Sequences

• A131689 → θ+1 → reverse
  1 · 2 · 6, 2 · 24, 18, 2 … Σ 1, 2, 8, 44, 308, 2612, 25988, 296564, …
  (−∞, 0]nonnegative
• A013609 → Veronese 2 (j=1) → basis A013610
  2 · 4 · 14, 24 · 40, 96 … Σ 0, 2, 4, 38, 136, 842, 3724, 20078, …
  (−∞, 0]nonnegative
• A059473 → basis A013609 → basis A013611
  1 · 8, 16 · 70, 272, 256 · 608, 3520, 6656, 4096 … Σ 1, 24, 598, 14880, 370276, 9213984, …
  (−∞, 0]nonnegative
• A159854 → x ↦ x+1 → (θ+1)²
  1, 8, 9 · 2, 20, 36, 16 · 4, 48, 117, 96, 25 … Σ 18, 74, 290, 1098, 4050, 14634, 52002, …
  (−∞, 0]nonnegative
• A290596 → x ↦ x+1
  1 · 3, 1 · 21, 12, 1 · 225, 171, 27, 1 … Σ 1, 4, 34, 424, 6880, 136672, 3202048, …
  (−∞, −1]nonnegative
• A132393 → D+1 → x ↦ x/(x+1)
  1 · 1, 2 · 1, 5, 5 · 2, 14, 28, 17 … Σ 1, 3, 11, 61, 457, 4323, 49443, 663549, …
  [−1, 0]nonnegative
• A133081 → basis A013611
  1 · 1 · 2, 12, 16 · 1, 8, 16 … Σ 1, 1, 30, 25, 750, 625, 18750, 15625, …
  (−∞, 0]nonnegativerational roots
• A118394 → basis A008277
  1 · 1 · 1 · 7, 6 … Σ 1, 1, 1, 13, 49, 121, 2041, 13021, …
  (−∞, 0]nonnegative
• A038208 → basis A013611 → D
  8 · 64, 128 · 384, 1536, 1536 … Σ 0, 8, 192, 3456, 55296, 829440, …
  (−∞, 0]nonnegativerational roots
• basis-map coefficients of A371080, shifted → x ↦ x/(x+1)
  1 · 0, 1 · 0, 3, 4 · 0, 18, 45, 28 … Σ 1, 1, 7, 91, 1729, 43225, 1339975, …
  [−1, 0]nonnegativerational roots
• A038320 → x ↦ x+1 → basis A008277
  529, 312, 36 · 12167, 12222, 3132, 216 … Σ 877, 27737, 919177, 31944965, …
  (−∞, 0]nonnegative
• basis-map coefficients of A112227 → basis A013611 → (θ+1)²
  1, 32, 144 · 1, 48, 432, 1024 … Σ 177, 1505, 11425, 80625, 540625, …
  (−∞, 0]nonnegative
• A225471 → D
  1 · 10, 2 · 131, 42, 3 · 2196, 892, 108, 4 … Σ 0, 1, 12, 176, 3200, 70144, 1806336, …
  (−∞, 0]nonnegative
• A122542 → D
  1 · 2, 2 · 2, 8, 3 · 2, 16, 18, 4 … Σ 0, 1, 4, 13, 40, 117, 332, 921, …
  (−∞, 0]nonnegative
• A062145 → x ↦ x+1 → x ↦ x/(x+1)
  1 · 5, 9 · 21, 72, 61 · 84, 420, 693, 377 … Σ 1, 14, 154, 1574, 15619, 152900, …
  [−1, 0]nonnegative
• A059344 → basis A013610 → D+1
  1 · 1 · 9, 6 · 25, 18 … Σ 1, 1, 15, 43, 565, 2541, 32371, 191815, …
  (−∞, 0]nonnegative
• A078812 → D → θ+1
  1 · 4, 4 · 10, 24, 9 · 20, 84, 72, 16 … Σ 0, 1, 8, 43, 192, 768, 2856, 10085, …
