sums 1, -2, 5, -15, 52, -203, 877, -4140, …
  (−∞, 0]
• A269944 → basis A013611
  1 · 1, 4 · 2, 12, 16 · 10, 68, 128, 64 … row sums 1, 5, 30, 270, 3780, 79380, 2381400, …
  (−∞, 0] nonnegative rational roots