Sequences

• A038314 → Pₙ + Pₙ₊₁
  1100, 3840, 4464, 1728 … Σ 11132, 244904, 5387888, 118533536, …
  (−∞, ∞)nonnegativerational roots
• A115951 → basis A013610
  1 · 2, 6 · 8, 42, 54 · 32, 252, 648, 540 … Σ 1, 8, 104, 1472, 21856, 333568, …
  (−∞, 0]nonnegative
• A153651: Triangle T(n, k) = T(n-1, k) + T(n-1, k-1) + (j+5)*prime(j)*T(n-2, k-1) with j=6, read by rows.
  2 · 13, 13 · 2, 334, 2 · 2, 2195, 2195, 2 … Σ 2, 26, 338, 4394, 57122, 742586, …
  (−∞, 0)nonnegative
• A207607 → basis A013611 → basis A008277
  1 · 11, 8 · 76, 132, 32 · 521, 1748, 1008, 128 … Σ 1, 19, 240, 3405, 53807, 935592, …
  (−∞, 0]nonnegative
• A079638 → basis A013611
  1 · 4, 4 · 24, 44, 16 · 192, 488, 336, 64 … Σ 1, 8, 84, 1080, 16344, 283680, 5544000, …
  (−∞, 0]nonnegative
• A152198 → basis A013609 → D
  2 · 2 · 8, 8 · 8, 8 … Σ 0, 0, 2, 2, 16, 16, 96, 96, …
  (−∞, 0]nonnegativerational roots
• A272867 → basis A013610 → basis A008277
  1 · 33, 45, 9 · 1089, 4995, 4401, 1134, 81 … Σ 1, 87, 11700, 2271051, 594272619, …
  (−∞, 0]nonnegative
• basis-map coefficients of A026729 → basis A007318 → basis A013609
  1 · 2, 2 · 4, 8, 4 · 8, 24, 24, 8 … Σ 1, 4, 16, 64, 256, 1024, 4096, 16384, …
  (−∞, 0]nonnegativerational roots
• A269947 → basis A013611
  1 · 1, 4 · 2, 12, 16 · 18, 116, 192, 64 … Σ 1, 5, 30, 390, 12480, 861120, …
  (−∞, 0]nonnegativerational roots
• A008459 → basis A013610 → x ↦ x+1
  1 · 5, 3 · 33, 36, 9 · 245, 387, 189, 27 … Σ 1, 8, 78, 848, 9766, 116208, 1411404, …
  (−∞, −1]nonnegative
• A038208 → Veronese 2 → (θ+1)²
  1 · 2 · 4, 16 · 8, 96 … Σ 1, 2, 20, 104, 544, 2752, 13568, 65536, …
  (−∞, 0]nonnegative
• A013609 → D → D+1
  2 · 12, 8 · 30, 72, 24 · 56, 240, 288, 64 … Σ 0, 2, 20, 126, 648, 2970, 12636, 51030, …
  (−∞, 0]nonnegativerational roots
• A063967 → basis A013611 → x ↦ x/(x+1)
  1 · 2, 6 · 6, 32, 42 · 16, 128, 336, 288 … Σ 1, 8, 80, 768, 7424, 71680, 692224, …
  [−1, 0]nonnegative
• basis-map coefficients of A026729, shifted → basis A013609 → basis A008277
  1 · -3, -2 · 9, 16, 4 · -27, -98, -60, -8 … Σ 1, -5, 29, -193, 1449, -12077, 110309, …
  (−∞, 0]
• A395972 → reverse
  8, 16, 4 · 48, 144, 72, 8 · 384, 1536, 1152, 256, 16 … Σ 28, 272, 3344, 49472, 852928, 16758016, …
