basis_map

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

1056 sequences

• A099093 → basis A007318
  1 · 3, 3 · 12, 21, 9 · 45, 117, 99, 27 … row sums 1, 6, 42, 288, 1980, 13608, 93528, …
  (−∞, −1] 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
• A125662 → basis A013611
  1 · 4, 4 · 15, 32, 16 · 56, 184, 192, 64 … row sums 1, 8, 63, 496, 3905, 30744, 242047, …
  (−∞, 0] nonnegative
• A299989 → basis A007318
  1, 1 · 8, 14, 7, 1 · 64, 160, 148, 64, 13, 1 … row sums 2, 30, 450, 6750, 101250, 1518750, …
  (−∞, 0] nonnegative rational roots
• A207824 → basis A007318
  1 · 6, 1 · 35, 12, 1 · 204, 106, 18, 1 … row sums 1, 7, 48, 329, 2255, 15456, 105937, …
  (−∞, 0] nonnegative
• A249252 → basis A007318
  1 · 5, 4 · 17, 24, 8 · 61, 124, 80, 16 … row sums 1, 9, 49, 281, 1601, 9129, 52049, …
  (−∞, −1] nonnegative
• A038314 → basis A008277
  484, 672, 144 · 10648, 28656, 14688, 1728 … row sums 1300, 55720, 2653072, 138846496, …
  (−∞, 0] nonnegative
• A013613 → basis A008277
  1 · 7, 6 · 49, 120, 36 · 343, 1854, 1404, 216 … row sums 1, 13, 205, 3817, 81481, 1949749, …
  (−∞, 0] nonnegative
• 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
• A120909 → basis A008277
  3 · 9, 6 · 27, 48, 12 · 81, 294, 180, 24 … row sums 3, 15, 87, 579, 4347, 36231, 330927, …
  (−∞, 0] nonnegative
• 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
• A038337 → basis A013611
  529, 2024, 1936 · 12167, 69828, 133584, 85184 … row sums 4489, 300763, 20151121, 1350125107, …
  (−∞, 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
• A038320 → basis A013611
  289, 816, 576 · 4913, 20808, 29376, 13824 … row sums 1681, 68921, 2825761, 115856201, …
  (−∞, 0] nonnegative rational roots
• A063967 → basis A013611
  1 · 2, 4 · 6, 20, 16 · 16, 80, 128, 64 … row sums 1, 6, 42, 288, 1980, 13608, 93528, …
  (−∞, 0] nonnegative
• A013611 → basis A008288
  1 · 5, 4 · 25, 56, 16 · 125, 476, 368, 64 … row sums 1, 9, 97, 1033, 11009, 117321, 1250273, …
  [−3−2√2, −3+2√2] nonnegative
• A249250 → x ↦ x+1
  1 · 4, 3 · 10, 12, 3 · 28, 48, 24, 3 … row sums 1, 7, 25, 103, 409, 1639, 6553, 26215, …
  (−∞, −1] nonnegative
• A030528: Triangle read by rows: T(n,k) = binomial(k,n-k).
  1 · 1, 1 · 0, 2, 1 · 0, 1, 3, 1 … row sums 1, 2, 3, 5, 8, 13, 21, 34, …
  A030528 (−4, 0] nonnegative
• A120909 → basis A013610
  3 · 9, 18 · 27, 108, 108 · 81, 486, 972, 648 … row sums 3, 27, 243, 2187, 19683, 177147, …
  (−∞, 0] nonnegative rational roots
• A038331 → basis A013611
  289, 680, 400 · 4913, 17340, 20400, 8000 … row sums 1369, 50653, 1874161, 69343957, …
  (−∞, 0] nonnegative rational roots
• A027467 → basis A013611
  1 · 16, 4 · 256, 128, 16 · 4096, 3072, 768, 64 … row sums 1, 20, 400, 8000, 160000, 3200000, …
  (−∞, 0] nonnegative rational roots
• A159854 → x ↦ x+1
  1, 2, 1 · 2, 5, 4, 1 · 4, 12, 13, 6, 1 … row sums 4, 12, 36, 108, 324, 972, 2916, 8748, …
  (−∞, −1] nonnegative rational roots
• A038255: Triangle whose (i,j)-th entry is binomial(i,j)*6^(i-j).
  1 · 6, 1 · 36, 12, 1 · 216, 108, 18, 1 … row sums 1, 7, 49, 343, 2401, 16807, 117649, …
  A038255 (−∞, 0) nonnegative rational roots
• A030528 → basis A013610
  1 · 2, 3 · 3, 12, 9 · 5, 30, 54, 27 … row sums 1, 5, 24, 116, 560, 2704, 13056, 63040, …
