Sequences

• A375853 → Pₙ + Pₙ₊₁
  10, 8 · 28, 64, 20 · 60, 272, 236, 40 … Σ 18, 112, 608, 3072, 14848, 69632, …
  (−∞, ∞)nonnegative
• A127648 → Veronese 2 → (θ+1)²
  1 · 0, 12 · 0, 0, 45 · 0, 0, 0, 112 … Σ 0, 1, 0, 12, 0, 45, 0, 112, …
  (−∞, 0]nonnegativerational roots
• A102662 → x ↦ x/(x+1)
  1 · 1, 4 · 1, 7, 9 · 1, 10, 28, 22 … Σ 1, 5, 17, 61, 217, 773, 2753, 9805, …
  [−1, 0]nonnegative
• A104684 → D
  1 · 6, 2 · 30, 24, 3 · 140, 180, 60, 4 … Σ 0, 1, 8, 57, 384, 2505, 16008, 100849, …
  (−∞, 0]nonnegative
• A038337 → basis A007318 → θ+1
  529, 1012, 363 · 12167, 34914, 25047, 5324 … Σ 1904, 77452, 3065712, 118933904, …
  (−∞, 0]nonnegativerational roots
• A038334 → basis A013610 → (θ+1)²
  400, 3840, 5184 · 8000, 115200, 311040, 221184 … Σ 9424, 655424, 41662720, 2495550464, …
  (−∞, 0]nonnegative
• A127773 → D → D
  12 · 0, 60 · 0, 0, 180 · 0, 0, 0, 420 … Σ 0, 0, 12, 60, 180, 420, 840, 1512, …
  (−∞, 0]nonnegativerational roots
• A125092 → basis A013609
  1 · 5, 8 · 18, 52, 36 · 56, 228, 300, 128 … Σ 1, 13, 106, 712, 4288, 24064, 128512, …
  (−∞, 0]nonnegative
• A038328 → basis A013611 → basis A008277
  484, 416, 64 · 10648, 16352, 5760, 512 … Σ 964, 33272, 1233424, 49006048, …
  (−∞, 0]nonnegative
• A085880 → D → basis A013611
  1 · 8, 16 · 60, 240, 240 · 448, 2688, 5376, 3584 … Σ 0, 1, 24, 540, 12096, 272160, 6158592, …
  (−∞, 0]nonnegativerational roots
• A038321 → basis A013610 → basis A013610
  1521, 4914, 3969 · 59319, 287469, 464373, 250047 … Σ 10404, 1061208, 108243216, 11040808032, …
  (−∞, 0]nonnegativerational roots
• A249252 → basis A007318
  1 · 5, 4 · 17, 24, 8 · 61, 124, 80, 16 … Σ 1, 9, 49, 281, 1601, 9129, 52049, …
  (−∞, −1]nonnegative
• A011973 → basis A013609 → basis A013609
  1 · 1 · 4, 4 · 7, 8 … Σ 1, 1, 8, 15, 71, 176, 673, 1905, …
  (−∞, 0]nonnegative
• A125662 → basis A013611 → θ+1
  1 · 4, 8 · 15, 64, 48 · 56, 368, 576, 256 … Σ 1, 12, 127, 1256, 11905, 109604, …
  (−∞, 0]nonnegative
• A095704: Triangle read by rows giving coefficients of the trigonometric expansion of sin(n*x).
