basis_map / A013609

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

210 sequences

• A232535 → basis A013609
  1 · 3, 4 · 12, 28, 12 · 48, 160, 148, 32 … row sums 1, 7, 52, 388, 2896, 21616, 161344, …
  (−∞, 0] nonnegative
• A154233 → basis A013609
  1 · 2, 2 · 9, 18, 4 · 40, 120, 88, 8 … row sums 1, 4, 31, 256, 2791, 33436, 477037, …
  (−∞, 0] nonnegative
• A169803 → basis A013609
  1 · 2, 2 · 3, 4 · 5, 10, 4 … row sums 1, 4, 7, 19, 40, 97, 217, 508, …
  (−∞, 0] nonnegative
• A299989 → basis A013609
  1, 2 · 8, 28, 28, 8 · 64, 320, 592, 512, 208, 32 … row sums 3, 72, 1728, 41472, 995328, 23887872, …
  (−∞, 0] nonnegative rational roots
• A038325 → basis A013609
  1 · 22, 22 · 484, 968, 484 … row sums 1, 44, 1936, 85184, 3748096, 164916224, …
  (−∞, 0] nonnegative rational roots
• A225471 → basis A013609
  1 · 4, 2 · 32, 24, 4 · 384, 352, 96, 8 … row sums 1, 6, 60, 840, 15120, 332640, 8648640, …
  (−∞, 0] nonnegative rational roots
• A081579 → basis A013609
  1 · 2, 2 · 8, 16, 4 · 24, 72, 56, 8 … row sums 1, 4, 28, 160, 976, 5824, 35008, …
  (−∞, 0] nonnegative
• A038220 → basis A013610
  1 · 5, 6 · 25, 60, 36 · 125, 450, 540, 216 … row sums 1, 11, 121, 1331, 14641, 161051, …
  (−∞, 0] nonnegative rational roots
• A081578 → basis A013609
  1 · 2, 2 · 7, 14, 4 · 20, 60, 48, 8 … row sums 1, 4, 25, 136, 769, 4300, 24121, …
  (−∞, 0] nonnegative
• A028338 → basis A013609
  1 · 2, 2 · 8, 12, 4 · 48, 88, 48, 8 … row sums 1, 4, 24, 192, 1920, 23040, 322560, …
  (−∞, 0] nonnegative rational roots
• A038336 → basis A013609
  484, 880, 400 · 10648, 29040, 26400, 8000 … row sums 1764, 74088, 3111696, 130691232, …
  (−∞, 0] nonnegative rational roots
• A038335 → basis A013609
  1 · 21, 18 · 441, 756, 324 · 9261, 23814, 20412, 5832 … row sums 1, 39, 1521, 59319, 2313441, 90224199, …
  (−∞, 0] nonnegative rational roots
• basis-map coefficients of A026729 → basis A013609
  1 · 1, 2 · 1, 4, 4 · 1, 6, 12, 8 … row sums 1, 3, 9, 27, 81, 243, 729, 2187, …
  (−∞, 0] nonnegative rational roots
• A081580 → basis A013609
  1 · 2, 2 · 9, 18, 4 · 28, 84, 64, 8 … row sums 1, 4, 31, 184, 1201, 7564, 48271, …
  (−∞, 0] nonnegative
• basis-map coefficients of A113214, shifted → basis A013609
  1 · -2, -2 · 4, 8, 4 · -8, -24, -24, -8 … row sums 1, -4, 16, -64, 256, -1024, 4096, …
  (−∞, 0] rational roots
• A038319 → basis A013609
  256, 320, 100 · 4096, 7680, 4800, 1000 … row sums 676, 17576, 456976, 11881376, …
  (−∞, 0] nonnegative rational roots
• A156992 → basis A013609
  1 · 4, 4 · 24, 48, 24 · 192, 576, 576, 192 … row sums 1, 8, 96, 1536, 30720, 737280, …
  (−∞, 0] nonnegative rational roots
• A013611 → basis A007318
  1 · 5, 4 · 25, 40, 16 · 125, 300, 240, 64 … row sums 1, 9, 81, 729, 6561, 59049, 531441, …
  (−∞, −1] nonnegative rational roots
• A038208: Triangle whose (i,j)-th entry is binomial(i,j)*2^i.
