basis_map

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

1056 sequences

• A035607 → basis A008277
  1 · 1 · 3, 2 · 7, 10, 2 … row sums 1, 1, 5, 19, 83, 391, 1989, 10841, …
  (−∞, 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
• A154602: Exponential Riordan array [exp(sinh(x)*exp(x)), sinh(x)*exp(x)].
  basis-map coefficients of A026729 → basis A154602
  1 · 1, 1 · 3, 4, 1 · 11, 19, 9, 1 … row sums 1, 2, 8, 40, 240, 1664, 12992, 112256, …
  A154602 (−∞, −1] nonnegative
• A038281 → basis A007318
  121, 66, 9 · 1331, 1089, 297, 27 … row sums 196, 2744, 38416, 537824, 7529536, …
  (−∞, 0] nonnegative rational roots
• A008288: Square array of Delannoy numbers D(i,j) (i >= 0, j >= 0) read by antidiagonals.
  1 · 1, 1 · 1, 3, 1 · 1, 5, 5, 1 … row sums 1, 2, 5, 12, 29, 70, 169, 408, …
  A008288 [−3−2√2, −3+2√2] nonnegative
• A136124 → basis A013611
  1 · 3, 4 · 12, 28, 16 · 60, 188, 192, 64 … row sums 1, 7, 56, 504, 5040, 55440, 665280, …
  (−∞, 0] nonnegative rational roots
• A100861 → basis A007318
  1 · 1 · 2, 1 · 4, 3 … row sums 1, 1, 3, 7, 25, 81, 331, 1303, …
  (−∞, −1] nonnegative
• A013622 → basis A013611
  1 · 8, 20 · 64, 320, 400 · 512, 3840, 9600, 8000 … row sums 1, 28, 784, 21952, 614656, 17210368, …
  (−∞, 0] nonnegative rational roots
• A116414 → basis A013609
  1 · 5, 2 · 22, 20, 4 · 95, 138, 60, 8 … row sums 1, 7, 46, 301, 1969, 12880, 84253, …
  (−∞, 0] nonnegative
• A116412 → basis A013609
  1 · 4, 2 · 13, 16, 4 · 43, 84, 48, 8 … row sums 1, 6, 33, 183, 1014, 5619, 31137, …
  (−∞, 0] nonnegative
• A033282 → basis A013609
  1 · 3, 4 · 11, 30, 20 · 45, 186, 252, 112 … row sums 1, 7, 61, 595, 6217, 68047, 770149, …
  (−∞, 0] nonnegative
• A225470: Triangle read by rows, s_3(n, k) where s_m(n, k) are the Stirling-Frobenius cycle numbers of order m; n >= 0, k >= 0.
  1 · 2, 1 · 10, 7, 1 · 80, 66, 15, 1 … row sums 1, 3, 18, 162, 1944, 29160, 524880, …
  A225470 (−∞, 0) nonnegative rational roots
• A038301 → basis A013610
  400, 1320, 1089 · 8000, 39600, 65340, 35937 … row sums 2809, 148877, 7890481, 418195493, …
  (−∞, 0] nonnegative rational roots
• A118394 → basis A013609
  1 · 1 · 1 · 7, 12 … row sums 1, 1, 1, 19, 73, 181, 3601, 23311, …
  (−∞, 0] nonnegative
• A086645 → basis A013610
  1 · 2, 3 · 8, 24, 9 · 32, 144, 162, 27 … row sums 1, 5, 41, 365, 3281, 29525, 265721, …
  (−∞, 0] nonnegative
• A200536 → basis A013609
  1 · 6, 14, 8 · 36, 168, 292, 224, 64 … row sums 1, 28, 784, 21952, 614656, 17210368, …
  (−∞, 0] nonnegative rational roots
• A126216 → basis A007318
  1 · 3, 1 · 11, 7, 1 · 45, 42, 12, 1 … row sums 1, 4, 19, 100, 562, 3304, 20071, …
  (−∞, −1] nonnegative
• A059364 → basis A013609
  1 · 3, 2 · 15, 22, 8 · 105, 244, 188, 48 … row sums 1, 5, 45, 585, 9945, 208845, 5221125, …
  (−∞, 0] nonnegative rational roots
• 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
• A079638 → basis A007318
  1 · 4, 1 · 24, 11, 1 · 192, 122, 21, 1 … row sums 1, 5, 36, 336, 3840, 51840, 806400, …
  (−∞, 0] nonnegative
• A038329 → basis A007318
  225, 90, 9 · 3375, 2025, 405, 27 … row sums 324, 5832, 104976, 1889568, 34012224, …
  (−∞, 0] nonnegative rational roots
• A318772 → x ↦ (1/243)x → basis A013609
  1 · 3 · 9 · 27 … row sums 1, 3, 9, 27, 84, 261, 810, 2511, …
  (−∞, 0] nonnegative
• A318772 → basis A008277
  1 · 1 · 1 · 1 … row sums 1, 1, 1, 1, 7, 13, 19, 25, …
  (−∞, 0] nonnegative
• A159854 → basis A013611
  1, 8, 16 · 2, 20, 64, 64 · 4, 48, 208, 384, 256 … row sums 25, 150, 900, 5400, 32400, 194400, …
