basis_map / A013609

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

210 sequences

• A143683 → basis A013609
  1 · 2, 2 · 12, 24, 4 · 40, 120, 88, 8 … row sums 1, 4, 40, 256, 1984, 14080, 103936, …
  (−∞, 0] nonnegative
• A038220: Triangle whose (i,j)-th entry is binomial(i,j)*3^(i-j)*2^j.
  1 · 3, 2 · 9, 12, 4 · 27, 54, 36, 8 … row sums 1, 5, 25, 125, 625, 3125, 15625, 78125, …
  A038220 (−∞, −1] nonnegative rational roots
• A013609 → basis A013609
  1 · 3, 4 · 9, 24, 16 · 27, 108, 144, 64 … row sums 1, 7, 49, 343, 2401, 16807, 117649, …
  (−∞, 0] nonnegative rational roots
• A038221 → basis A013609
  1 · 6, 6 · 36, 72, 36 · 216, 648, 648, 216 … row sums 1, 12, 144, 1728, 20736, 248832, …
  (−∞, 0] nonnegative rational roots
• basis-map coefficients of A026729, shifted → basis A013609
  1 · -1, -2 · 1, 4, 4 · -1, -6, -12, -8 … row sums 1, -3, 9, -27, 81, -243, 729, -2187, …
  (−∞, 0] rational roots
• A030528 → basis A013609
  1 · 2, 2 · 3, 8, 4 · 5, 20, 24, 8 … row sums 1, 4, 15, 57, 216, 819, 3105, 11772, …
  (−∞, 0] nonnegative
• A013622 → basis A013609
  1 · 8, 10 · 64, 160, 100 · 512, 1920, 2400, 1000 … row sums 1, 18, 324, 5832, 104976, 1889568, …
  (−∞, 0] nonnegative rational roots
• A249250 → basis A013609
  1 · 4, 6 · 10, 24, 12 · 28, 96, 96, 24 … row sums 1, 10, 46, 244, 1252, 6472, 33400, …
  (−∞, 0] nonnegative
• A145597 → basis A013609
  1 · 6, 6 · 27, 54, 24 · 110, 330, 300, 80 … row sums 1, 12, 105, 820, 6081, 43932, 313012, …
  (−∞, 0] nonnegative
• A034870 → basis A013609
  1 · 4, 8, 4 · 16, 64, 96, 64, 16 … row sums 1, 16, 256, 4096, 65536, 1048576, …
  (−∞, 0] nonnegative rational roots
• A128099 → x ↦ x+1
  1 · 1 · 3, 2 · 5, 4 … row sums 1, 1, 5, 9, 29, 65, 181, 441, …
  (−∞, −1] nonnegative
• A110441 → basis A013609
  1 · 4, 2 · 14, 16, 4 · 48, 88, 48, 8 … row sums 1, 6, 34, 192, 1084, 6120, 34552, …
  (−∞, 0] nonnegative
• A038303 → basis A013609
  1 · 11, 2 · 121, 44, 4 · 1331, 726, 132, 8 … row sums 1, 13, 169, 2197, 28561, 371293, …
  (−∞, 0] nonnegative rational roots
• A154228 → basis A013609
  1 · 2, 2 · 18, 36, 4 · 96, 288, 200, 8 … row sums 1, 4, 58, 592, 11938, 209368, 5851432, …
  (−∞, 0] nonnegative
• A114687 → basis A013609
  1 · 3, 4 · 11, 28, 16 · 45, 168, 192, 64 … row sums 1, 7, 55, 469, 4237, 39907, 387739, …
  (−∞, 0] nonnegative
• A038226 → basis A013609
  121, 352, 256 · 1331, 5808, 8448, 4096 … row sums 729, 19683, 531441, 14348907, …
  (−∞, 0] nonnegative rational roots
• A249251 → basis A013609
  1 · 4, 6 · 13, 36, 24 · 43, 174, 228, 96 … row sums 1, 10, 73, 541, 4006, 29665, 219673, …
  (−∞, 0] nonnegative
• A081581 → basis A013609
  1 · 2, 2 · 10, 20, 4 · 32, 96, 72, 8 … row sums 1, 4, 34, 208, 1444, 9520, 64072, …
  (−∞, 0] nonnegative
• A165253 → basis A013609
  1 · 1 · 2, 2 · 5, 10, 4 … row sums 1, 1, 4, 19, 91, 436, 2089, 10009, …
  (−∞, 0] nonnegative
• A085881 → basis A013609