  1 · 2, 2 · 4, 8, 4 · 8, 24, 24, 8 … row sums 1, 4, 16, 64, 256, 1024, 4096, 16384, …
  A038208 (−∞, −1] nonnegative rational roots
• A013612 → basis A013609
  36, 120, 100 · 216, 1080, 1800, 1000 … row sums 256, 4096, 65536, 1048576, 16777216, …
  (−∞, 0] nonnegative rational roots
• A123519 → basis A013609
  11, 28, 16 · 41, 152, 176, 64 … row sums 55, 433, 3409, 26839, 211303, 1663585, …
  (−∞, 0] nonnegative
• A113413 → basis A013609
  1 · 3, 2 · 7, 12, 4 · 17, 46, 36, 8 … row sums 1, 5, 23, 107, 497, 2309, 10727, 49835, …
  (−∞, 0] nonnegative
• A196347 → basis A013609
  1 · 2, 2 · 8, 16, 8 · 48, 144, 144, 48 … row sums 1, 4, 32, 384, 6144, 122880, 2949120, …
  (−∞, 0] nonnegative rational roots
• A121574 → basis A013609
  1 · 3, 2 · 10, 14, 4 · 33, 70, 44, 8 … row sums 1, 5, 28, 155, 859, 4760, 26377, …
  (−∞, 0] nonnegative
• A102547 → reverse → basis A013609
  1, 2 · 1, 4, 4 · 1, 6, 12, 8 · 2, 14, 36, 40, 16 … row sums 3, 9, 27, 108, 405, 1458, 5346, 19683, …
  (−∞, 0] nonnegative
• A069466 → basis A013609
  1 · 4, 4 · 36, 72, 24 · 400, 1200, 960, 160 … row sums 1, 8, 132, 2720, 62020, 1497888, …
  (−∞, 0] nonnegative
• A038330 → basis A013609
  256, 256, 64 · 4096, 6144, 3072, 512 … row sums 576, 13824, 331776, 7962624, 191102976, …
  (−∞, 0] nonnegative rational roots
• A290319 → basis A013609
  1 · 2, 2 · 12, 16, 4 · 120, 184, 72, 8 … row sums 1, 4, 32, 384, 6144, 122880, 2949120, …
  (−∞, 0] nonnegative rational roots
• A063007 → basis A013609
  1 · 3, 4 · 13, 36, 24 · 63, 264, 360, 160 … row sums 1, 7, 73, 847, 10321, 129367, 1651609, …
  (−∞, 0] nonnegative
• A133214 → basis A013609
  13, 32, 16 · 63, 228, 240, 64 … row sums 61, 595, 6145, 65527, 712909, 7863667, …
  (−∞, 0] nonnegative
• A038324: Triangle read by rows whose (i,j)-th entry is binomial(i,j)*11^(i-j)*10^j.
