Sequences

• A081579 → γ → D+1
  1 · 1 · 5, 4 · 9, 8 … Σ 1, 1, 9, 17, 73, 177, 585, 1553, …
  (−∞, 0]nonnegative
• A152198 → basis A013611 → D+1
  1 · 1 · 6, 4 · 6, 4 … Σ 1, 1, 10, 10, 84, 84, 648, 648, …
  (−∞, 0]nonnegativerational roots
• type_b_eulerian → D
  1 · 6, 2 · 23, 46, 3 · 76, 460, 228, 4 … Σ 0, 1, 8, 72, 768, 9600, 138240, …
  (−∞, 0]nonnegative
• A126216 → D
  1 · 5, 2 · 21, 18, 3 · 84, 112, 42, 4 … Σ 0, 1, 7, 42, 242, 1375, 7773, 43876, …
  (−∞, −1]nonnegative
• A038207 → Veronese 2 (j=1) → x ↦ x+1
  1 · 4 · 13, 1 · 40, 8 … Σ 0, 1, 4, 14, 48, 164, 560, 1912, …
  (−∞, −1]nonnegative
• A103406 → D+1
  1 · 3, 2 · 5, 10, 3 · 7, 24, 21, 4 … Σ 1, 5, 18, 56, 160, 432, 1120, 2816, …
  (−∞, 0]nonnegative
• A038281 → basis A013611 → basis A013609
  529, 1104, 576 · 12167, 38088, 39744, 13824 … Σ 2209, 103823, 4879681, 229345007, …
  (−∞, 0]nonnegativerational roots
• A049403 → basis A013610
  4, 15, 9 · 10, 54, 81, 27 · 26, 192, 459, 378, 81 … Σ 28, 172, 1136, 7984, 59200, 460352, …
  (−∞, 0]nonnegative
• A178821 → basis A013610 → θ+1
  1 · 10, 30 · 60, 360, 405 · 280, 2520, 5670, 3780 … Σ 1, 40, 825, 12250, 148750, 1575000, …
  (−∞, 0]nonnegativerational roots
• A290319 → basis A013611 → x ↦ x/(x+1)
  1 · 2, 6 · 12, 56, 60 · 120, 728, 1384, 840 … Σ 1, 8, 128, 3072, 98304, 3932160, …
  [−1, 0]nonnegativerational roots
• A156365 → D
  8, 8 · 22, 88, 24 · 52, 528, 624, 64 … Σ 16, 134, 1268, 13586, 163560, 2191934, …
  (−∞, 0]nonnegative
• A055151 → basis A007318
  1 · 1 · 2, 1 · 4, 3 … Σ 1, 1, 3, 7, 21, 61, 191, 603, …
  (−∞, −1]nonnegative
• A130850 → θ+1
  1 · 1, 2 · 2, 6, 3 · 6, 24, 21, 4 … Σ 1, 3, 11, 55, 359, 2891, 27635, 305439, …
  (−∞, 0]nonnegative
• mobius_x_over_x_plus_one of Irregular triangle T(n, k) = [x^k]( p(n, x) ), where p(n, x) = (1/x)*(1-x)^n*(1+x)^(n+2)*( Sum_{j >= 0} j^(n+1)*x^j ), read by rows.
