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8,704 sequences

• A116412 → basis A013609 → x ↦ x/(x+1)
  1 · 4, 6 · 13, 42, 33 · 43, 213, 345, 183 … Σ 1, 10, 88, 784, 6976, 62080, 552448, …
  [−1, 0]nonnegative
• A145324 → basis A013611 → θ+1
  1 · 3, 16 · 12, 136, 288 · 60, 1064, 4704, 6144 … Σ 1, 19, 436, 11972, 385192, 14247256, …
  (−∞, 0]nonnegative
• A143491 → basis A013609 → x ↦ x/(x+1)
  12, 38, 30 · 60, 274, 416, 210 … Σ 80, 960, 13440, 215040, 3870720, …
  [−1, 0]nonnegativerational roots
• A088996 → basis A013609 → D+1
  1 · 3, 2 · 13, 26, 8 · 83, 268, 244, 48 … Σ 1, 5, 47, 643, 11493, 253017, 6609411, …
  (−∞, 0]nonnegative
• A082985 → x ↦ x+1 → D
  3 · 15, 10 · 56, 70, 21 · 189, 342, 198, 36 … Σ 0, 3, 25, 147, 765, 3751, 17745, 81915, …
  (−∞, 0]nonnegative
• A207606 → basis A013610 → D
  33, 36 · 132, 306, 162 · 465, 1674, 1863, 648 … Σ 69, 600, 4650, 33822, 236295, 1605504, …
  (−∞, 0]nonnegative
• A078812 → Veronese 2 (j=1) → x ↦ x+1
  1 · 4 · 11, 1 · 28, 8 … Σ 0, 1, 4, 12, 36, 111, 344, 1064, …
  (−∞, −1]nonnegative
• A116414 → reverse
  1 · 1, 4 · 1, 8, 13 · 1, 12, 42, 40 … Σ 1, 5, 22, 95, 409, 1760, 7573, 32585, …
  (−∞, 0]nonnegative
• A391533 → basis A013609 → x ↦ x/(x+1)
  9, 30, 25 · 18, 96, 170, 100 · 36, 264, 724, 880, 400 … Σ 64, 384, 2304, 13824, 82944, 497664, …
  [−1, 0]nonnegativerational roots
• A008517 → D
  2 · 8, 12 · 22, 116, 72 · 52, 656, 1332, 480 … Σ 0, 2, 20, 210, 2520, 34650, 540540, …
  (−∞, 0]nonnegative
• A152198 → basis A013609 → θ+1
  1 · 1 · 2, 4 · 2, 4 … Σ 1, 1, 6, 6, 32, 32, 160, 160, …
  (−∞, 0]nonnegativerational roots
• A136572 → D+1
  1 · 1, 1 · 0, 4, 2 · 0, 0, 18, 6 … Σ 1, 2, 6, 24, 120, 720, 5040, 40320, …
  (−∞, 0]nonnegativerational roots
• A105070 → D
  2 · 8 · 20, 8 · 40, 48 … Σ 0, 0, 2, 8, 28, 88, 262, 752, …
  (−∞, 0]nonnegative
• A122431 → D+1
  4, 9, 6, 1 · 1, 7, 12, 7, 1 · 0, 2, 10, 15, 8, 1 … Σ 20, 28, 36, 44, 52, 60, 68, 76, …
  (−∞, 0]nonnegative
• A111125 → basis A007318 → reverse
  1 · 1, 4 · 1, 7, 11 · 1, 10, 31, 29 … Σ 1, 5, 19, 71, 265, 989, 3691, 13775, …