  1 · 11, 10 · 121, 220, 100 · 1331, 3630, 3300, 1000 … row sums 1, 21, 441, 9261, 194481, 4084101, …
  A038324 (−∞, 0) nonnegative rational roots
• A103633 → basis A013609
  1 · 1, 2 · 2, 6, 4 · 2, 10, 16, 8 … row sums 1, 3, 12, 36, 144, 432, 1728, 5184, …
  (−∞, 0] nonnegative rational roots
• A135838 → basis A013609
  1 · 4, 4 · 8, 16, 8 · 32, 96, 96, 32 … row sums 1, 8, 32, 256, 1024, 8192, 32768, …
  (−∞, 0] nonnegative rational roots
• A011973 → x ↦ x+2 (shift +1) → basis A013609
  1 · 4, 2 · 7, 4 · 19, 18, 4 … row sums 1, 6, 11, 41, 96, 301, 781, 2286, …
  (−∞, 0] nonnegative
• A038327 → basis A013609
  1 · 13, 2 · 169, 52, 4 · 2197, 1014, 156, 8 … row sums 1, 15, 225, 3375, 50625, 759375, …
  (−∞, 0] nonnegative rational roots
• A085880 → basis A013609
  1 · 2, 2 · 8, 16, 8 · 40, 120, 120, 40 … row sums 1, 4, 32, 320, 3584, 43008, 540672, …
  (−∞, 0] nonnegative rational roots
• A147716 → basis A013609
  1 · 15, 2 · 225, 60, 4 · 3375, 1350, 180, 8 … row sums 1, 17, 289, 4913, 83521, 1419857, …
  (−∞, 0] nonnegative rational roots
• A100862 → basis A013609
  1 · 2, 2 · 5, 10, 4 · 14, 42, 36, 8 … row sums 1, 4, 19, 100, 571, 3484, 22501, …
  (−∞, 0] nonnegative
• A143685 → basis A013609
  1 · 2, 2 · 13, 26, 4 · 44, 132, 96, 8 … row sums 1, 4, 43, 280, 2281, 16684, 128323, …
  (−∞, 0] nonnegative
• A059473 → basis A013609
  1 · 4, 4 · 18, 36, 16 · 80, 240, 224, 64 … row sums 1, 8, 70, 608, 5284, 45920, 399064, …
  (−∞, 0] nonnegative
• A304236 → basis A013609
  1 · 1 · 4, 6 · 7, 12 … row sums 1, 1, 10, 19, 109, 280, 1261, 3781, …
  (−∞, 0] nonnegative
• A133080 → basis A013609
  1 · 2, 2 · 1, 4, 4 · 2, 10, 16, 8 … row sums 1, 4, 9, 36, 81, 324, 729, 2916, …
  (−∞, 0] nonnegative rational roots
• A286718 → basis A013609
  1 · 2, 2 · 10, 14, 4 · 80, 132, 60, 8 … row sums 1, 4, 28, 280, 3640, 58240, 1106560, …
  (−∞, 0] nonnegative rational roots
• A082985 → basis A013609
  1 · 4, 6 · 11, 30, 20 · 29, 112, 140, 56 … row sums 1, 10, 61, 337, 1810, 9637, 51169, …
  (−∞, 0] nonnegative
• A344565 → basis A013609
  3 · 30, 30 · 180, 360, 180 · 840, 2520, 2520, 840 … row sums 3, 60, 720, 6720, 53760, 387072, …
  (−∞, 0] nonnegative rational roots
• A054142 → basis A013609
  1 · 2, 2 · 5, 10, 4 · 13, 40, 36, 8 … row sums 1, 4, 19, 97, 508, 2683, 14209, 75316, …
  (−∞, 0] nonnegative
• A027465 → basis A013611
  1 · 4, 4 · 16, 32, 16 · 64, 192, 192, 64 … row sums 1, 8, 64, 512, 4096, 32768, 262144, …
  (−∞, 0] nonnegative rational roots
• A120910 → basis A013609
  3 · 9, 6 · 27, 36, 12 · 81, 162, 108, 24 … row sums 3, 15, 75, 375, 1875, 9375, 46875, …
  (−∞, −1] nonnegative rational roots
• A118933 → basis A013609
  1 · 1 · 1 · 1 … row sums 1, 1, 1, 1, 19, 91, 271, 631, …
  (−∞, 0] nonnegative
• A100861 → reverse → basis A013609
  1 · 1, 2 · 2, 6, 4 · 4, 18, 24, 8 … row sums 1, 3, 12, 54, 270, 1458, 8424, 51516, …
  (−∞, 0] nonnegative