Sequences

• A193685 → D
  1 · 11, 2 · 91, 36, 3 · 671, 434, 78, 4 … Σ 0, 1, 13, 130, 1187, 10451, 90954, …
  (−∞, 0]nonnegative
• A142462 → Pₙ + Pₙ₊₁
  2, 1 · 2, 17, 1 · 2, 159, 144, 1 … Σ 3, 20, 306, 6912, 205344, 7551360, …
  (−∞, ∞)nonnegative
• A038335 → basis A013609 → reverse
  1 · 18, 21 · 324, 756, 441 · 5832, 20412, 23814, 9261 … Σ 1, 39, 1521, 59319, 2313441, 90224199, …
  (−∞, 0]nonnegativerational roots
• A095660 → basis A008277
  3 · 4, 3 · 8, 13, 3 · 16, 47, 25, 3 … Σ 3, 7, 24, 91, 379, 1720, 8441, 44495, …
  (−∞, 0]nonnegative
• A132440 → θ+1 → x ↦ x+1
  1 · 4, 4 · 9, 18, 9 · 16, 48, 48, 16 … Σ 0, 1, 8, 36, 128, 400, 1152, 3136, …
  (−∞, −1]nonnegativerational roots
• A136572 → basis A013611 → basis A013610
  1 · 5, 12 · 50, 240, 288 · 750, 5400, 12960, 10368 … Σ 1, 17, 578, 29478, 2004504, 170382840, …
  (−∞, 0]nonnegativerational roots
• A035607 → basis A013609 → θ+1
  1 · 1 · 3, 8 · 7, 32, 24 … Σ 1, 1, 11, 63, 361, 1985, 10659, 56191, …
  (−∞, 0]nonnegative
• A225470 → basis A013609 → (θ+1)²
  1 · 3, 8 · 18, 72, 36 · 162, 792, 648, 128 … Σ 1, 11, 126, 1730, 28324, 542484, …
  (−∞, 0]nonnegative
• A094305 → x ↦ x+1 → basis A013610
  1 · 9, 9 · 54, 108, 54 · 270, 810, 810, 270 … Σ 1, 18, 216, 2160, 19440, 163296, …
  (−∞, 0]nonnegativerational roots
• A086915 → D+1
  2 · 8, 4 · 36, 40, 8 · 192, 336, 144, 16 … Σ 2, 12, 84, 688, 6480, 69024, 820064, …
  (−∞, 0]nonnegative
• A038303 → basis A007318 → (θ+1)²
  1 · 11, 4 · 121, 88, 9 · 1331, 1452, 297, 16 … Σ 1, 15, 218, 3096, 43200, 594432, …
  (−∞, 0]nonnegative
• A038321 → basis A007318
  324, 252, 49 · 5832, 6804, 2646, 343 … Σ 625, 15625, 390625, 9765625, 244140625, …
  (−∞, −1]nonnegativerational roots
• A225470 → basis A013609 → reverse
  1 · 2, 3 · 4, 18, 18 · 8, 72, 198, 162 … Σ 1, 5, 40, 440, 6160, 104720, 2094400, …
  (−∞, 0]nonnegativerational roots
• A028326 → basis A013610 → D+1
  2 · 10, 6 · 32, 60, 18 · 88, 288, 270, 54 … Σ 2, 16, 110, 700, 4250, 25000, 143750, …
  (−∞, 0]nonnegativerational roots
• A127648 → Veronese 2 → x ↦ x+1
  1 · 3, 3 · 5, 10, 5 · 7, 21, 21, 7 … Σ 0, 1, 0, 6, 0, 20, 0, 56, …
  (−∞, −1]nonnegativerational roots
• A038331 → θ+1
  144, 240, 75 · 1728, 4320, 2700, 500 … Σ 459, 9248, 181781, 3507882, 66733279, …
  (−∞, 0]nonnegativerational roots
• A103406 → x ↦ x+1
  1 · 3, 2 · 8, 10, 3 · 20, 36, 21, 4 … Σ 1, 5, 21, 81, 297, 1053, 3645, 12393, …
  (−∞, −1]nonnegativerational roots
• A144439 → D
  1 · 8, 2 · 31, 62, 3 · 102, 652, 306, 4 … Σ 0, 1, 10, 96, 1064, 13620, 199320, …
  (−∞, 0]nonnegative
• A159854 → Veronese 2 (j=1) → D+1