  (−1, 0]nonnegative
• A166344 → x ↦ x/(x+1)
  1, 8, 8 · 1, 18, 48, 32 · 1, 38, 198, 320, 160 … Σ 17, 99, 717, 6219, 62877, 726219, …
  [−1, 0]nonnegative
• A099097 → x ↦ x−4
  1 · -12, 3 · 140, -71, 9 · -1632, 1248, -318, 27 … Σ 1, -9, 78, -675, 5841, -50544, 437373, …
  (32/9, 4]
• A330510 → x ↦ x+1
  2 · 6, 3 · 18, 18, 4 · 54, 81, 37, 5 … Σ 2, 9, 40, 177, 782, 3453, 15244, 67293, …
  (−∞, −1]nonnegative
• basis-map coefficients of A112227 → D+1
  0, 2, 1 · 0, 0, 3, 1 · 0, 0, 0, 4, 1 … Σ 3, 4, 5, 6, 7, 8, 9, 10, …
  (−∞, 0]nonnegativerational roots
• A099093 → basis A013609 → x ↦ x/(x+1)
  1 · 3, 9 · 12, 66, 90 · 45, 369, 999, 891 … Σ 1, 12, 168, 2304, 31680, 435456, …
  [−1, 0]nonnegative
• A225469 → D+1
  1 · 4, 1 · 19, 12, 1 · 106, 121, 24, 1 … Σ 1, 5, 32, 252, 2320, 24176, 280192, …
  (−∞, 0]nonnegative
• basis-map coefficients of A030528, shifted → basis A013609
  1 · -1, -2 · 1, 4, 4 · -1, -6, -12, -8 … Σ 1, -3, 9, -27, 81, -243, 729, -2187, …
  (−∞, 0]rational roots
• A038271 → basis A013611 → (θ+1)²
  1 · 12, 80 · 144, 1920, 3600 … Σ 1, 92, 5664, 293888, 13828096, …
  (−∞, 0]nonnegative
• A085881 → basis A013609 → D
  2 · 24, 24 · 360, 720, 360 · 6720, 20160, 20160, 6720 … Σ 0, 2, 48, 1440, 53760, 2419200, …
  (−∞, 0]nonnegativerational roots
• A094816 → basis A013611 → θ+1
  1 · 2, 8 · 5, 40, 48 · 16, 184, 432, 256 … Σ 1, 10, 93, 888, 8977, 97102, 1127021, …
  (−∞, 0]nonnegative
• image under θ+1 → θ+1 → D → D
  18 · 0, 96 · 0, 0, 300 · 0, 0, 0, 720 … Σ 0, 0, 18, 96, 300, 720, 1470, 2688, …
  (−∞, 0]nonnegativerational roots
• A013609 → D → (θ+1)²
  2 · 4, 32 · 6, 96, 216 · 8, 192, 864, 1024 … Σ 0, 2, 36, 318, 2088, 11610, 57996, …
  (−∞, 0]nonnegative
• A367270 → basis A013610 → θ+1
  1 · 1 · 3, 12 · 10, 72, 81 … Σ 1, 1, 15, 163, 1637, 15981, 153795, …
  (−∞, 0]nonnegative
• basis-map coefficients of A030528, 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
• A082985: Coefficient table for Chebyshev's U(2*n,x) polynomial expanded in decreasing powers of (-4*(1-x^2)).