  (−∞, 0]nonnegative
• A059364 → basis A007318 → basis A013609
  1 · 4, 2 · 28, 30, 8 · 280, 468, 260, 48 … Σ 1, 6, 66, 1056, 22176, 576576, …
  (−∞, −1]nonnegativerational roots
• A081579 → x ↦ x+1 → basis A008277
  1 · 3, 1 · 17, 11, 1 · 75, 85, 20, 1 … Σ 1, 4, 29, 181, 1252, 8891, 66269, …
  (−∞, 0]nonnegative
• A038320 → basis A013611 → basis A013609
  1681, 3936, 2304 · 68921, 242064, 283392, 110592 … Σ 7921, 704969, 62742241, 5584059449, …
  (−∞, 0]nonnegativerational roots
• A152830 → x ↦ x+1 → basis A013611
  1 · 1 · 1 · 1 … Σ 1, 1, 1, 1, 7, 7, 7, 7, …
  (−∞, 0]nonnegativerational roots
• A290319 → basis A013611 → basis A008277
  1 · 6, 4 · 60, 80, 16 · 840, 1680, 672, 64 … Σ 1, 10, 156, 3256, 84496, 2611104, …
  (−∞, 0]nonnegative
• A035607 → basis A013609 → basis A013610
  1 · 1 · 7, 12 · 31, 96, 72 … Σ 1, 1, 19, 199, 2161, 23401, 253459, …
  (−∞, 0]nonnegative
• basis-map coefficients of A026729 → (θ+1)² → D
  4 · 0, 18 · 0, 0, 48 · 0, 0, 0, 100 … Σ 0, 4, 18, 48, 100, 180, 294, 448, …
  (−∞, 0]nonnegativerational roots
• A038338 → basis A013609 → basis A007318
  2304, 2304, 576 · 110592, 165888, 82944, 13824 … Σ 5184, 373248, 26873856, 1934917632, …
  (−∞, −1]nonnegativerational roots
• A119808 → basis A013609
  1 · 3, 2 · 9, 10 · 27, 42, 8 … Σ 1, 5, 19, 77, 307, 1229, 4915, 19661, …
  (−∞, 0]nonnegative
• A154602 → x ↦ x+1
  1 · 2, 1 · 8, 6, 1 · 40, 40, 12, 1 … Σ 1, 3, 15, 93, 681, 5691, 53079, 544053, …
  (−∞, −1]nonnegative
• A063967 → basis A013609 → D
  2 · 10, 8 · 40, 64, 24 · 144, 344, 264, 64 … Σ 0, 2, 18, 128, 816, 4896, 28256, …
  (−∞, 0]nonnegative
• A356546 → x ↦ x+1 → basis A008277
  1 · 6, 2 · 54, 42, 6 · 540, 740, 240, 20 … Σ 1, 8, 102, 1540, 26040, 482580, …
  (−∞, 0]nonnegative
• A144445 → θ+1
  1 · 1, 2 · 1, 46, 3 · 1, 412, 618, 4 … Σ 1, 3, 50, 1035, 29091, 1028328, …
  (−∞, 0]nonnegative
• A011973 → D → D+1
  1 · 2 · 5, 2 · 10, 6 … Σ 0, 0, 1, 2, 7, 16, 38, 82, …
  (−∞, 0]nonnegative
• A257615 → Pₙ + Pₙ₊₁
  6, 5 · 30, 75, 25 · 150, 785, 740, 125 … Σ 11, 130, 1800, 28560, 510720, 10160640, …
  (−∞, ∞)nonnegative
• basis-map coefficients of A026729, shifted → (θ+1)² → D
  -4 · 0, 18 · 0, 0, -48 · 0, 0, 0, 100 … Σ 0, -4, 18, -48, 100, -180, 294, -448, …
  (−∞, 0]rational roots
