Sequences

• A007318 → −D²+(−1+n)D+1+n → x ↦ x/(x+1)
  1 · 2, 4 · 3, 14, 14 · 4, 30, 66, 44 … Σ 1, 6, 31, 144, 621, 2538, 9963, 37908, …
  [−1, 0]nonnegative
• A056242 → θ+1
  1 · 1, 4 · 1, 10, 12 · 1, 18, 48, 32 … Σ 1, 5, 23, 99, 408, 1632, 6388, 24596, …
  (−∞, 0]nonnegative
• A056241 → basis A013609
  1 · 2, 2 · 5, 10, 4 · 14, 42, 36, 8 … Σ 1, 4, 19, 100, 553, 3124, 17803, …
  (−∞, 0]nonnegative
• A102413 → D+1
  1 · 2, 1 · 5, 6, 1 · 7, 18, 9, 1 … Σ 1, 3, 12, 35, 102, 287, 792, 2151, …
  (−∞, 0]nonnegative
• A034870 → basis A013610 → x ↦ x/(x+1)
  1 · 4, 20, 25 · 16, 160, 600, 1000, 625 … Σ 1, 49, 2401, 117649, 5764801, …
  [−1, 0]nonnegativerational roots
• image under θ+1 → θ+1 → (θ+1)²
  1 · 0, 16 · 0, 0, 81 · 0, 0, 0, 256 … Σ 1, 16, 81, 256, 625, 1296, 2401, 4096, …
  (−∞, 0]nonnegativerational roots
• A127773 → θ+1 → reverse
  1 · 6 · 18 · 40 … Σ 1, 6, 18, 40, 75, 126, 196, 288, …
  (−∞, 0]nonnegativerational roots
• A008288 → basis A013609 → θ+1
  1 · 2, 4 · 5, 20, 12 · 12, 72, 96, 32 … Σ 1, 6, 37, 212, 1173, 6322, 33425, …
  (−∞, 0]nonnegative
• A128099 → basis A013609 → basis A013611
  1 · 1 · 7, 16 · 13, 32 … Σ 1, 1, 23, 45, 551, 1541, 13663, 47565, …
  (−∞, 0]nonnegative
• Hadamard-factor parent of A155495 → x ↦ x+1
  8, 8, 1 · 32, 48, 18, 1 · 128, 256, 160, 32, 1 … Σ 17, 99, 577, 3363, 19601, 114243, …
  (−∞, −1]nonnegative
• A038322 → basis A007318 → θ+1
  1 · 19, 16 · 361, 608, 192 · 6859, 17328, 10944, 2048 … Σ 1, 35, 1161, 37179, 1161297, 35606547, …
  (−∞, 0]nonnegativerational roots
• A113214 → Veronese 2 (j=1) → x ↦ x+1
  1 · 3 · 3, 1 · 5, 5 … Σ 0, 1, 3, 4, 10, 22, 42, 92, …
  (−∞, −1]nonnegative
• A038320 → x ↦ x+1 → D+1
  493, 276, 36 · 10115, 8874, 2484, 216 … Σ 805, 21689, 571849, 14831573, …
  (−∞, 0]nonnegativerational roots
• A038321 → basis A013609 → x ↦ x/(x+1)
  324, 1152, 1024 · 5832, 31104, 55296, 32768 … Σ 2500, 125000, 6250000, 312500000, …
  [−1, 0]nonnegativerational roots
• A137320 → reverse → x ↦ x+1
  1 · 2 · 6, 2 · 24, 20, 4 … Σ 1, 2, 8, 48, 384, 3840, 46080, 645120, …
  (−∞, −1]nonnegativerational roots
• A322944 → x ↦ x+1
  1 · 2, 1 · 9, 8, 1 · 60, 71, 18, 1 … Σ 1, 3, 18, 150, 1560, 19272, 274416, …
  (−∞, −1]nonnegative
• A128100 → basis A013610 → x ↦ x+1
  1 · 1 · 6, 3 · 11, 6 … Σ 1, 1, 9, 17, 89, 225, 937, 2737, …
