basis_map / A007318

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

219 sequences

• A013610 → basis A007318
  1 · 4, 3 · 16, 24, 9 · 64, 144, 108, 27 … row sums 1, 7, 49, 343, 2401, 16807, 117649, …
  (−∞, −1] nonnegative rational roots
• A344565 → basis A007318
  3 · 30, 15 · 180, 180, 45 · 840, 1260, 630, 105 … row sums 3, 45, 405, 2835, 17010, 91854, 459270, …
  (−∞, −1] nonnegative rational roots
• A122542 → x ↦ x+1
  1 · 1, 1 · 3, 4, 1 · 7, 13, 7, 1 … row sums 1, 2, 8, 28, 100, 356, 1268, 4516, …
  (−∞, −1] nonnegative
• A069466 → basis A007318
  1 · 4, 2 · 36, 36, 6 · 400, 600, 240, 20 … row sums 1, 6, 78, 1260, 22470, 424116, 8305836, …
  (−∞, 0] nonnegative
• A038330 → basis A007318
  256, 128, 16 · 4096, 3072, 768, 64 … row sums 400, 8000, 160000, 3200000, 64000000, …
  (−∞, 0] nonnegative rational roots
• A038328 → basis A007318
  196, 56, 4 · 2744, 1176, 168, 8 … row sums 256, 4096, 65536, 1048576, 16777216, …
  (−∞, 0] nonnegative rational roots
• A130534: Triangle T(n,k), 0 <= k <= n, read by rows, giving coefficients of the polynomial (x+1)(x+2)...(x+n), expanded in increasing powers of x. T(n,k) is also the unsigned Stirling number |s(n+1, …
  1 · 1, 1 · 2, 3, 1 · 6, 11, 6, 1 … row sums 1, 2, 6, 24, 120, 720, 5040, 40320, …
  A130534 (−∞, −1] nonnegative rational roots
• A027466: Triangle whose (i,j)-th entry is binomial(i,j)*7^(i-j).
  1 · 7, 1 · 49, 14, 1 · 343, 147, 21, 1 … row sums 1, 8, 64, 512, 4096, 32768, 262144, …
  A027466 (−∞, 0) nonnegative rational roots
• A099040: Riordan array (1, 2+2x).
  1 · 0, 2 · 0, 2, 4 · 0, 0, 8, 8 … row sums 1, 2, 6, 16, 44, 120, 328, 896, …
  A099040 (−2, 0] nonnegative
• A120910 → basis A013609
  3 · 9, 6 · 27, 36, 12 · 81, 162, 108, 24 … row sums 3, 15, 75, 375, 1875, 9375, 46875, …
  (−∞, −1] nonnegative rational roots
• A046716 → basis A007318
  1 · 2, 1 · 5, 5, 1 · 16, 25, 11, 1 … row sums 1, 3, 11, 53, 345, 2947, 31411, 400437, …
  (−∞, −1] nonnegative
• basis-map coefficients of A113214, shifted → x ↦ x+1
  1 · -2, -1 · 4, 4, 1 · -8, -12, -6, -1 … row sums 1, -3, 9, -27, 81, -243, 729, -2187, …
  (−∞, −1] rational roots
• A060920: Bisection of Fibonacci triangle A037027: even-indexed members of column sequences of A037027 (not counting leading zeros).
  1 · 2, 1 · 5, 5, 1 · 13, 20, 9, 1 … row sums 1, 3, 11, 43, 171, 683, 2731, 10923, …
  A060920 (−∞, −1] nonnegative
• A113214 → basis A007318
  1 · 3, 1 · 4, 5, 1 · 7, 13, 7, 1 … row sums 1, 4, 10, 28, 76, 208, 568, 1552, …
  (−∞, −1] nonnegative
• A028338 → basis A007318
  1 · 2, 1 · 8, 6, 1 · 48, 44, 12, 1 … row sums 1, 3, 15, 105, 945, 10395, 135135, …
  (−∞, 0] nonnegative rational roots
• A011973 → basis A007318 → x ↦ x+1
  1 · 1 · 3, 1 · 5, 2 … row sums 1, 1, 4, 7, 19, 40, 97, 217, …
  (−∞, −1] nonnegative
• A178821 → basis A007318
  1 · 10, 5 · 60, 60, 15 · 280, 420, 210, 35 … row sums 1, 15, 135, 945, 5670, 30618, 153090, …
  (−∞, −1] nonnegative rational roots
• A027467: Triangle whose (n,k)-th entry is 15^(n-k)*binomial(n,k).
  1 · 15, 1 · 225, 30, 1 · 3375, 675, 45, 1 … row sums 1, 16, 256, 4096, 65536, 1048576, …
  A027467 (−∞, 0) nonnegative rational roots
• A038208 → basis A007318
  1 · 4, 2 · 16, 16, 4 · 64, 96, 48, 8 … row sums 1, 6, 36, 216, 1296, 7776, 46656, …
  (−∞, −1] nonnegative rational roots