  1 · 2 · 3, 0, -1 · 4, 0, -4 … Σ 1, 2, 2, 0, -4, -8, -8, 0, …
  (−∞, ∞)
• A113413 → x ↦ x+1 → basis A013610
  1 · 4, 3 · 14, 24, 9 · 50, 132, 108, 27 … Σ 1, 7, 47, 317, 2137, 14407, 97127, …
  (−∞, 0]nonnegative
• A091044 → basis A007318 → (θ+1)²
  1 · 4, 8 · 16, 64, 27 · 64, 384, 360, 64 … Σ 1, 12, 107, 872, 6733, 50052, 361655, …
  (−∞, 0]nonnegative
• A125662 → basis A013611 → basis A013610
  1 · 8, 12 · 63, 192, 144 · 496, 2280, 3456, 1728 … Σ 1, 20, 399, 7960, 158801, 3168060, …
  (−∞, 0]nonnegative
• A120910 → basis A013611 → D+1
  3 · 21, 12 · 99, 168, 48 · 405, 1188, 1008, 192 … Σ 3, 33, 315, 2793, 23667, 194481, …
  (−∞, 0]nonnegativerational roots
• A119462 → (θ+1)²
  1 · 2 · 2, 8 · 2, 24 … Σ 1, 2, 10, 26, 68, 172, 424, 1024, …
  (−∞, 0]nonnegative
• A046716 → basis A013609 → D+1
  1 · 4, 2 · 15, 18, 4 · 66, 138, 68, 8 … Σ 1, 6, 37, 280, 2901, 40882, 730009, …
  (−∞, 0]nonnegative
• A013612 → x ↦ x+1 → D
  60, 50 · 540, 900, 375 · 4320, 10800, 9000, 2500 … Σ 110, 1815, 26620, 366025, 4831530, …
  (−∞, 0]nonnegativerational roots
• A011973 → Veronese 2 (j=1) → x ↦ x+1
  1 · 2 · 3 · 4 … Σ 0, 0, 1, 2, 3, 4, 7, 14, …
  (−∞, −1]nonnegative
• A038314 → basis A008277
  484, 672, 144 · 10648, 28656, 14688, 1728 … Σ 1300, 55720, 2653072, 138846496, …
  (−∞, 0]nonnegative
• basis-map coefficients of A026729 → basis A013611 → θ+1
  1 · 1, 8 · 1, 16, 48 · 1, 24, 144, 256 … Σ 1, 9, 65, 425, 2625, 15625, 90625, …
  (−∞, 0]nonnegativerational roots
• A028326 → Veronese 2 (j=1) → θ+1
  2 · 4 · 6, 4 · 8, 16 … Σ 0, 2, 4, 10, 24, 56, 128, 288, …
  (−∞, 0]nonnegative
• A038279 → basis A013610 → x ↦ x/(x+1)
  1 · 9, 12 · 81, 216, 144 · 729, 2916, 3888, 1728 … Σ 1, 21, 441, 9261, 194481, 4084101, …
  [−1, 0]nonnegativerational roots
• narayana → basis A013609 → x ↦ x/(x+1)
  1 · 2, 4 · 5, 20, 19 · 14, 84, 162, 100 … Σ 1, 6, 44, 360, 3152, 28896, 273856, …
  [−1, 0]nonnegative
• A122848 → basis A013609 → θ+1
  1 · 1, 4 · 2, 12, 12 · 4, 36, 72, 32 … Σ 1, 5, 26, 144, 846, 5238, 34020, …
  (−∞, 0]nonnegative
• A286718 → basis A013610 → reverse
  1 · 3, 2 · 9, 21, 10 · 27, 135, 198, 80 … Σ 1, 5, 40, 440, 6160, 104720, 2094400, …
  (−∞, 0]nonnegativerational roots
• A113413 → x ↦ x+1 → D+1
  1 · 4, 1 · 13, 8, 1 · 40, 41, 12, 1 … Σ 1, 5, 22, 94, 390, 1586, 6350, 25114, …
  (−∞, 0]nonnegative
• A356546 → basis A013611 → basis A007318
  1 · 12, 8 · 216, 288, 96 · 4320, 8640, 5760, 1280 … Σ 1, 20, 600, 20000, 700000, 25200000, …
  (−∞, −1]nonnegativerational roots
• A316649 → basis A013610
  1 · 3, 15, 18 · 26, 225, 711, 972, 486 … Σ 1, 36, 2420, 180900, 14200500, …