  (−∞, −1]nonnegative
• A132812 → basis A007318 → reverse
  1 · 2, 4 · 3, 15, 15 · 4, 36, 84, 56 … Σ 1, 6, 33, 180, 985, 5418, 29953, …
  (−∞, 0]nonnegative
• A145596 → x ↦ x+1 → D+1
  1 · 6, 2 · 28, 20, 3 · 120, 136, 44, 4 … Σ 1, 8, 51, 304, 1765, 10128, 57799, …
  (−∞, 0]nonnegative
• A038208 → Veronese 2 → D+1
  1 · 2 · 8, 4 · 32, 24 … Σ 1, 2, 12, 56, 256, 1152, 5120, 22528, …
  (−∞, 0]nonnegative
• A116412 → basis A013610 → D+1
  1 · 7, 3 · 37, 42, 9 · 169, 342, 189, 27 … Σ 1, 10, 88, 727, 5764, 44428, 335440, …
  (−∞, 0]nonnegative
• A204420 → basis A007318
  1 · 1, 1 · 9, 12, 3 · 225, 345, 135, 15 … Σ 1, 2, 24, 720, 40320, 3628800, …
  (−∞, −1]nonnegativerational roots
• A008288 → basis A013609 → x ↦ x+1
  1 · 4, 2 · 19, 18, 4 · 88, 124, 56, 8 … Σ 1, 6, 41, 276, 1861, 12546, 84581, …
  (−∞, −1]nonnegative
• A008459 → basis A013609 → basis A008277
  1 · 4, 2 · 22, 24, 4 · 136, 260, 96, 8 … Σ 1, 6, 50, 500, 5662, 70628, 955012, …
  (−∞, 0]nonnegative
• A169803 → D → θ+1
  1 · 2 · 3, 4 · 4, 12 … Σ 0, 1, 2, 7, 16, 38, 82, 173, …
  (−∞, 0]nonnegative
• A038338 → x ↦ x+1
  576, 576, 144 · 13824, 20736, 10368, 1728 … Σ 1296, 46656, 1679616, 60466176, …
  (−∞, −1]nonnegativerational roots
• A008288 → θ+1
  1 · 1, 2 · 1, 6, 3 · 1, 10, 15, 4 … Σ 1, 3, 10, 30, 87, 245, 676, 1836, …
  (−∞, 0]nonnegative
• basis-map coefficients of A112227 → basis A013610 → basis A013611
  16, 96, 144 · 64, 576, 1728, 1728 … Σ 256, 4096, 65536, 1048576, 16777216, …
  (−∞, 0]nonnegativerational roots
• A129186 → basis A007318
  1 · 1 · 1, 1 · 1, 2, 1 … Σ 1, 1, 2, 4, 8, 16, 32, 64, …
  (−∞, 0]nonnegativerational roots
• A207607 → D
  2 · 5, 4 · 9, 18, 6 · 14, 50, 39, 8 … Σ 0, 2, 9, 33, 111, 355, 1098, 3316, …
  (−∞, 0]nonnegative
• A304236 → basis A013610 → basis A013609
  1 · 1 · 13, 18 · 25, 36 … Σ 1, 1, 31, 61, 991, 2821, 32551, 117181, …
  (−∞, 0]nonnegative
• A013622 → basis A013609 → (θ+1)²
  1 · 8, 40 · 64, 640, 900 · 512, 7680, 21600, 16000 … Σ 1, 48, 1604, 45792, 1193616, 29299968, …
  (−∞, 0]nonnegative
• A038303 → basis A013610 → D
  3 · 66, 18 · 1089, 594, 81 · 15972, 13068, 3564, 324 … Σ 0, 3, 84, 1764, 32928, 576240, 9680832, …
  (−∞, 0]nonnegativerational roots
• A091044 → basis A013611 → basis A013609
