Sequences

• A033282 → x ↦ x+1 → basis A008288
  1 · 5, 2 · 31, 30, 5 · 215, 352, 133, 14 … Σ 1, 7, 66, 714, 8331, 102013, 1292302, …
  [−3−2√2, −3+2√2]nonnegative
• A232535 → D
  2 · 8, 6 · 18, 50, 12 · 32, 196, 168, 20 … Σ 0, 2, 14, 80, 416, 2048, 9728, 45056, …
  (−∞, 0]nonnegative
• A146986 → basis A013611
  1 · 2, 4 · 6, 24, 16 · 16, 96, 160, 64 … Σ 1, 6, 46, 336, 2736, 25056, 254016, …
  (−∞, 0]nonnegative
• A249252 → basis A008277
  1 · 5, 4 · 17, 32, 8 · 61, 220, 128, 16 … Σ 1, 9, 57, 425, 3497, 31545, 308697, …
  (−∞, 0]nonnegative
• A207606 → basis A013611 → basis A013610
  89, 324, 288 · 610, 3312, 5904, 3456 … Σ 701, 13282, 251657, 4768201, 90344162, …
  (−∞, 0]nonnegative
• A196347 → basis A013609 → D
  2 · 16, 16 · 144, 288, 144 · 1536, 4608, 4608, 1536 … Σ 0, 2, 32, 576, 12288, 307200, 8847360, …
  (−∞, 0]nonnegativerational roots
• A245962: Triangle read by rows: T(n,k) is the number of induced subgraphs of the Lucas cube Lambda(n) that are isomorphic to the hypercube Q(k).
  1 · 1 · 3, 2 · 4, 3 … Σ 1, 1, 5, 7, 17, 31, 65, 127, …
  (−∞, −1]nonnegative
• A039755 → reverse → x ↦ x+1
  1 · 2, 1 · 6, 6, 1 · 24, 38, 16, 1 … Σ 1, 3, 13, 79, 601, 5339, 53861, 607527, …
  (−∞, −1]nonnegative
• basis-map coefficients of A113214, shifted → D → D
  2 · -6, -6 · 12, 24, 12 · -20, -60, -60, -20 … Σ 0, 0, 2, -12, 48, -160, 480, -1344, …
  (−∞, 0]rational roots
• A207606 → basis A013609
  13, 22, 8 · 34, 88, 68, 16 · 89, 310, 372, 184, 32 … Σ 43, 206, 987, 4729, 22658, 108561, …
  (−∞, 0]nonnegative
• A038291 → basis A013611 → D
  4 · 80, 32 · 1200, 960, 192 … Σ 0, 4, 112, 2352, 43904, 768320, …
  (−∞, 0]nonnegativerational roots
• A207606 → basis A013611 → basis A008277
  89, 140, 32 · 610, 1888, 1040, 128 … Σ 261, 3666, 57473, 993065, 18707298, …
  (−∞, 0]nonnegative
• A143491 → basis A008277 → D
  8, 2 · 60, 30, 3 · 480, 360, 72, 4 … Σ 10, 93, 916, 9805, 114486, 1454425, …
  (−∞, 0]nonnegative
• A116412 → basis A007318 → x ↦ x+1
  1 · 5, 1 · 22, 10, 1 · 98, 69, 15, 1 … Σ 1, 6, 33, 183, 1014, 5619, 31137, …
  (−∞, −1]nonnegative
• A169803 → x ↦ x+1 → θ+1
  1 · 2, 2 · 3, 4 · 5, 10, 3 … Σ 1, 4, 7, 18, 37, 84, 179, 390, …
  (−∞, 0]nonnegative
• A136157 → basis A013609
  3 · 4, 6 · 4, 14, 12 · 4, 22, 40, 24 … Σ 3, 10, 30, 90, 270, 810, 2430, 7290, …
  (−∞, 0]nonnegativerational roots
• Triangle whose (i,j)-th entry is binomial(i,j)*10^(i-j)*12^j.