  (−∞, 0] nonnegative
• 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
• A013620 → basis A008277
  1 · 5, 3 · 25, 39, 9 · 125, 387, 216, 27 … row sums 1, 8, 73, 755, 8740, 111761, 1560817, …
  (−∞, 0] nonnegative
• A102662 → basis A013610
  1 · 4, 9 · 9, 33, 27 · 22, 114, 180, 81 … row sums 1, 13, 69, 397, 2261, 12893, 73509, …
  (−∞, 0] nonnegative
• 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
• A081577 → basis A008277
  1 · 2, 1 · 6, 7, 1 · 16, 35, 13, 1 … row sums 1, 3, 14, 65, 333, 1826, 10701, 66579, …
  (−∞, 0] nonnegative
• A286718: Triangle read by rows: T(n, k) is the Sheffer triangle ((1 - 3*x)^(-1/3), (-1/3)*log(1 - 3*x)). A generalized Stirling1 triangle.
  1 · 1, 1 · 4, 5, 1 · 28, 39, 12, 1 … row sums 1, 2, 10, 80, 880, 12320, 209440, …
  A286718 (−∞, 0) nonnegative rational roots
• A109692 → basis A007318
  1 · 2, 1 · 8, 10, 3 · 48, 100, 68, 15 … row sums 1, 3, 21, 231, 3465, 65835, 1514205, …
  (−∞, 0] nonnegative rational roots
• A102547 → reverse → basis A013610
  1, 3 · 1, 6, 9 · 1, 9, 27, 27 · 2, 21, 81, 135, 81 … row sums 4, 16, 64, 320, 1536, 7168, 33792, …
  (−∞, 0] nonnegative
• A269944 → basis A013610
  1 · 1, 3 · 2, 9, 9 · 10, 51, 72, 27 … row sums 1, 4, 20, 160, 2080, 41600, 1206400, …
  (−∞, 0] nonnegative rational roots
• A069466 → basis A013611
  1 · 4, 8 · 36, 144, 96 · 400, 2400, 3840, 1280 … row sums 1, 12, 276, 7920, 252420, 8536752, …
  (−∞, 0] nonnegative
• A143491 → basis A008277
  12, 8, 1 · 60, 60, 15, 1 · 360, 480, 180, 24, 1 … row sums 21, 136, 1045, 9276, 93289, 1047376, …
  (−∞, 0] nonnegative
• A344565 → basis A008277
  3 · 30, 15 · 180, 225, 45 · 840, 1995, 945, 105 … row sums 3, 45, 450, 3885, 31710, 254772, …
  (−∞, 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
• A056242: Triangle read by rows: T(n,k) = number of k-part order-consecutive partition of {1,2,...,n} (1 <= k <= n).
  basis-map coefficients of A026729 → basis A056242
  1 · 1, 2 · 1, 5, 4 · 1, 9, 16, 8 … row sums 1, 3, 10, 34, 116, 396, 1352, 4616, …
  A056242 [−1, 0] nonnegative
• A064861 → basis A013611
  6, 28, 32 · 18, 132, 320, 256 … row sums 66, 726, 4356, 47916, 287496, 3162456, …
  (−∞, 0] nonnegative rational roots
• A063007 → basis A008277
  1 · 3, 2 · 13, 24, 6 · 63, 242, 150, 20 … row sums 1, 5, 43, 475, 6231, 93427, 1564249, …
  (−∞, 0] nonnegative
• A091042 → basis A007318
  1 · 4, 3 · 16, 20, 5 · 64, 112, 56, 7 … row sums 1, 7, 41, 239, 1393, 8119, 47321, …
  (−∞, −1] nonnegative
• A274498 → basis A013611
  1 · 3 · 9, 24 · 27, 72 … row sums 1, 3, 33, 99, 1089, 3267, 35937, …
  (−∞, 0] nonnegative rational roots
• A249252 → basis A008277
  1 · 5, 4 · 17, 32, 8 · 61, 220, 128, 16 … row sums 1, 9, 57, 425, 3497, 31545, 308697, …
  (−∞, 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
• A135838 → basis A008277
  1 · 4, 2 · 8, 10, 2 · 32, 76, 36, 4 … row sums 1, 6, 20, 148, 604, 5392, 26104, …
  (−∞, 0] nonnegative
• delannoy → x ↦ x+1
  1 · 2, 1 · 5, 5, 1 · 12, 18, 8, 1 … row sums 1, 3, 11, 39, 139, 495, 1763, 6279, …
  (−∞, −1] nonnegative
• A038314 → basis A013609
  484, 1056, 576 · 10648, 34848, 38016, 13824 … row sums 2116, 97336, 4477456, 205962976, …
  (−∞, 0] nonnegative rational roots