basis_map

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

1056 sequences

• A116412 → basis A013611
  1 · 4, 4 · 13, 32, 16 · 43, 168, 192, 64 … row sums 1, 8, 61, 467, 3574, 27353, 209341, …
  (−∞, 0] nonnegative
• A079638 → basis A013611
  1 · 4, 4 · 24, 44, 16 · 192, 488, 336, 64 … row sums 1, 8, 84, 1080, 16344, 283680, 5544000, …
  (−∞, 0] nonnegative
• A269947 → basis A013611
  1 · 1, 4 · 2, 12, 16 · 18, 116, 192, 64 … row sums 1, 5, 30, 390, 12480, 861120, …
  (−∞, 0] nonnegative rational roots
• A274498 → basis A013610
  1 · 3 · 9, 18 · 27, 54 … row sums 1, 3, 27, 81, 729, 2187, 19683, 59049, …
  (−∞, 0] nonnegative rational roots
• A274496 → basis A013609
  1 · 2 · 4, 4 · 8, 8 … row sums 1, 2, 8, 16, 64, 128, 512, 1024, …
  (−∞, 0] nonnegative rational roots
• A249252 → basis A013609
  1 · 5, 8 · 17, 48, 32 · 61, 248, 320, 128 … row sums 1, 13, 97, 757, 5881, 45709, 355249, …
  (−∞, 0] nonnegative
• A038322 → basis A008277
  1 · 19, 8 · 361, 368, 64 · 6859, 12824, 5184, 512 … row sums 1, 27, 793, 25379, 883057, 33250795, …
  (−∞, 0] nonnegative
• A272866 → basis A007318
  1 · 5, 5, 1 · 25, 50, 35, 10, 1 … row sums 1, 11, 121, 1331, 14641, 161051, …
  (−∞, −1] nonnegative
• A204420 → basis A007318
  1 · 1, 1 · 9, 12, 3 · 225, 345, 135, 15 … row sums 1, 2, 24, 720, 40320, 3628800, …
  (−∞, 0] nonnegative rational roots
• A038338 → basis A007318
  576, 576, 144 · 13824, 20736, 10368, 1728 … row sums 1296, 46656, 1679616, 60466176, …
  (−∞, 0] nonnegative rational roots
• A013611: Triangle of coefficients in expansion of (1+4x)^n.
  1 · 1, 4 · 1, 8, 16 · 1, 12, 48, 64 … row sums 1, 5, 25, 125, 625, 3125, 15625, 78125, …
  A013611 (−∞, 0) [−1, 0] nonnegative rational roots
• A038226 → basis A007318
  121, 176, 64 · 1331, 2904, 2112, 512 … row sums 361, 6859, 130321, 2476099, 47045881, …
  (−∞, 0] nonnegative rational roots
• A081581 → basis A013610
  1 · 2, 3 · 10, 30, 9 · 32, 144, 162, 27 … row sums 1, 5, 49, 365, 3001, 23765, 190849, …
  (−∞, 0] nonnegative
• A143685 → basis A007318
  1 · 2, 1 · 13, 13, 1 · 44, 66, 24, 1 … row sums 1, 3, 27, 135, 891, 5103, 31347, …
  (−∞, −1] nonnegative
• A079638 → basis A013610
  1 · 4, 3 · 24, 33, 9 · 192, 366, 189, 27 … row sums 1, 7, 66, 774, 10800, 174240, 3185280, …
  (−∞, 0] nonnegative
• A145324 → basis A013611
  1 · 3, 8 · 12, 68, 96 · 60, 532, 1568, 1536 … row sums 1, 11, 176, 3696, 96096, 2978976, …
  (−∞, 0] nonnegative rational roots
• A391533 → basis A013609
  9, 12, 4 · 18, 42, 32, 8 · 36, 120, 148, 80, 16 … row sums 25, 100, 400, 1600, 6400, 25600, …
  (−∞, 0] nonnegative rational roots
• A200536 → basis A013610
  1 · 6, 21, 18 · 36, 252, 657, 756, 324 … row sums 1, 45, 2025, 91125, 4100625, 184528125, …
  (−∞, 0] nonnegative rational roots
• A113214 → basis A013609
  1 · 3, 2 · 4, 10, 4 · 7, 26, 28, 8 … row sums 1, 5, 18, 69, 261, 990, 3753, 14229, …
  (−∞, 0] nonnegative
• A132393 → basis A013609
  1 · 1, 2 · 2, 6, 4 · 6, 22, 24, 8 … row sums 1, 3, 12, 60, 360, 2520, 20160, 181440, …
  (−∞, 0] nonnegative rational roots
• A128813 → basis A008277
  1 · 2, 1 · 8, 13, 3 · 56, 217, 135, 18 … row sums 1, 3, 24, 426, 14356, 817201, 72259579, …
  (−∞, 0] nonnegative
• A207823: Triangle of coefficients of Chebyshev's S(n,x+4) polynomials (exponents of x in increasing order).
  1 · 4, 1 · 15, 8, 1 · 56, 46, 12, 1 … row sums 1, 5, 24, 115, 551, 2640, 12649, 60605, …
  A207823 (−6, −2) nonnegative
• A013618 → basis A013611
  144, 1056, 1936 · 1728, 19008, 69696, 85184 … row sums 3136, 175616, 9834496, 550731776, …
  (−∞, 0] nonnegative rational roots
• A116414 → basis A007318
  1 · 5, 1 · 22, 10, 1 · 95, 69, 15, 1 … row sums 1, 6, 33, 180, 981, 5346, 29133, …
  (−9, −1) nonnegative
• A013612 → basis A013610