  1 · 12, 16 · 128, 320, 192 · 1344, 4864, 5632, 2048 … Σ 1, 28, 640, 13888, 296704, 6307840, …
  (−∞, 0]nonnegative
• A053122 → x ↦ x+1
  1 · -1, 1 · 0, -2, 1 · 1, 1, -3, 1 … Σ 1, 0, -1, 0, 1, 0, -1, 0, …
  (−1, 3)
• A080248 → θ+1
  1 · 1, 2 · 1, 8, 3 · 1, 26, 30, 4 … Σ 1, 3, 12, 61, 385, 2950, 26861, 285687, …
  (−∞, 0]nonnegative
• A321434 → (θ+1)²
  1 · 0, 4 · 0, 4 · 0, 4, 18 … Σ 1, 4, 4, 22, 22, 154, 154, 1306, …
  (−∞, 0]nonnegative
• basis-map coefficients of A026729 → basis A013610 → D
  3 · 6, 18 · 9, 54, 81 · 12, 108, 324, 324 … Σ 0, 3, 24, 144, 768, 3840, 18432, 86016, …
  (−∞, 0]nonnegativerational roots
• basis-map coefficients of A371080, shifted → x ↦ x−1
  1 · -1, 1 · -2, 1, 1 · -10, 3, 6, 1 … Σ 1, 0, 0, 0, 0, 0, 0, 0, …
  (−∞, 1]rational roots
• A013611: Triangle of coefficients in expansion of (1+4x)^n.
  1 · 1, 4 · 1, 8, 16 · 1, 12, 48, 64 … Σ 1, 5, 25, 125, 625, 3125, 15625, 78125, …
  (−∞, 0)[−1, 0]nonnegative+1
• A094816 → x ↦ x+1 → basis A013611
  1 · 3, 4 · 11, 28, 16 · 49, 176, 192, 64 … Σ 1, 7, 55, 481, 4645, 49171, 566827, …
  (−∞, 0]nonnegative
• A038226 → basis A007318
  121, 176, 64 · 1331, 2904, 2112, 512 … Σ 361, 6859, 130321, 2476099, 47045881, …
  (−∞, −1]nonnegativerational roots
• A038291 → θ+1
  1 · 9, 2 · 81, 36, 3 · 729, 486, 81, 4 … Σ 1, 11, 120, 1300, 14000, 150000, …
  (−∞, 0]nonnegativerational roots
• A257615 → D
  5 · 70, 50 · 715, 1430, 375 … Σ 0, 5, 120, 2520, 53760, 1209600, …
  (−∞, 0]nonnegative
• A225470 → basis A013609 → basis A013609
  1 · 5, 4 · 40, 52, 16 · 440, 732, 384, 64 … Σ 1, 9, 108, 1620, 29160, 612360, …
  (−∞, −1]nonnegativerational roots
• A082985 → x ↦ x+1 → x ↦ x/(x+1)
  1 · 4, 7 · 11, 37, 31 · 29, 143, 234, 127 … Σ 1, 11, 79, 533, 3553, 23627, 157039, …
  [−1, 0]nonnegative
• A102365 → x ↦ x+1 → θ+1
  1 · 1 · 2, 2 · 7, 14, 3 … Σ 1, 1, 4, 24, 195, 1995, 24570, 353430, …
  (−∞, 0]nonnegative
• A178820 → basis A013611 → basis A013610
  1 · 24, 48 · 360, 1440, 1440 … Σ 1, 72, 3240, 116640, 3674160, …
  (−∞, 0]nonnegativerational roots
• A013610 → basis A007318 → θ+1
  1 · 4, 6 · 16, 48, 27 · 64, 288, 324, 108 … Σ 1, 10, 91, 784, 6517, 52822, 420175, …
  (−∞, 0]nonnegativerational roots
• A081577 → basis A013611 → D+1
  1 · 6, 4 · 30, 56, 16 · 112, 416, 352, 64 … Σ 1, 10, 102, 944, 8396, 72408, 611080, …
  (−∞, 0]nonnegative