  1, 1 · 2, 2 · 3, 5, 1 · 4, 12, 4 … Σ 0, 2, 4, 9, 20, 44, 96, 208, …
  (−∞, 0]nonnegative
• A027465 → basis A013611 → θ+1
  1 · 4, 8 · 16, 64, 48 · 64, 384, 576, 256 … Σ 1, 12, 128, 1280, 12288, 114688, …
  (−∞, 0]nonnegativerational roots
• basis-map coefficients of A371080, shifted → basis A013610 → D
  3 · 15, 18 · 117, 216, 81 · 1254, 2862, 1782, 324 … Σ 0, 3, 33, 414, 6222, 110472, 2273688, …
  (−∞, 0]nonnegative
• A111125 → basis A013610 → D
  3 · 21, 18 · 93, 180, 81 · 345, 1080, 1053, 324 … Σ 0, 3, 39, 354, 2802, 20637, 145377, …
  (−∞, 0]nonnegative
• A136011 → θ+1
  1 · 1 · 1, 2 · 1, 6 … Σ 1, 1, 3, 7, 18, 49, 142, 437, …
  (−∞, 0]nonnegative
• A114656 → θ+1 → x ↦ x+1
  1 · 4, 2 · 19, 18, 3 · 96, 132, 48, 4 … Σ 1, 6, 40, 280, 2016, 14784, 109824, …
  (−∞, −1]nonnegative
• A200139 → basis A013610
  1 · 2, 3 · 6, 15, 9 · 18, 63, 72, 27 … Σ 1, 5, 30, 180, 1080, 6480, 38880, …
  (−∞, 0]nonnegativerational roots
• A113953 → basis A013610 → basis A008277
  1 · 4, 3 · 24, 39, 9 · 128, 411, 225, 27 … Σ 1, 7, 72, 791, 9713, 130644, 1908019, …
  (−∞, 0]nonnegative
• A093375 → Veronese 2 (j=1) → D+1
  1 · 4 · 10, 1 · 24, 8 … Σ 0, 1, 4, 11, 32, 88, 232, 592, …
  (−∞, 0]nonnegative
• A038255 → x ↦ x/(x+1)
  1 · 6, 7 · 36, 84, 49 · 216, 756, 882, 343 … Σ 1, 13, 169, 2197, 28561, 371293, …
  [−1, 0]nonnegativerational roots
• A103327 → D → D
  2 · 42, 6 · 252, 216, 12 · 924, 1980, 660, 20 … Σ 0, 0, 2, 48, 480, 3584, 23040, 135168, …
  (−∞, 0]nonnegative
• A151775: Triangle read by rows: T(n,k) = value of (d^2n/dx^2n) (tan^(2k)(x)/cos(x)) at the point x = 0.
  1 · 1, 2 · 5, 28, 24 · 61, 662, 1320, 720 … Σ 1, 3, 57, 2763, 250737, 36581523, …
  (−∞, 0]nonnegative
• A001263 → basis A013611
  1 · 2, 4 · 5, 20, 16 · 14, 84, 144, 64 … Σ 1, 6, 41, 306, 2426, 20076, 171481, …
  (−∞, 0]nonnegative
• A178820 → Veronese 2 → basis A013610
  1 · 4 · 20, 30 · 80, 180 … Σ 1, 4, 50, 260, 1435, 6776, 30660, …
  (−∞, 0]nonnegative
• A116666 → basis A013610
  1 · 4, 9 · 12, 48, 45 · 32, 180, 324, 189 … Σ 1, 13, 105, 725, 4625, 28125, 165625, …
  (−∞, 0]nonnegativerational roots
• A096956 → basis A013610
  6 · 7, 18 · 14, 57, 54 · 28, 156, 279, 162 … Σ 6, 25, 125, 625, 3125, 15625, 78125, …
  (−∞, 0]nonnegativerational roots
• A178821 → basis A007318 → (θ+1)²
  1 · 10, 20 · 60, 240, 135 · 280, 1680, 1890, 560 … Σ 1, 30, 435, 4410, 35910, 251748, …
  (−∞, 0]nonnegative
• A145597 → γ → D
  3 · 15 · 45, 18 · 105, 126 … Σ 0, 0, 3, 15, 63, 231, 798, 2646, …
  (−∞, 0]nonnegative
• A139548: Triangle T(n,k) with the coefficient of [x^k] of the polynomial (2*(x+1)^2)^n in row n, column k, 0<=k<=2n.