  1 · 2, 2 · 12, 24, 12 · 120, 360, 360, 120 … row sums 1, 4, 48, 960, 26880, 967680, 42577920, …
  (−∞, 0] nonnegative rational roots
• A038305 → basis A013609
  169, 156, 36 · 2197, 3042, 1404, 216 … row sums 361, 6859, 130321, 2476099, 47045881, …
  (−∞, 0] nonnegative rational roots
• A318772 → basis A013609
  1 · 1 · 1 · 1 … row sums 1, 1, 1, 1, 10, 19, 28, 37, …
  (−∞, 0] nonnegative
• A152828 → basis A013609
  1 · 1 · 1 · 2, 2 … row sums 1, 1, 1, 4, 4, 4, 16, 16, …
  (−∞, 0] nonnegative rational roots
• A088996 → basis A013609
  1 · 1, 2 · 3, 10, 8 · 15, 68, 100, 48 … row sums 1, 3, 21, 231, 3465, 65835, 1514205, …
  (−∞, 0] nonnegative rational roots
• A052553 → basis A013609
  1 · 1 · 2, 2 · 3, 4 … row sums 1, 1, 4, 7, 19, 40, 97, 217, …
  (−∞, 0] nonnegative
• Triangle whose (i,j)-th entry is binomial(i,j)*11^(i-j)*6^j.
  121, 132, 36 · 1331, 2178, 1188, 216 … row sums 289, 4913, 83521, 1419857, 24137569, …
  (−∞, 0) nonnegative rational roots
• A038279 → basis A013609
  1 · 9, 2 · 81, 36, 4 · 729, 486, 108, 8 … row sums 1, 11, 121, 1331, 14641, 161051, …
  (−∞, 0] nonnegative rational roots
• basis-map coefficients of A371080, shifted → basis A013609
  1 · 1, 2 · 4, 10, 4 · 28, 78, 48, 8 … row sums 1, 3, 18, 162, 1944, 29160, 524880, …
  (−∞, 0] nonnegative rational roots
• A038220 → basis A013611
  1 · 5, 8 · 25, 80, 64 · 125, 600, 960, 512 … row sums 1, 13, 169, 2197, 28561, 371293, …
  (−∞, 0] nonnegative rational roots
• A188440 → basis A013609
  1 · 1 · 3, 4 · 3, 4 … row sums 1, 1, 7, 7, 49, 49, 343, 343, …
  (−∞, 0] nonnegative rational roots
• A204420 → basis A013609
  1 · 1, 2 · 9, 24, 12 · 225, 690, 540, 120 … row sums 1, 3, 45, 1575, 99225, 9823275, …
  (−∞, 0] nonnegative rational roots
• A272867 → basis A013609
  1 · 6, 12, 4 · 36, 144, 192, 96, 16 … row sums 1, 22, 484, 10648, 234256, 5153632, …
  (−∞, 0] nonnegative
• A102547 → x ↦ (1/27)x → basis A013609
  1 · 3 · 9 · 28, 2 … row sums 1, 3, 9, 30, 99, 324, 1062, 3483, …
  (−∞, 0] nonnegative
• A026729 → basis A013609
  1 · 1, 2 · 2, 6, 4 · 3, 14, 20, 8 … row sums 1, 3, 12, 45, 171, 648, 2457, 9315, …
  (−∞, 0] nonnegative
• A102547 → basis A013609
  1 · 1 · 1 · 2, 2 … row sums 1, 1, 1, 4, 7, 10, 22, 43, …
  (−∞, 0] nonnegative
• A207606 → basis A013609
  13, 22, 8 · 34, 88, 68, 16 · 89, 310, 372, 184, 32 … row sums 43, 206, 987, 4729, 22658, 108561, …
  (−∞, 0] nonnegative
• A038314 → basis A013609
  484, 1056, 576 · 10648, 34848, 38016, 13824 … row sums 2116, 97336, 4477456, 205962976, …
  (−∞, 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
• 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
• 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
• 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
• A081582 → basis A013609
  1 · 2, 2 · 11, 22, 4 · 36, 108, 80, 8 … row sums 1, 4, 37, 232, 1705, 11692, 82573, …
  (−∞, 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
• 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