  36, 180, 225 · 216, 1620, 4050, 3375 … row sums 441, 9261, 194481, 4084101, 85766121, …
  (−∞, 0] nonnegative rational roots
• A038303 → basis A007318
  1 · 11, 1 · 121, 22, 1 · 1331, 363, 33, 1 … row sums 1, 12, 144, 1728, 20736, 248832, …
  (−∞, 0] nonnegative rational roots
• A038328 → basis A013609
  196, 112, 16 · 2744, 2352, 672, 64 … row sums 324, 5832, 104976, 1889568, 34012224, …
  (−∞, 0] nonnegative rational roots
• A139548 → basis A013609
  1 · 8, 16, 8 · 64, 256, 384, 256, 64 … row sums 1, 32, 1024, 32768, 1048576, 33554432, …
  (−∞, 0] nonnegative rational roots
• A269944 → basis A013609
  1 · 1, 2 · 2, 6, 4 · 10, 34, 32, 8 … row sums 1, 3, 12, 84, 1008, 19152, 536256, …
  (−∞, 0] nonnegative rational roots
• A027467 → basis A013609
  1 · 16, 2 · 256, 64, 4 · 4096, 1536, 192, 8 … row sums 1, 18, 324, 5832, 104976, 1889568, …
  (−∞, 0] nonnegative rational roots
• A113953 → basis A013611
  1 · 1, 4 · 3, 16, 16 · 5, 44, 112, 64 … row sums 1, 5, 35, 225, 1475, 9625, 62875, …
  (−∞, 0] nonnegative
• A038330 → basis A008277
  256, 144, 16 · 4096, 3904, 960, 64 … row sums 416, 9024, 204544, 4849664, 120303616, …
  (−∞, 0] nonnegative
• A038321 → basis A007318
  324, 252, 49 · 5832, 6804, 2646, 343 … row sums 625, 15625, 390625, 9765625, 244140625, …
  (−∞, 0] nonnegative rational roots
• A001263 → basis A013611
  1 · 2, 4 · 5, 20, 16 · 14, 84, 144, 64 … row sums 1, 6, 41, 306, 2426, 20076, 171481, …
  (−∞, 0] nonnegative
• A013609 → basis A008288
  1 · 3, 2 · 9, 16, 4 · 27, 82, 52, 8 … row sums 1, 5, 29, 169, 985, 5741, 33461, …
  [−3−2√2, −3+2√2] nonnegative
• Triangle whose (i,j)-th entry is binomial(i,j)*12^(i-j)*11^j.
  144, 264, 121 · 1728, 4752, 4356, 1331 … row sums 529, 12167, 279841, 6436343, 148035889, …
  (−∞, 0) nonnegative rational roots
• A178820 → basis A008277
  1 · 8, 4 · 40, 50, 10 · 160, 380, 180, 20 … row sums 1, 12, 100, 740, 5285, 37744, 274092, …
  (−∞, 0] nonnegative
• A154228 → basis A007318
  1 · 2, 1 · 18, 18, 1 · 96, 144, 50, 1 … row sums 1, 3, 37, 291, 4943, 67791, 1587413, …
  (−∞, 0] nonnegative
• A272867 → basis A007318
  1 · 6, 6, 1 · 36, 72, 48, 12, 1 … row sums 1, 13, 169, 2197, 28561, 371293, …
  (−∞, 0] nonnegative
• A081582 → basis A013609
  1 · 2, 2 · 11, 22, 4 · 36, 108, 80, 8 … row sums 1, 4, 37, 232, 1705, 11692, 82573, …
  (−∞, 0] nonnegative
• A110441 → basis A013611
  1 · 4, 4 · 14, 32, 16 · 48, 176, 192, 64 … row sums 1, 8, 62, 480, 3716, 28768, 222712, …
  (−∞, 0] nonnegative
• A046716 → basis A008277
  1 · 2, 1 · 5, 6, 1 · 16, 37, 14, 1 … row sums 1, 3, 12, 68, 578, 7412, 136468, …
  (−∞, 0] nonnegative
• delannoy → basis A013610
  1 · 2, 3 · 5, 15, 9 · 12, 54, 72, 27 … row sums 1, 5, 29, 165, 941, 5365, 30589, …
  (−∞, 0] nonnegative
• A249251 → basis A007318
  1 · 4, 3 · 13, 18, 6 · 43, 87, 57, 12 … row sums 1, 7, 37, 199, 1069, 5743, 30853, …
  (−∞, −1] nonnegative
• A207824 → basis A008277
  1 · 6, 1 · 35, 13, 1 · 204, 125, 21, 1 … row sums 1, 7, 49, 351, 2578, 19439, 150631, …
  (−∞, 0] nonnegative
• A085881 → basis A013610
  1 · 2, 3 · 12, 36, 27 · 120, 540, 810, 405 … row sums 1, 5, 75, 1875, 65625, 2953125, …
  (−∞, 0] nonnegative rational roots
• A113214 → basis A008277
  1 · 3, 1 · 4, 6, 1 · 7, 21, 10, 1 … row sums 1, 4, 11, 39, 152, 660, 3131, 16078, …
  (−∞, 0] nonnegative
• A038279: Triangle whose (i,j)-th entry is binomial(i,j)*8^(i-j)*1^j.
  1 · 8, 1 · 64, 16, 1 · 512, 192, 24, 1 … row sums 1, 9, 81, 729, 6561, 59049, 531441, …
  A038279 (−∞, 0) nonnegative rational roots
• A100861 → basis A013611
  1 · 1 · 2, 4 · 4, 12 … row sums 1, 1, 6, 16, 106, 426, 3076, 15856, …
  (−∞, 0] nonnegative
• A081577 → basis A013609
  1 · 2, 2 · 6, 12, 4 · 16, 48, 40, 8 … row sums 1, 4, 22, 112, 580, 2992, 15448, 79744, …
  (−∞, 0] nonnegative