  100, 240, 144 · 1000, 3600, 4320, 1728 … Σ 484, 10648, 234256, 5153632, 113379904, …
  (−∞, 0)nonnegativerational roots
• A013620 → basis A013611 → x ↦ x+1
  1 · 17, 12 · 289, 408, 144 · 4913, 10404, 7344, 1728 … Σ 1, 29, 841, 24389, 707281, 20511149, …
  (−∞, −1]nonnegativerational roots
• A127952 → basis A007318
  1 · 2, 2 · 6, 9, 3 · 16, 32, 20, 4 … Σ 1, 4, 18, 72, 270, 972, 3402, 11664, …
  (−∞, 0]nonnegativerational roots
• A027467 → basis A013610 → x ↦ x/(x+1)
  1 · 16, 19 · 256, 608, 361 · 4096, 14592, 17328, 6859 … Σ 1, 35, 1225, 42875, 1500625, 52521875, …
  [−1, 0]nonnegativerational roots
• A063967 → x ↦ x−9
  1 · -8, 1 · 56, -15, 1 · -384, 160, -22, 1 … Σ 1, -7, 42, -245, 1421, -8232, 47677, …
  (4, 8]
• A178822 → Veronese 2 (j=1)
  6 · 42 · 168, 56 · 504, 504 … Σ 0, 6, 42, 224, 1008, 4032, 14784, …
  (−∞, 0]nonnegative
• A304236 → basis A013610 → basis A007318
  1 · 1 · 13, 9 · 25, 18 … Σ 1, 1, 22, 43, 505, 1408, 12013, 41581, …
  (−∞, 0]nonnegative
• A135838 → basis A008277
  1 · 4, 2 · 8, 10, 2 · 32, 76, 36, 4 … Σ 1, 6, 20, 148, 604, 5392, 26104, …
  (−∞, 0]nonnegative
• A038271 → Pₙ + Pₙ₊₁
  8, 5 · 56, 75, 25 · 392, 805, 550, 125 … Σ 13, 156, 1872, 22464, 269568, 3234816, …
  (−∞, ∞)nonnegativerational roots
• A225473 → D+1
  1 · 7, 4 · 49, 104, 32 · 343, 1660, 1824, 384 … Σ 1, 11, 185, 4211, 120497, 4148891, …
  (−∞, 0]nonnegative
• A225469 → x ↦ x/(x+1)
  1 · 3, 4 · 9, 28, 20 · 27, 160, 260, 128 … Σ 1, 7, 57, 575, 7249, 109463, 1892169, …
  [−1, 0]nonnegative
• A200536 → basis A007318 → basis A008277
  1 · 15, 13, 2 · 225, 559, 341, 68, 4 … Σ 1, 30, 1197, 63023, 4257572, 358263647, …
  (−∞, 0]nonnegative
• narayana
  1 · 1, 1 · 1, 3, 1 · 1, 6, 6, 1 … Σ 1, 2, 5, 14, 42, 132, 429, 1430, …
  (−∞, 0)nonnegative
• A069466 → γ → basis A013610
  1 · 2 · 18, 36 · 140, 360 … Σ 1, 2, 54, 500, 10150, 141372, 2625084, …
  (−∞, 0]nonnegative
• basis-map coefficients of A021012 → basis A008277 → θ+1
  1 · -1, -2 · 2, 12, 6 · -6, -84, -108, -24 … Σ 1, -3, 20, -222, 3624, -80880, 2349360, …
  (−∞, 0]
• A126216 → basis A007318 → reverse
  1 · 1, 3 · 1, 7, 11 · 1, 12, 42, 45 … Σ 1, 4, 19, 100, 562, 3304, 20071, …
  (−∞, 0]nonnegative
• delannoy → x ↦ x+1
  1 · 2, 1 · 5, 5, 1 · 12, 18, 8, 1 … Σ 1, 3, 11, 39, 139, 495, 1763, 6279, …
  (−∞, −1]nonnegative
• basis-map coefficients of A026729, shifted → θ+1 → D+1
