basis_map / A013610

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

210 sequences

• 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
• 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
• A136572 → basis A013610
  1 · 1, 3 · 2, 12, 18 · 6, 54, 162, 162 … row sums 1, 4, 32, 384, 6144, 122880, 2949120, …
  (−∞, 0] nonnegative rational roots
• A266213 → basis A013610
  1 · 1 · 3, 6 · 7, 24, 18 … row sums 1, 1, 9, 49, 281, 1601, 9129, 52049, …
  (−∞, 0] nonnegative
• A100862 → basis A013610
  1 · 2, 3 · 5, 15, 9 · 14, 63, 81, 27 … row sums 1, 5, 29, 185, 1273, 9325, 72085, …
  (−∞, 0] nonnegative
• A113413 → basis A013610
  1 · 3, 3 · 7, 18, 9 · 17, 69, 81, 27 … row sums 1, 6, 34, 194, 1106, 6306, 35954, …
  (−∞, 0] nonnegative
• basis-map coefficients of A113214, shifted → basis A013610
  1 · -2, -3 · 4, 12, 9 · -8, -36, -54, -27 … row sums 1, -5, 25, -125, 625, -3125, 15625, …
  (−∞, 0] rational roots
• A038325 → basis A013610
  1 · 22, 33 · 484, 1452, 1089 … row sums 1, 55, 3025, 166375, 9150625, …
  (−∞, 0] nonnegative rational roots
• A356546 → basis A013610
  1 · 4, 6 · 24, 72, 54 · 160, 720, 1080, 540 … row sums 1, 10, 150, 2500, 43750, 787500, …
  (−∞, 0] nonnegative rational roots
• A128813 → basis A013610
  1 · 2, 3 · 8, 30, 27 · 56, 354, 729, 486 … row sums 1, 5, 65, 1625, 66625, 4064125, …
  (−∞, 0] nonnegative rational roots
• A038208 → basis A013610
  1 · 4, 6 · 16, 48, 36 · 64, 288, 432, 216 … row sums 1, 10, 100, 1000, 10000, 100000, …
  (−∞, 0] nonnegative rational roots
• A038335 → basis A013610
  1 · 21, 27 · 441, 1134, 729 … row sums 1, 48, 2304, 110592, 5308416, …
  (−∞, 0] nonnegative rational roots
• A290319 → basis A013610
  1 · 2, 3 · 12, 24, 9 · 120, 276, 162, 27 … row sums 1, 5, 45, 585, 9945, 208845, 5221125, …
  (−∞, 0] nonnegative rational roots
• A063967 → basis A013610
  1 · 2, 3 · 6, 15, 9 · 16, 60, 72, 27 … row sums 1, 5, 30, 175, 1025, 6000, 35125, …
  (−∞, 0] nonnegative
• A013609 → basis A013610
  1 · 3, 6 · 9, 36, 36 · 27, 162, 324, 216 … row sums 1, 9, 81, 729, 6561, 59049, 531441, …
  (−∞, 0] nonnegative rational roots
• A178821 → basis A013610
  1 · 10, 15 · 60, 180, 135 · 280, 1260, 1890, 945 … row sums 1, 25, 375, 4375, 43750, 393750, …
  (−∞, 0] nonnegative rational roots
• A135838 → basis A013610
  1 · 4, 6 · 8, 24, 18 · 32, 144, 216, 108 … row sums 1, 10, 50, 500, 2500, 25000, 125000, …
  (−∞, 0] nonnegative rational roots
• A207824 → basis A013610
  1 · 6, 3 · 35, 36, 9 · 204, 318, 162, 27 … row sums 1, 9, 80, 711, 6319, 56160, 499121, …
  (−∞, 0] nonnegative
• A154986 → basis A013610
  1 · 2, 3 · 6, 18, 9 · 24, 108, 126, 27 … row sums 1, 5, 33, 285, 3009, 37845, 550305, …
  (−∞, 0] nonnegative
• A013620: Triangle of coefficients in expansion of (2+3x)^n.
  1 · 2, 3 · 4, 12, 9 · 8, 36, 54, 27 … row sums 1, 5, 25, 125, 625, 3125, 15625, 78125, …
  A013620 (−∞, 0) [−1, 0] nonnegative rational roots
• A078812 → basis A013610
  1 · 3, 3 · 8, 18, 9 · 21, 75, 81, 27 … row sums 1, 6, 35, 204, 1189, 6930, 40391, …
  (−∞, 0] nonnegative
• A038322 → basis A013610
  1 · 19, 24 · 361, 912, 576 … row sums 1, 43, 1849, 79507, 3418801, 147008443, …
  (−∞, 0] nonnegative rational roots
• A121574 → basis A013610
  1 · 3, 3 · 10, 21, 9 · 33, 105, 99, 27 … row sums 1, 6, 40, 264, 1744, 11520, 76096, …
  (−∞, 0] nonnegative
• A125662 → basis A013610