  (−∞, 0]nonnegative
• A007318 → −D²+(−1+n)D+1+n → x ↦ x+1 → D+1
  1 · 6, 2 · 28, 20, 3 · 110, 126, 42, 4 … Σ 1, 8, 51, 282, 1413, 6588, 29079, …
  (−∞, 0]nonnegative
• A086645 → basis A013610 → x ↦ x/(x+1)
  1 · 2, 5 · 8, 40, 41 · 32, 240, 546, 365 … Σ 1, 7, 89, 1183, 15761, 210007, 2798249, …
  [−1, 0]nonnegative
• A225470 → D+1
  1 · 3, 1 · 17, 9, 1 · 146, 96, 18, 1 … Σ 1, 4, 27, 261, 3294, 51354, 953532, …
  (−∞, 0]nonnegative
• A013612 → basis A013611 → x ↦ x/(x+1)
  36, 312, 676 · 216, 2808, 12168, 17576 … Σ 1024, 32768, 1048576, 33554432, …
  [−1, 0]nonnegativerational roots
• A116414 → Veronese 2
  1 · 4 · 13, 1 · 40, 12 … Σ 1, 4, 14, 52, 209, 880, 3773, 16252, …
  (−∞, 0]nonnegative
• A028326 → Pₙ + Pₙ₊₁
  4, 2 · 4, 6, 2 · 4, 10, 8, 2 · 4, 14, 18, 10, 2 … Σ 6, 12, 24, 48, 96, 192, 384, 768, …
  (−∞, ∞)nonnegativerational roots
• A113953 → basis A013610 → θ+1
  1 · 1, 6 · 3, 24, 27 · 5, 66, 189, 108 … Σ 1, 7, 54, 368, 2432, 15552, 97408, …
  (−∞, 0]nonnegative
• image under θ+1 → D+1
  1 · 2, 2 · 0, 6, 3 · 0, 0, 12, 4 … Σ 1, 4, 9, 16, 25, 36, 49, 64, …
  (−∞, 0]nonnegativerational roots
• A100861 → basis A013609 → basis A008277
  1 · 1 · 4, 2 · 10, 6 … Σ 1, 1, 6, 16, 118, 486, 4276, 23416, …
  (−∞, 0]nonnegative
• A038336 → x ↦ x+1 → basis A008277
  1024, 740, 100 · 32768, 41320, 12600, 1000 … Σ 1864, 87688, 4378096, 231919232, …
  (−∞, 0]nonnegative
• A128813 → basis A007318 → x ↦ x+1
  1 · 3, 1 · 21, 16, 3 · 273, 334, 135, 18 … Σ 1, 4, 40, 760, 23560, 1083760, …
  (−∞, −1]nonnegativerational roots
• A304236 → θ+1
  1 · 1 · 1, 6 · 1, 12 … Σ 1, 1, 7, 13, 46, 106, 301, 739, …
  (−∞, 0]nonnegative
• A113953 → basis A013609 → basis A008277
  1 · 3, 2 · 15, 20, 4 · 63, 162, 76, 8 … Σ 1, 5, 39, 309, 2723, 25985, 267399, …
  (−∞, 0]nonnegative
• A143491 → D+1
  11, 7, 1 · 50, 44, 12, 1 · 274, 296, 113, 18, 1 … Σ 19, 107, 702, 5274, 44712, 422568, …
  (−∞, 0]nonnegative
• A013612 → basis A013609 → D+1
  156, 320, 100 · 1296, 4680, 4800, 1000 … Σ 576, 11776, 229376, 4325376, 79691776, …
  (−∞, 0]nonnegativerational roots
• A163626: Triangle read by rows: The n-th derivative of the logistic function written in terms of y, where y = 1/(1 + exp(-x)).