  1 · 2, 4, 2 · 4, 16, 24, 16, 4 … Σ 1, 8, 64, 512, 4096, 32768, 262144, …
  (−∞, 0)nonnegativerational roots
• A136124 → basis A013611 → (θ+1)²
  1 · 3, 16 · 12, 112, 144 · 60, 752, 1728, 1024 … Σ 1, 19, 268, 3564, 47800, 663528, …
  (−∞, 0]nonnegative
• A125662 → basis A013609 → reverse
  1 · 2, 4 · 4, 16, 15 · 8, 48, 92, 56 … Σ 1, 6, 35, 204, 1189, 6930, 40391, …
  (−1, 0]nonnegative
• A132166 → D+1
  378, 44, 1 · 5649, 1239, 66, 1 … Σ 423, 6955, 108134, 1635402, 24367069, …
  (−∞, 0]nonnegative
• A116414 → basis A007318 → basis A013610
  1 · 6, 3 · 33, 36, 9 · 180, 306, 162, 27 … Σ 1, 9, 78, 675, 5841, 50544, 437373, …
  (−∞, 0]nonnegative
• A094816 → x ↦ x+1 → basis A008277
  1 · 3, 1 · 11, 8, 1 · 49, 57, 15, 1 … Σ 1, 4, 20, 122, 884, 7432, 71128, …
  (−∞, 0]nonnegative
• A013609 → Veronese 2 → basis A008277
  1 · 1 · 5, 4 · 13, 12 … Σ 1, 1, 9, 25, 129, 481, 2281, 9689, …
  (−∞, 0]nonnegative
• A119808 → basis A013611
  1 · 3, 4 · 9, 20 · 27, 84, 32 … Σ 1, 7, 29, 143, 661, 3127, 14669, 69023, …
  (−∞, 0]nonnegative
• A181543 → x ↦ x+1
  1 · 2, 1 · 10, 10, 1 · 56, 84, 30, 1 … Σ 1, 3, 21, 171, 1521, 14283, 138909, …
  (−∞, −1]nonnegative
• A056939 → x ↦ x+1 → D+1
  1 · 3, 1 · 12, 8, 1 · 55, 59, 16, 1 … Σ 1, 4, 21, 131, 909, 6798, 53737, …
  (−∞, 0]nonnegative
• A143495 → x ↦ x+1 → reverse
  1 · 1, 4 · 1, 9, 17 · 1, 15, 64, 77 … Σ 1, 5, 27, 157, 979, 6517, 46107, …
  (−∞, 0]nonnegative
• A013609 → basis A008288
  1 · 3, 2 · 9, 16, 4 · 27, 82, 52, 8 … Σ 1, 5, 29, 169, 985, 5741, 33461, …
  [−3−2√2, −3+2√2]nonnegative
• A133214 → θ+1
  1, 16, 12 · 1, 36, 108, 32 · 1, 64, 432, 512, 80 … Σ 29, 177, 1089, 6693, 41005, 250337, …
  (−∞, 0]nonnegative
• A136157 → basis A013610
  3 · 4, 9 · 4, 21, 27 · 4, 33, 90, 81 … Σ 3, 13, 52, 208, 832, 3328, 13312, …
  (−∞, 0]nonnegativerational roots