• A125092 → basis A013611
  1 · 5, 16 · 18, 104, 144 · 56, 456, 1200, 1024 … Σ 1, 21, 266, 2736, 25056, 212976, …
  (−∞, 0]nonnegative
• A228955 → D+1
  1 · 2, 1 · 8, 6 · 42, 48, 6 … Σ 1, 3, 14, 96, 864, 9600, 126720, …
  (−∞, 0]nonnegative
• A121574 → x ↦ x+1 → θ+1
  1 · 3, 2 · 10, 14, 3 · 33, 70, 33, 4 … Σ 1, 5, 27, 140, 712, 3564, 17620, 86240, …
  (−∞, 0]nonnegative
• A397048 → x ↦ x/(x+1)
  1 · 1, 2 · 4, 13, 10 · 27, 118, 167, 77 … Σ 1, 3, 27, 389, 7697, 193707, 5918139, …
  [−1, 0]nonnegative
• A330510 → x ↦ x/(x+1)
  2 · 3, 6 · 4, 18, 18 · 5, 37, 81, 54 … Σ 2, 9, 40, 177, 782, 3453, 15244, 67293, …
  [−1, 0]nonnegative
• A081579 → basis A013610 → basis A008277
  1 · 5, 3 · 41, 51, 9 · 285, 675, 288, 27 … Σ 1, 8, 101, 1275, 17852, 269137, …
  (−∞, 0]nonnegative
• A003506 → D
  2 · 6, 6 · 12, 24, 12 · 20, 60, 60, 20 … Σ 0, 0, 2, 12, 48, 160, 480, 1344, …
  (−∞, −1]nonnegativerational roots
• A034870 → (θ+1)²
  1 · 1, 8, 9 · 1, 16, 54, 64, 25 … Σ 1, 18, 160, 1120, 6912, 39424, 212992, …
  (−∞, 0]nonnegative
• A100862 → basis A013610
  1 · 2, 3 · 5, 15, 9 · 14, 63, 81, 27 … Σ 1, 5, 29, 185, 1273, 9325, 72085, …
  (−∞, 0]nonnegative
• A286718 → basis A013611 → basis A013609
  1 · 6, 8 · 54, 120, 64 · 648, 1872, 1728, 512 … Σ 1, 14, 238, 4760, 109480, 2846480, …
  (−∞, 0]nonnegativerational roots
• A120910 → basis A007318 → basis A008277
  3 · 12, 3 · 48, 27, 3 · 192, 183, 45, 3 … Σ 3, 15, 78, 423, 2397, 14208, 88113, …
  (−∞, 0]nonnegative
• A120909 → basis A013610 → basis A013611
  3 · 27, 72 · 243, 1296, 1728 … Σ 3, 99, 3267, 107811, 3557763, …
  (−∞, 0]nonnegativerational roots
• A200536 → (θ+1)²
  1 · 1, 12, 18 · 1, 24, 117, 192, 100 … Σ 1, 31, 434, 4680, 44064, 381456, …
  (−∞, 0]nonnegative
• A008277 → (θ+1)² → reverse
  1 · 4, 1 · 9, 12, 1 · 16, 54, 28, 1 … Σ 1, 5, 22, 99, 471, 2386, 12867, 73681, …
  (−∞, 0]nonnegative
• A145597 → basis A007318
  1 · 6, 3 · 27, 27, 6 · 110, 165, 75, 10 … Σ 1, 9, 60, 360, 2061, 11529, 63728, …
  (−∞, −1]nonnegative
• A103633 → basis A013611
  1 · 1, 4 · 2, 12, 16 · 2, 20, 64, 64 … Σ 1, 5, 30, 150, 900, 4500, 27000, …
  (−∞, 0]nonnegativerational roots
• A114655 → reverse
  2 · 2, 4 · 2, 12, 8 · 2, 24, 48, 16 … Σ 2, 6, 22, 90, 394, 1806, 8558, 41586, …
  (−∞, 0]nonnegative