  1 · 4, 3 · 15, 24, 9 · 56, 138, 108, 27 … row sums 1, 7, 48, 329, 2255, 15456, 105937, …
  (−∞, 0] nonnegative
• A114656 → basis A013610
  1 · 3, 3 · 11, 24, 9 · 45, 153, 135, 27 … row sums 1, 6, 44, 360, 3152, 28896, 273856, …
  (−∞, 0] nonnegative
• A225470 → basis A013610
  1 · 3, 3 · 18, 27, 9 · 162, 297, 162, 27 … row sums 1, 6, 54, 648, 9720, 174960, 3674160, …
  (−∞, 0] nonnegative rational roots
• A249251 → basis A013610
  1 · 4, 9 · 13, 54, 54 · 43, 261, 513, 324 … row sums 1, 13, 121, 1141, 10753, 101341, …
  (−∞, 0] nonnegative
• A008955 → basis A013610
  1 · 2, 3 · 10, 39, 36 · 100, 660, 1413, 972 … row sums 1, 5, 85, 3145, 204425, 20646925, …
  (−∞, 0] nonnegative rational roots
• A038334 → basis A013610
  400, 960, 576 · 8000, 28800, 34560, 13824 … row sums 1936, 85184, 3748096, 164916224, …
  (−∞, 0] nonnegative rational roots
• A059364 → basis A013610
  1 · 3, 3 · 15, 33, 18 · 105, 366, 423, 162 … row sums 1, 6, 66, 1056, 22176, 576576, …
  (−∞, 0] nonnegative rational roots
• A038321 → basis A013610
  324, 756, 441 · 5832, 20412, 23814, 9261 … row sums 1521, 59319, 2313441, 90224199, …
  (−∞, 0] nonnegative rational roots
• A358735 → basis A013610
  1 · 2, 3 · 7, 24, 18 · 33, 180, 306, 162 … row sums 1, 5, 49, 681, 12209, 267917, 6953633, …
  (−∞, 0] nonnegative
• A038255 → basis A013610
  1 · 7, 3 · 49, 42, 9 · 343, 441, 189, 27 … row sums 1, 10, 100, 1000, 10000, 100000, …
  (−∞, 0] nonnegative rational roots
• A038338 → basis A013610
  576, 1728, 1296 · 13824, 62208, 93312, 46656 … row sums 3600, 216000, 12960000, 777600000, …
  (−∞, 0] nonnegative rational roots
• A118933 → basis A013610
  1 · 1 · 1 · 1 … row sums 1, 1, 1, 1, 25, 121, 361, 841, …
  (−∞, 0] nonnegative
• A013610: Triangle of coefficients in expansion of (1+3*x)^n.
  1 · 1, 3 · 1, 6, 9 · 1, 9, 27, 27 … row sums 1, 4, 16, 64, 256, 1024, 4096, 16384, …
  A013610 (−∞, 0) [−1, 0] nonnegative rational roots
• A232535 → basis A013610
  1 · 3, 6 · 12, 42, 27 · 48, 240, 333, 108 … row sums 1, 9, 81, 729, 6561, 59049, 531441, …
  (−∞, 0] nonnegative
• A152198 → basis A013610
  1 · 1 · 2, 3 · 2, 3 … row sums 1, 1, 5, 5, 25, 25, 125, 125, …
  (−∞, 0] nonnegative rational roots
• A046716 → basis A013610
  1 · 2, 3 · 5, 15, 9 · 16, 75, 99, 27 … row sums 1, 5, 29, 217, 2297, 34349, 674965, …
  (−∞, 0] nonnegative
• A038291 → basis A013610
  1 · 10, 3 · 100, 60, 9 · 1000, 900, 270, 27 … row sums 1, 13, 169, 2197, 28561, 371293, …
  (−∞, 0] nonnegative rational roots
• A272866 → basis A013610
  1 · 5, 15, 9 · 25, 150, 315, 270, 81 … row sums 1, 29, 841, 24389, 707281, 20511149, …
  (−∞, 0] nonnegative
• A145324 → basis A013610
  1 · 3, 6 · 12, 51, 54 · 60, 399, 882, 648 … row sums 1, 9, 117, 1989, 41769, 1044225, …
  (−∞, 0] nonnegative rational roots
• A038284 → basis A007318
  196, 168, 36 · 2744, 3528, 1512, 216 … row sums 400, 8000, 160000, 3200000, 64000000, …
  (−∞, 0] nonnegative rational roots
• A188440 → basis A013610
  1 · 1 · 3, 6 · 3, 6 … row sums 1, 1, 9, 9, 81, 81, 729, 729, …
  (−∞, 0] nonnegative rational roots
• A204420 → basis A013610
  1 · 1, 3 · 9, 36, 27 · 225, 1035, 1215, 405 … row sums 1, 4, 72, 2880, 201600, 21772800, …
  (−∞, 0] nonnegative rational roots
• A038279 → basis A013610
  1 · 9, 3 · 81, 54, 9 · 729, 729, 243, 27 … row sums 1, 12, 144, 1728, 20736, 248832, …
  (−∞, 0] nonnegative rational roots