  (−∞, 0] nonnegative rational roots
• A038337 → basis A013610
  529, 1518, 1089 · 12167, 52371, 75141, 35937 … row sums 3136, 175616, 9834496, 550731776, …
  (−∞, 0] nonnegative rational roots
• A122542 → basis A013609
  1 · 1, 2 · 3, 8, 4 · 7, 26, 28, 8 … row sums 1, 3, 15, 69, 321, 1491, 6927, 32181, …
  (−∞, 0] nonnegative
• A038305 → basis A008277
  169, 87, 9 · 2197, 1899, 432, 27 … row sums 265, 4555, 81412, 1514929, 29367073, …
  (−∞, 0] nonnegative
• A038323 → basis A008277
  1 · 20, 9 · 400, 441, 81 · 8000, 16389, 7047, 729 … row sums 1, 29, 922, 32165, 1226815, 50852048, …
  (−∞, 0] nonnegative
• basis-map coefficients of A030528, shifted → basis A013611
  1 · -1, -4 · 1, 8, 16 · -1, -12, -48, -64 … row sums 1, -5, 25, -125, 625, -3125, 15625, …
  (−∞, 0] rational roots
• A249250 → basis A013611
  1 · 4, 12 · 10, 48, 48 · 28, 192, 384, 192 … row sums 1, 16, 106, 796, 5836, 42976, 316216, …
  (−∞, 0] nonnegative
• A099040 → basis A013611
  1 · 2, 8 · 6, 40, 64 · 16, 160, 512, 512 … row sums 1, 10, 110, 1200, 13100, 143000, …
  (−∞, 0] nonnegative
• A008288 → basis A007318
  1 · 2, 1 · 5, 5, 1 · 12, 18, 8, 1 … row sums 1, 3, 11, 39, 139, 495, 1763, 6279, …
  (−∞, −1] nonnegative
• 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
• A136572 → basis A013611
  1 · 1, 4 · 2, 16, 32 · 6, 72, 288, 384 … row sums 1, 5, 50, 750, 15000, 375000, 11250000, …
  (−∞, 0] nonnegative rational roots
• A038208 → basis A008277
  1 · 4, 2 · 16, 20, 4 · 64, 152, 72, 8 … row sums 1, 6, 40, 296, 2416, 21568, 208832, …
  (−∞, 0] nonnegative
• A059364 → basis A008277
  1 · 3, 1 · 15, 13, 2 · 105, 175, 65, 6 … row sums 1, 4, 30, 351, 5855, 131475, 3812529, …
  (−∞, 0] nonnegative
• A139548 → basis A013610
  1 · 8, 24, 18 · 64, 384, 864, 864, 324 … row sums 1, 50, 2500, 125000, 6250000, …
  (−∞, 0] nonnegative rational roots
• A143685 → basis A013611
  1 · 2, 4 · 13, 52, 16 · 44, 264, 384, 64 … row sums 1, 6, 81, 756, 8181, 83106, 866781, …
  (−∞, 0] nonnegative
• A103327 → basis A007318
  1 · 4, 1 · 16, 12, 1 · 64, 80, 24, 1 … row sums 1, 5, 29, 169, 985, 5741, 33461, …
  (−∞, −1] nonnegative
• A059344 → basis A007318
  1 · 1 · 3, 2 · 7, 6 … row sums 1, 1, 5, 13, 73, 281, 1741, 8485, …
  (−∞, −1] nonnegative
• A152842 → basis A013611
  1 · 4, 12 · 8, 40, 48 · 32, 256, 672, 576 … row sums 1, 16, 96, 1536, 9216, 147456, 884736, …
  (−∞, 0] nonnegative rational roots
• A207607 → basis A008277
  1 · 3, 2 · 8, 11, 2 · 21, 50, 21, 2 … row sums 1, 5, 21, 94, 453, 2341, 12909, 75609, …
  (−∞, 0] nonnegative
• A110441 → basis A013610
  1 · 4, 3 · 14, 24, 9 · 48, 132, 108, 27 … row sums 1, 7, 47, 315, 2111, 14147, 94807, …
  (−∞, 0] nonnegative
• A008955 → basis A008277
  1 · 2, 1 · 10, 17, 4 · 100, 413, 265, 36 … row sums 1, 3, 31, 814, 43678, 4139053, …
  (−∞, 0] nonnegative
• A038326 → basis A007318
  1 · 23, 12 · 529, 552, 144 · 12167, 19044, 9936, 1728 … row sums 1, 35, 1225, 42875, 1500625, 52521875, …
  (−∞, 0] nonnegative rational roots
• A188440 → basis A013611
  1 · 1 · 3, 8 · 3, 8 … row sums 1, 1, 11, 11, 121, 121, 1331, 1331, …
  (−∞, 0] nonnegative rational roots
• 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
• A132393 → basis A008277
  1 · 1, 1 · 2, 4, 1 · 6, 18, 9, 1 … row sums 1, 2, 7, 34, 209, 1546, 13327, 130922, …
  (−∞, 0] nonnegative
• A094816 → x ↦ x+1
  1 · 2, 1 · 5, 5, 1 · 16, 23, 9, 1 … row sums 1, 3, 11, 49, 261, 1631, 11743, 95901, …
  (−∞, −1] nonnegative