  (−∞, 0]nonnegative
• A103327 → basis A013611 → x ↦ x+1
  1 · 8, 4 · 80, 80, 16 · 832, 1280, 576, 64 … Σ 1, 12, 176, 2752, 43776, 699392, …
  (−∞, −1]nonnegative
• A013613 → basis A008277
  1 · 7, 6 · 49, 120, 36 · 343, 1854, 1404, 216 … Σ 1, 13, 205, 3817, 81481, 1949749, …
  (−∞, 0]nonnegative
• A038319 → basis A013611 → x ↦ x+1
  1296, 1440, 400 · 46656, 77760, 43200, 8000 … Σ 3136, 175616, 9834496, 550731776, …
  (−∞, −1]nonnegativerational roots
• A008459 → basis A013611 → basis A008277
  1 · 6, 4 · 46, 72, 16 · 396, 1144, 576, 64 … Σ 1, 10, 134, 2180, 40902, 858924, …
  (−∞, 0]nonnegative
• A038301 → basis A013609 → basis A007318
  1764, 1848, 484 · 74088, 116424, 60984, 10648 … Σ 4096, 262144, 16777216, 1073741824, …
  (−∞, −1]nonnegativerational roots
• basis-map coefficients of A113214, shifted → D → (θ+1)²
  -1 · 2, 8 · -3, -24, -27 · 4, 48, 108, 64 … Σ 0, -1, 10, -54, 224, -800, 2592, -7840, …
  (−∞, 0]
• A048993 → reverse → (θ+1)²
  1 · 1 · 1, 4 · 1, 12, 9 … Σ 1, 1, 5, 22, 104, 531, 2897, 16787, …
  (−∞, 0]nonnegative
• A038279 → basis A013609
  1 · 9, 2 · 81, 36, 4 · 729, 486, 108, 8 … Σ 1, 11, 121, 1331, 14641, 161051, …
  (−∞, −1]nonnegativerational roots
• A204420 → basis A007318 → basis A008277
  1 · 2, 1 · 24, 21, 3 · 720, 855, 225, 15 … Σ 1, 3, 48, 1815, 123795, 13254570, …
  (−∞, 0]nonnegative
• A085880 → basis A013611 → basis A013609
  1 · 6, 8 · 72, 192, 128 · 1080, 4320, 5760, 2560 … Σ 1, 14, 392, 13720, 537824, 22588608, …
  (−∞, 0]nonnegativerational roots
• A169803 → basis A013611 → D+1
  1 · 6, 4 · 11, 8 · 25, 52, 16 … Σ 1, 10, 19, 93, 232, 861, 2405, 7914, …
  (−∞, 0]nonnegative
• A137320 → basis A013611 → D
  8 · 40, 128 · 208, 1152, 1536 … Σ 0, 8, 168, 2896, 48208, 812192, …
  (−∞, 0]nonnegative
• basis-map coefficients of A297191, shifted → θ+1 → basis A013610
  1 · 3, 18, 27 · 5, 60, 270, 540, 405 … Σ 1, 48, 1280, 28672, 589824, 11534336, …
  (−∞, 0]nonnegativerational roots
• A038336 → basis A013609 → D
  880, 800 · 29040, 52800, 24000 … Σ 1680, 105840, 5927040, 311169600, …
  (−∞, 0]nonnegativerational roots
• A038281 → x ↦ x+1 → x ↦ x/(x+1)
  121, 308, 196 · 1331, 5082, 6468, 2744 … Σ 625, 15625, 390625, 9765625, 244140625, …
  [−1, 0]nonnegativerational roots
• basis-map coefficients of A371080, shifted → basis A013609
  1 · 1, 2 · 4, 10, 4 · 28, 78, 48, 8 … Σ 1, 3, 18, 162, 1944, 29160, 524880, …
  (−∞, 0]nonnegativerational roots
• A185263 → basis A013609
  1 · 1 · 2, 2 · 6, 10 … Σ 1, 1, 4, 16, 118, 862, 9292, 99388, …
  (−∞, 0]nonnegative