  1 · 1, 3 · 1, 5, 5 · 1, 7, 14, 7 … Σ 1, 4, 11, 29, 76, 199, 521, 1364, …
  (−∞, 0)nonnegative
• A122848 → basis A013610 → D+1
  1 · 4, 3 · 11, 27, 9 · 31, 135, 135, 27 … Σ 1, 7, 47, 328, 2392, 18224, 144688, …
  (−∞, 0]nonnegative
• A227450 → D+1
  2 · 6, 4 · 14, 28, 8 · 30, 124, 96, 16 … Σ 2, 10, 50, 266, 1522, 9354, 61490, …
  (−∞, 0]nonnegative
• A038330 → basis A013610 → reverse
  144, 384, 256 · 1728, 6912, 9216, 4096 … Σ 784, 21952, 614656, 17210368, …
  (−∞, 0]nonnegativerational roots
• A122542 → basis A013611 → x ↦ x/(x+1)
  1 · 1, 5 · 3, 22, 35 · 7, 73, 237, 235 … Σ 1, 6, 60, 552, 5136, 47712, 443328, …
  [−1, 0]nonnegative
• A008292 → x ↦ x+1 → θ+1
  1 · 2, 2 · 6, 12, 3 · 24, 72, 42, 4 … Σ 1, 4, 21, 142, 1175, 11476, 129073, …
  (−∞, 0]nonnegative
• A013622 → basis A013611 → reverse
  1 · 20, 8 · 400, 320, 64 · 8000, 9600, 3840, 512 … Σ 1, 28, 784, 21952, 614656, 17210368, …
  (−∞, 0]nonnegativerational roots
• A266213 → θ+1
  1 · 1 · 1, 4 · 1, 8, 6 … Σ 1, 1, 5, 15, 45, 129, 361, 991, …
  (−∞, 0]nonnegative
• A038221 → basis A013611 → (θ+1)²
  1 · 6, 48 · 36, 576, 1296 · 216, 5184, 23328, 27648 … Σ 1, 54, 1908, 56376, 1504656, 37581408, …
  (−∞, 0]nonnegative
• A116414 → basis A007318 → x ↦ x/(x+1)
  1 · 5, 6 · 22, 54, 33 · 95, 354, 438, 180 … Σ 1, 11, 109, 1067, 10429, 101915, …
  [−1, −1/2)nonnegative
• A038284 → basis A007318 → reverse
  36, 168, 196 · 216, 1512, 3528, 2744 … Σ 400, 8000, 160000, 3200000, 64000000, …
  (−∞, 0]nonnegativerational roots
• A081580 → basis A007318 → θ+1
  1 · 2, 2 · 9, 18, 3 · 28, 84, 48, 4 … Σ 1, 4, 30, 164, 974, 5448, 30562, …
  (−∞, 0]nonnegative
• A121574 → basis A013611 → D+1
  1 · 7, 4 · 38, 60, 16 · 173, 492, 368, 64 … Σ 1, 11, 114, 1097, 10117, 90600, 794197, …
  (−∞, 0]nonnegative
• A038327 → basis A013611 → D
  4 · 104, 32 · 2028, 1248, 192 … Σ 0, 4, 136, 3468, 78608, 1670420, …
  (−∞, 0]nonnegativerational roots
• basis-map coefficients of A026729, shifted → basis A007318
  1 · -1, -1 · 1, 2, 1 · -1, -3, -3, -1 … Σ 1, -2, 4, -8, 16, -32, 64, -128, …
  (−∞, −1]rational roots
• A081577 → basis A013609 → D
  2 · 12, 8 · 48, 80, 24 · 176, 464, 336, 64 … Σ 0, 2, 20, 152, 1040, 6680, 41264, …
  (−∞, 0]nonnegative
• A062196 → reverse → (θ+1)²
  1 · 3, 4 · 6, 32, 9 · 10, 120, 135, 16 … Σ 1, 7, 47, 281, 1554, 8142, 41019, …
  (−∞, 0]nonnegative
• A075497 → θ+1 → x ↦ x/(x+1)
  1 · 2, 4 · 4, 20, 19 · 8, 80, 172, 104 … Σ 1, 6, 43, 364, 3541, 38642, 465599, …
  [−1, 0]nonnegative
• A038329 → basis A013611 → x ↦ x/(x+1)
  225, 810, 729 · 3375, 18225, 32805, 19683 … Σ 1764, 74088, 3111696, 130691232, …
  [−1, 0]nonnegativerational roots
• A249252 → reverse
  1 · 4, 1 · 8, 8, 1 · 16, 32, 12, 1 … Σ 1, 5, 17, 61, 217, 773, 2753, 9805, …
  (−∞, 0]nonnegative
• A225470 → basis A008277 → reverse
  1 · 1, 3 · 1, 10, 18 · 1, 21, 118, 162 … Σ 1, 4, 29, 302, 4089, 68056, 1342949, …
  (−∞, 0]nonnegative