basis_map / A013610

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

210 sequences

• A013620 → basis A013611
  1 · 5, 12 · 25, 120, 144 · 125, 900, 2160, 1728 … row sums 1, 17, 289, 4913, 83521, 1419857, …
  (−∞, 0] nonnegative rational roots
• A152828 → basis A013610
  1 · 1 · 1 · 2, 3 … row sums 1, 1, 1, 5, 5, 5, 25, 25, …
  (−∞, 0] nonnegative rational roots
• A038305 → basis A013610
  169, 234, 81 · 2197, 4563, 3159, 729 … row sums 484, 10648, 234256, 5153632, 113379904, …
  (−∞, 0] nonnegative rational roots
• A038243 → basis A013610
  1 · 6, 3 · 36, 36, 9 · 216, 324, 162, 27 … row sums 1, 9, 81, 729, 6561, 59049, 531441, …
  (−∞, 0] nonnegative rational roots
• A026729 → basis A013610
  1 · 1, 3 · 2, 9, 9 · 3, 21, 45, 27 … row sums 1, 4, 20, 96, 464, 2240, 10816, 52224, …
  (−∞, 0] nonnegative
• A249250 → basis A013610
  1 · 4, 9 · 10, 36, 27 · 28, 144, 216, 81 … row sums 1, 13, 73, 469, 2929, 18397, 115417, …
  (−∞, 0] nonnegative
• A147716 → basis A013610
  1 · 15, 3 · 225, 90, 9 · 3375, 2025, 405, 27 … row sums 1, 18, 324, 5832, 104976, 1889568, …
  (−∞, 0] nonnegative rational roots
• A038301 → basis A013610
  400, 1320, 1089 · 8000, 39600, 65340, 35937 … row sums 2809, 148877, 7890481, 418195493, …
  (−∞, 0] nonnegative rational roots
• A086645 → basis A013610
  1 · 2, 3 · 8, 24, 9 · 32, 144, 162, 27 … row sums 1, 5, 41, 365, 3281, 29525, 265721, …
  (−∞, 0] nonnegative
• A100861 → reverse → basis A013610
  1 · 1, 3 · 2, 9, 9 · 4, 27, 54, 27 … row sums 1, 4, 20, 112, 688, 4544, 31936, …
  (−∞, 0] nonnegative
• A038337 → basis A013610
  529, 1518, 1089 · 12167, 52371, 75141, 35937 … row sums 3136, 175616, 9834496, 550731776, …
  (−∞, 0] nonnegative rational roots
• A299989 → basis A013610
  1, 3 · 8, 42, 63, 27 · 64, 480, 1332, 1728, 1053, 243 … row sums 4, 140, 4900, 171500, 6002500, …
  (−∞, 0] nonnegative rational roots
• A139548 → basis A013610
  1 · 8, 24, 18 · 64, 384, 864, 864, 324 … row sums 1, 50, 2500, 125000, 6250000, …
  (−∞, 0] nonnegative rational roots
• A110441 → basis A013610
  1 · 4, 3 · 14, 24, 9 · 48, 132, 108, 27 … row sums 1, 7, 47, 315, 2111, 14147, 94807, …
  (−∞, 0] nonnegative
• A038331 → basis A013610
  289, 510, 225 · 4913, 13005, 11475, 3375 … row sums 1024, 32768, 1048576, 33554432, …
  (−∞, 0] nonnegative rational roots
• A137320 → basis A013610
  1 · 2, 6 · 6, 30, 36 · 24, 156, 324, 216 … row sums 1, 8, 72, 720, 7920, 95040, 1235520, …
  (−∞, 0] nonnegative rational roots
• A304236 → basis A013610
  1 · 1 · 4, 9 · 7, 18 … row sums 1, 1, 13, 25, 181, 481, 2653, 8425, …
  (−∞, 0] nonnegative
• A038221: Triangle whose (i,j)-th entry is binomial(i,j)*3^(i-j)*3^j.
  1 · 3, 3 · 9, 18, 9 · 27, 81, 81, 27 … row sums 1, 6, 36, 216, 1296, 7776, 46656, …
  A038221 (−∞, 0) nonnegative rational roots
• A178822 → basis A013610
  1 · 12, 18 · 84, 252, 189 · 448, 2016, 3024, 1512 … row sums 1, 30, 525, 7000, 78750, 787500, …
  (−∞, 0] nonnegative rational roots
• A103633 → basis A013610
  1 · 1, 3 · 2, 9, 9 · 2, 15, 36, 27 … row sums 1, 4, 20, 80, 400, 1600, 8000, 32000, …
  (−∞, 0] nonnegative rational roots
• A011973 → x ↦ x+2 (shift +1) → basis A013610
  1 · 4, 3 · 7, 6 · 19, 27, 9 … row sums 1, 7, 13, 55, 133, 463, 1261, 4039, …
  (−∞, 0] nonnegative
• A133080 → basis A013610
  1 · 2, 3 · 1, 6, 9 · 2, 15, 36, 27 … row sums 1, 5, 16, 80, 256, 1280, 4096, 20480, …
  (−∞, 0] nonnegative rational roots
• A104684 → basis A013610
  1 · 3, 3 · 13, 24, 9 · 63, 171, 135, 27 … row sums 1, 6, 46, 396, 3606, 33876, 324556, …
  (−∞, 0] nonnegative