  1 · 1, 4, 4 · 1, 10, 34, 48, 24 … Σ 1, 9, 117, 2025, 43821, 1137969, …
  [−1, 0]nonnegative
• A094638 → D+1 → basis A008277
  1 · 3, 1 · 13, 13, 2 · 70, 157, 65, 6 … Σ 1, 4, 28, 298, 4534, 93809, 2530709, …
  (−∞, 0]nonnegative
• A038319 → basis A013610 → basis A013610
  961, 2790, 2025 · 29791, 129735, 188325, 91125 … Σ 5776, 438976, 33362176, 2535525376, …
  (−∞, 0]nonnegativerational roots
• basis-map coefficients of A021012 → basis A008277 → x ↦ x+1
  1 · -2, -1 · 10, 10, 2 · -90, -132, -54, -6 … Σ 1, -3, 22, -282, 5448, -145800, …
  (−∞, −1]
• A367270 → D → D+1
  2 · 12, 6 · 48, 60, 12 · 140, 360, 180, 20 … Σ 0, 0, 2, 18, 120, 700, 3780, 19404, …
  (−∞, 0]nonnegative
• A030528 → basis A013609 → D
  2 · 8, 8 · 20, 48, 24 · 44, 168, 192, 64 … Σ 0, 2, 16, 92, 468, 2226, 10152, 44982, …
  (−∞, 0]nonnegative
• A013612 → basis A013610 → D
  180, 450 · 1620, 8100, 10125 … Σ 630, 19845, 555660, 14586075, …
  (−∞, 0]nonnegativerational roots
• A253284 → basis A013609
  1 · 4, 4 · 36, 84, 48 · 528, 1968, 2400, 960 … Σ 1, 8, 168, 5856, 285600, 17904960, …
  (−∞, 0]nonnegative
• basis-map coefficients of A026729 → basis A013610
  1 · 1, 3 · 1, 6, 9 · 1, 9, 27, 27 … Σ 1, 4, 16, 64, 256, 1024, 4096, 16384, …
  [−1, 0]nonnegativerational roots
• A038331 → basis A013610 → D+1
  799, 960, 225 · 17918, 35955, 21600, 3375 … Σ 1984, 78848, 3014656, 112197632, …
  (−∞, 0]nonnegativerational roots
• A081578 → basis A013610 → reverse
  1 · 3, 2 · 9, 21, 7 · 27, 108, 90, 20 … Σ 1, 5, 37, 245, 1669, 11285, 76453, …
  (−∞, 0]nonnegative
• A207607 → basis A013610 → basis A013611
  1 · 9, 24 · 53, 252, 288 · 309, 2124, 4752, 3456 … Σ 1, 33, 593, 10641, 190945, 3426369, …
  (−∞, 0]nonnegative
• A102547 → x ↦ (1/27)x → basis A013610
  1 · 3 · 9 · 28, 3 … Σ 1, 3, 9, 31, 105, 351, 1177, 3951, …
  (−∞, 0]nonnegative
• A136572 → (θ+1)² → basis A008277
  1 · 4, 4 · 18, 54, 18 · 96, 672, 576, 96 … Σ 1, 8, 90, 1440, 31200, 876960, …
  (−∞, 0]nonnegative
• A269944 → x ↦ x/(x+1)
  1 · 0, 1 · 0, 1, 2 · 0, 4, 13, 10 … Σ 1, 1, 3, 27, 513, 16929, 863379, …
  [−1, 0]nonnegativerational roots
• A078812 → basis A013611 → D
  4 · 24, 32 · 100, 288, 192 · 360, 1632, 2304, 1024 … Σ 0, 4, 56, 580, 5320, 45680, 376264, …
  (−∞, 0]nonnegative
• A034870 → basis A013610 → θ+1
  1 · 4, 24, 27 · 16, 192, 648, 864, 405 … Σ 1, 55, 2125, 71875, 2265625, 68359375, …
  (−∞, 0]nonnegativerational roots
• A178820 → Veronese 2 (j=1) → D
  20 · 140 · 560, 112 · 1680, 1008 … Σ 0, 0, 0, 20, 140, 672, 2688, 9600, …
  (−∞, 0]nonnegative
• A274496 → D → θ+1
  2 · 4 · 8, 16 · 16, 32 … Σ 0, 0, 2, 4, 24, 48, 192, 384, …