  1 · -2, -2 · 0, 6, 3 · 0, 0, -12, -4 … Σ 1, -4, 9, -16, 25, -36, 49, -64, …
  (−∞, 0]rational roots
• A130534 → D²∘x (shift +1) → D
  3 · 18, 12 · 105, 120, 30 · 675, 1020, 450, 60 … Σ 0, 3, 30, 255, 2205, 20307, 201852, …
  (−∞, 0]nonnegative
• A207606 → D
  7, 4 · 16, 22, 6 · 30, 72, 45, 8 … Σ 11, 44, 155, 510, 1608, 4924, 14761, …
  (−∞, 0]nonnegative
• A207607 → basis A007318 → D+1
  1 · 5, 2 · 17, 13, 2 · 54, 63, 21, 2 … Σ 1, 7, 32, 140, 599, 2521, 10474, 43066, …
  (−∞, 0]nonnegative
• A131431 → θ+1 → basis A008277
  1 · 8, 8 · 21, 63, 21 · 40, 280, 240, 40 … Σ 1, 16, 105, 600, 3380, 19488, 116641, …
  (−∞, 0]nonnegative
• A028246 → (θ+1)²
  1 · 1, 4 · 1, 12, 18 · 1, 28, 108, 96 … Σ 1, 5, 31, 233, 2071, 21305, 249271, …
  (−∞, 0]nonnegative
• A059344 → basis A007318 → basis A013611
  1 · 1 · 5, 8 · 13, 24 … Σ 1, 1, 13, 37, 505, 2281, 32581, 196813, …
  (−∞, 0]nonnegative
• A154986 → θ+1
  1 · 1, 2 · 1, 8, 3 · 1, 22, 33, 4 … Σ 1, 3, 12, 60, 360, 2520, 20160, 181440, …
  (−∞, 0]nonnegative
• A130123 → basis A013609 → basis A013611
  1 · 6, 16 · 36, 192, 256 · 216, 1728, 4608, 4096 … Σ 1, 22, 484, 10648, 234256, 5153632, …
  (−∞, 0]nonnegativerational roots
• A038255 → basis A013609 → reverse
  1 · 2, 7 · 4, 28, 49 · 8, 84, 294, 343 … Σ 1, 9, 81, 729, 6561, 59049, 531441, …
  (−∞, 0]nonnegativerational roots
• A038314 → basis A013609
  484, 1056, 576 · 10648, 34848, 38016, 13824 … Σ 2116, 97336, 4477456, 205962976, …
  (−∞, 0]nonnegativerational roots
• A178822 → x ↦ x+1 → basis A013609
  1 · 18, 12 · 189, 252, 84 · 1512, 3024, 2016, 448 … Σ 1, 30, 525, 7000, 78750, 787500, …
  (−∞, 0]nonnegativerational roots
• A116412 → basis A013611
  1 · 4, 4 · 13, 32, 16 · 43, 168, 192, 64 … Σ 1, 8, 61, 467, 3574, 27353, 209341, …
  (−∞, 0]nonnegative
• basis-map coefficients of A371080, shifted → basis A013610 → basis A013611
  1 · 4, 12 · 28, 132, 144 · 280, 1656, 3024, 1728 … Σ 1, 16, 304, 6688, 167200, 4681600, …
  (−∞, 0]nonnegativerational roots
• A114687 → reverse → x ↦ x+1
  1 · 3, 1 · 11, 8, 1 · 45, 51, 15, 1 … Σ 1, 4, 20, 112, 672, 4224, 27456, …
  (−∞, −1]nonnegative
• A169803 → Veronese 2 (j=1) → x ↦ x+1
  1 · 2 · 3 · 4 … Σ 0, 1, 2, 3, 4, 7, 14, 27, …
  (−∞, −1]nonnegative
• A102537: Triangle T(n,k) read by rows: (1/n) * C(2n+k,k-1) * C(n,k); n, k >= 1.
  1 · 1, 3 · 1, 8, 12 · 1, 15, 55, 55 … Σ 1, 4, 21, 126, 818, 5594, 39693, …
  (−∞, 0)nonnegative