• A038284 → basis A013610
  196, 504, 324 · 2744, 10584, 13608, 5832 … row sums 1024, 32768, 1048576, 33554432, …
  (−∞, 0] nonnegative rational roots
• A344565 → basis A013610
  3 · 30, 45 · 180, 540, 405 · 840, 3780, 5670, 2835 … row sums 3, 75, 1125, 13125, 131250, 1181250, …
  (−∞, 0] nonnegative rational roots
• A081580 → basis A013610
  1 · 2, 3 · 9, 27, 9 · 28, 126, 144, 27 … row sums 1, 5, 45, 325, 2525, 19125, 146125, …
  (−∞, 0] nonnegative
• A178820 → basis A013610
  1 · 8, 12 · 40, 120, 90 · 160, 720, 1080, 540 … row sums 1, 20, 250, 2500, 21875, 175000, …
  (−∞, 0] nonnegative rational roots
• A103327 → basis A013610
  1 · 4, 3 · 16, 36, 9 · 64, 240, 216, 27 … row sums 1, 7, 61, 547, 4921, 44287, 398581, …
  (−∞, 0] nonnegative
• basis-map coefficients of A030528, shifted → basis A013610
  1 · -1, -3 · 1, 6, 9 · -1, -9, -27, -27 … row sums 1, -4, 16, -64, 256, -1024, 4096, …
  (−∞, 0] rational roots
• A286718 → basis A013610
  1 · 2, 3 · 10, 21, 9 · 80, 198, 135, 27 … row sums 1, 5, 40, 440, 6160, 104720, 2094400, …
  (−∞, 0] nonnegative rational roots
• A120910 → basis A013610
  3 · 9, 9 · 27, 54, 27 · 81, 243, 243, 81 … row sums 3, 18, 108, 648, 3888, 23328, 139968, …
  (−∞, 0] nonnegative rational roots
• A081578 → basis A013610
  1 · 2, 3 · 7, 21, 9 · 20, 90, 108, 27 … row sums 1, 5, 37, 245, 1669, 11285, 76453, …
  (−∞, 0] nonnegative
• A207606 → basis A013610
  13, 33, 18 · 34, 132, 153, 54 … row sums 64, 373, 2174, 12671, 73852, 430441, …
  (−∞, 0] nonnegative
• A156992 → basis A013610
  1 · 4, 6 · 24, 72, 54 · 192, 864, 1296, 648 … row sums 1, 10, 150, 3000, 75000, 2250000, …
  (−∞, 0] nonnegative rational roots
• A122542 → basis A013610
  1 · 1, 3 · 3, 12, 9 · 7, 39, 63, 27 … row sums 1, 4, 24, 136, 776, 4424, 25224, …
  (−∞, 0] nonnegative
• narayana → basis A013610
  1 · 2, 3 · 5, 15, 9 · 14, 63, 81, 27 … row sums 1, 5, 29, 185, 1257, 8925, 65445, …
  (−∞, 0] nonnegative
• A038221 → basis A013610
  1 · 6, 9 · 36, 108, 81 · 216, 972, 1458, 729 … row sums 1, 15, 225, 3375, 50625, 759375, …
  (−∞, 0] nonnegative rational roots
• A225471 → basis A013610
  1 · 4, 3 · 32, 36, 9 · 384, 528, 216, 27 … row sums 1, 7, 77, 1155, 21945, 504735, …
  (−∞, 0] nonnegative rational roots
• A013620 → basis A013610
  1 · 5, 9 · 25, 90, 81 · 125, 675, 1215, 729 … row sums 1, 14, 196, 2744, 38416, 537824, …
  (−∞, 0] nonnegative rational roots
• A027466 → basis A013610
  1 · 8, 3 · 64, 48, 9 · 512, 576, 216, 27 … row sums 1, 11, 121, 1331, 14641, 161051, …
  (−∞, 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
• A099097 → basis A013610
  1 · 3, 9 · 10, 57, 81 · 33, 279, 783, 729 … row sums 1, 12, 148, 1824, 22480, 277056, …
  (−∞, 0] nonnegative
• A038323 → basis A013610
  1 · 20, 27 · 400, 1080, 729 … row sums 1, 47, 2209, 103823, 4879681, …
  (−∞, 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
• A038319 → basis A013610
  256, 480, 225 · 4096, 11520, 10800, 3375 … row sums 961, 29791, 923521, 28629151, …
  (−∞, 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
• A113953 → basis A013610
  1 · 1, 3 · 3, 12, 9 · 5, 33, 63, 27 … row sums 1, 4, 24, 128, 704, 3840, 20992, …
  (−∞, 0] 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
• basis-map coefficients of A371080, shifted → basis A013610
  1 · 1, 3 · 4, 15, 9 · 28, 117, 108, 27 … row sums 1, 4, 28, 280, 3640, 58240, 1106560, …
  (−∞, 0] nonnegative rational roots
• A172431 → basis A013610
  1 · 3, 6 · 8, 30, 27 · 21, 114, 198, 108 … row sums 1, 9, 65, 441, 2929, 19305, 126881, …
  (−∞, 0] nonnegative