  (−∞, 0]nonnegativerational roots
• A193728 → basis A013609
  1 · 3, 2 · 21, 32, 12 · 147, 350, 276, 72 … Σ 1, 5, 65, 845, 10985, 142805, 1856465, …
  (−∞, 0]nonnegativerational roots
• A145324 → basis A013609 → (θ+1)²
  1 · 3, 16 · 12, 136, 216 · 60, 1064, 3528, 3072 … Σ 1, 19, 364, 7724, 183404, 4851620, …
  (−∞, 0]nonnegative
• A391533 → Pₙ + Pₙ₊₁ → basis A013611
  27, 108, 144, 64 · 54, 324, 720, 704, 256 … Σ 343, 2058, 12348, 74088, 444528, …
  (−∞, 0]nonnegativerational roots
• A109692 → basis A013610 → basis A013610
  1 · 5, 9 · 65, 252, 243 · 1365, 8217, 16443, 10935 … Σ 1, 14, 560, 36960, 3400320, 401237760, …
  (−∞, 0]nonnegativerational roots
• A154986 → γ → D
  2 · 8 · 20, 48 · 40, 368 … Σ 0, 0, 2, 8, 68, 408, 3798, 30384, …
  (−∞, 0]nonnegative
• A099040 → basis A013611 → D
  8 · 40, 128 · 160, 1024, 1536 … Σ 0, 8, 168, 2720, 39360, 535200, …
  (−∞, 0]nonnegative
• A111125 → Veronese 2 (j=1)
  1 · 5 · 14, 1 · 30, 9 … Σ 0, 1, 5, 15, 39, 100, 260, 681, …
  (−∞, 0]nonnegative
• A036969 → D+1
  1 · 2, 1 · 6, 7, 1 · 22, 49, 17, 1 … Σ 1, 3, 14, 89, 737, 7696, 98093, …
  (−∞, 0]nonnegative
• A039756 → reverse → (θ+1)²
  1 · 1, 4 · 1, 16, 9 · 1, 52, 81, 16 … Σ 1, 5, 26, 150, 964, 6836, 52936, …
  (−∞, 0]nonnegative
• A134059 → basis A013611
  1 · 6, 12 · 12, 48, 48 · 24, 144, 288, 192 … Σ 1, 18, 108, 648, 3888, 23328, 139968, …
  (−∞, 0]nonnegativerational roots
• A099040 → basis A013610 → D
  6 · 30, 72 · 120, 576, 648 · 432, 3096, 7128, 5184 … Σ 0, 6, 102, 1344, 15840, 175488, …
  (−∞, 0]nonnegative
• A358735 → basis A007318 → x ↦ x/(x+1)
  1 · 2, 3 · 7, 22, 17 · 33, 159, 253, 133 … Σ 1, 5, 46, 578, 9064, 169904, 3701632, …
  [−1, −1/2)nonnegative
• A130534 → Veronese 2 (j=1) → D+1
  1 · 3 · 12, 1 · 60, 10 … Σ 0, 1, 3, 13, 70, 447, 3297, 27576, …
  (−∞, 0]nonnegative
• A132774 → Veronese 2 (j=1) → (θ+1)²
  3 · 4 · 0, 28 · 0, 32 … Σ 0, 3, 4, 28, 32, 99, 108, 240, …
  (−∞, 0]nonnegativerational roots
• A257615: Triangle read by rows: T(n,k) = t(n-k, k); t(n,m) = f(m)*t(n-1,m) + f(n)*t(n,m-1), where f(x) = 2*x + 5.
  1 · 5, 5 · 25, 70, 25 · 125, 715, 715, 125 … Σ 1, 10, 120, 1680, 26880, 483840, …
  (−∞, 0)nonnegative
• A008459 → D → θ+1
  1 · 4, 4 · 9, 36, 9 · 16, 144, 144, 16 … Σ 0, 1, 8, 54, 320, 1750, 9072, 45276, …
  (−∞, 0]nonnegative
• A127648 → Veronese 2 (j=1) → D
  4 · 0, 12 · 0, 0, 24 · 0, 0, 0, 40 … Σ 0, 0, 0, 0, 4, 0, 12, 0, …
  (−∞, 0]nonnegativerational roots
• A146987 → basis A013611
  1 · 2, 4 · 7, 28, 16 · 26, 156, 240, 64 … Σ 1, 6, 51, 486, 6156, 95256, 1621296, …
  (−∞, 0]nonnegative