  1 · 1, -1 · 1, -3, 2 · 1, -7, 12, -6 … Σ 1, 0, 0, 0, 0, 0, 0, 0, …
  (0, 1]
• A113214 → x ↦ x−7
  1 · -5, 1 · 28, -11, 1 · -161, 93, -17, 1 … Σ 1, -4, 18, -84, 396, -1872, 8856, …
  (3, 7]
• A082985 → Veronese 2 (j=1)
  3 · 5 · 7, 7 · 9, 30 … Σ 0, 3, 5, 14, 39, 99, 260, 683, …
  (−∞, 0]nonnegative
• A026729 → basis A013610 → reverse
  1 · 3, 1 · 9, 9, 2 · 27, 45, 21, 3 … Σ 1, 4, 20, 96, 464, 2240, 10816, 52224, …
  (−∞, 0]nonnegative
• A274498 → basis A013610
  1 · 3 · 9, 18 · 27, 54 … Σ 1, 3, 27, 81, 729, 2187, 19683, 59049, …
  (−∞, 0]nonnegativerational roots
• A116414 → D+1
  1 · 5, 1 · 21, 10, 1 · 82, 66, 15, 1 … Σ 1, 6, 32, 164, 819, 4012, 19363, 92352, …
  (−∞, 0]nonnegative
• A075502 → x ↦ x+1
  71, 23, 1 · 729, 430, 45, 1 · 8842, 7809, 1441, 74, 1 … Σ 95, 1205, 18167, 316341, 6201063, …
  (−∞, −1]nonnegative
• A094638 → D+1 → basis A013610
  1 · 3, 3 · 13, 33, 18 · 70, 312, 423, 162 … Σ 1, 6, 64, 967, 18779, 444084, 12355170, …
  (−∞, 0]nonnegative
• A013612 → basis A013611 → D+1
  276, 1040, 400 · 2376, 16560, 31200, 8000 … Σ 1716, 58136, 1863056, 57578976, …
  (−∞, 0]nonnegativerational roots
• A080248 → D+1
  1 · 2, 1 · 5, 6, 1 · 14, 33, 13, 1 … Σ 1, 3, 12, 61, 385, 2950, 26861, 285687, …
  (−∞, 0]nonnegative
• A028326 → basis A007318 → basis A013609
  2 · 6, 4 · 18, 24, 8 · 54, 108, 72, 16 … Σ 2, 10, 50, 250, 1250, 6250, 31250, …
  (−∞, 0]nonnegativerational roots
• A099040 → basis A007318 → x ↦ x+1
  1 · 4, 2 · 20, 18, 4 · 96, 128, 56, 8 … Σ 1, 6, 42, 288, 1980, 13608, 93528, …
  (−∞, −1]nonnegative
• A274496 → basis A013609
  1 · 2 · 4, 4 · 8, 8 … Σ 1, 2, 8, 16, 64, 128, 512, 1024, …
  (−∞, 0]nonnegativerational roots
• A129710 → (θ+1)²
  1 · 2 · 2, 4 · 2, 12 … Σ 1, 2, 6, 14, 31, 66, 135, 270, …
  (−∞, 0]nonnegative
• A038271 → basis A013610 → reverse
  1 · 15, 12 · 225, 360, 144 · 3375, 8100, 6480, 1728 … Σ 1, 27, 729, 19683, 531441, 14348907, …
  (−∞, 0]nonnegativerational roots
• A207606 → basis A013610 → basis A007318
  64, 69, 18 · 373, 600, 315, 54 … Σ 151, 1342, 11927, 106001, 942082, …
  (−∞, 0]nonnegative
• A030528 → basis A013610 → x ↦ x/(x+1)
  1 · 2, 5 · 3, 18, 24 · 5, 45, 129, 116 … Σ 1, 7, 45, 295, 1925, 12575, 82125, …
  [−1, 0]nonnegative
• A367270 → x ↦ x+1 → basis A013611
  1 · 1 · 5, 8 · 25, 72, 48 … Σ 1, 1, 13, 145, 1585, 17401, 192637, …
  (−∞, 0]nonnegative
• A133087 → reverse → θ+1
  1 · 1, 4 · 1, 4, 3 · 1, 8, 15, 8 … Σ 1, 5, 8, 32, 48, 176, 256, 896, …
  (−∞, 0]nonnegative
• A081577 → basis A013609 → D+1
  1 · 4, 2 · 18, 20, 4 · 64, 128, 64, 8 … Σ 1, 6, 42, 264, 1620, 9672, 56712, …
  (−∞, 0]nonnegative