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8,704 sequences

• basis-map coefficients of A112227 → x ↦ x+1 → (θ+1)²
  1, 8, 9 · 1, 12, 27, 16 · 1, 16, 54, 64, 25 … Σ 18, 56, 160, 432, 1120, 2816, 6912, …
  (−∞, 0]nonnegative
• A347823 → reverse → x ↦ x/(x+1)
  1 · 3, 5 · 5, 18, 16 · 7, 39, 72, 44 … Σ 1, 8, 39, 162, 621, 2268, 8019, 27702, …
  [−1, 0]nonnegativerational roots
• A069466 → γ → basis A007318
  1 · 2 · 18, 12 · 140, 120 … Σ 1, 2, 30, 260, 3430, 40572, 536844, …
  (−∞, −1]nonnegative
• A099040 → basis A013611 → reverse
  1 · 8, 2 · 64, 40, 6 · 512, 512, 160, 16 … Σ 1, 10, 110, 1200, 13100, 143000, …
  (−∞, 0]nonnegative
• A116666 → reverse
  1 · 3, 1 · 5, 6, 1 · 7, 15, 9, 1 … Σ 1, 4, 12, 32, 80, 192, 448, 1024, …
  (−∞, 0]nonnegativerational roots
• A038338 → basis A013611
  576, 2304, 2304 · 13824, 82944, 165888, 110592 … Σ 5184, 373248, 26873856, 1934917632, …
  [−1, 0]nonnegativerational roots
• A027467 → x ↦ x+1
  1 · 16, 1 · 256, 32, 1 · 4096, 768, 48, 1 … Σ 1, 17, 289, 4913, 83521, 1419857, …
  (−∞, −1]nonnegativerational roots
• A196347 → basis A013610
  1 · 2, 3 · 8, 24, 18 · 48, 216, 324, 162 … Σ 1, 5, 50, 750, 15000, 375000, 11250000, …
  [−1, 0]nonnegativerational roots
• A142462 → D
  1 · 16, 2 · 143, 286, 3 · 1166, 8580, 3498, 4 … Σ 0, 1, 18, 432, 13248, 496800, 22057920, …
  (−∞, 0]nonnegative
• A267482 → D+1
  1 · 2, 1 · 0, 3, 1 · -3, 0, 4, 1 … Σ 1, 3, 4, 2, -3, -7, -5, 3, …
  (−∞, ∞)
• A108838 → D → (θ+1)²
  2 · 8, 16 · 20, 120, 54 · 40, 480, 648, 128 … Σ 0, 2, 24, 194, 1296, 7740, 42944, …
  (−∞, 0]nonnegative
• A290595 → x ↦ x+1
  1 · 3, 2 · 27, 27, 4 · 405, 540, 171, 8 … Σ 1, 5, 58, 1124, 30532, 1066640, …
  (−∞, −1]nonnegative
• basis-map coefficients of A030528, shifted → θ+1
  1 · 0, -2 · 0, 0, 3 · 0, 0, 0, -4 … Σ 1, -2, 3, -4, 5, -6, 7, -8, …
  [−1, 0]rational roots
• A137320 → basis A013610 → D+1
  1 · 8, 6 · 36, 102, 36 · 180, 804, 972, 216 … Σ 1, 14, 174, 2172, 28212, 386064, …
  (−∞, 0]nonnegative
• A008957: Triangle of central factorial numbers T(2*n,2*n-2*k), k >= 0, n >= 1 (in Riordan's notation).
  1 · 1, 1 · 1, 5, 1 · 1, 14, 21, 1 … Σ 1, 2, 7, 37, 264, 2433, 27913, 386906, …
  (−∞, 0]nonnegative
• A163936 → x ↦ x+1
  1 · 1 · 3, 1 · 15, 10, 1 … Σ 1, 1, 4, 26, 236, 2752, 39208, 660032, …
  (−∞, −1]nonnegative
• A232535 → basis A007318 → D+1
  1 · 5, 2 · 26, 20, 3 · 128, 154, 49, 4 … Σ 1, 7, 49, 335, 2241, 14743, 95729, …
  (−∞, 0]nonnegative
• A142963 → x ↦ x+1
  1 · 3, 2 · 15, 18, 4 · 111, 198, 96, 8 … Σ 1, 5, 37, 413, 6181, 113645, 2469397, …
  (−∞, −1]nonnegative
• A207607 → basis A007318
  1 · 3, 2 · 8, 9, 2 · 21, 33, 15, 2 … Σ 1, 5, 19, 71, 265, 989, 3691, 13775, …
  (−5, −1)nonnegative
• A147716 → (θ+1)²
  1 · 14, 4 · 196, 112, 9 · 2744, 2352, 378, 16 … Σ 1, 18, 317, 5490, 93825, 1586250, …
  (−∞, 0]nonnegative
• A008278 → (θ+1)²
  1 · 1, 4 · 1, 12, 9 · 1, 24, 63, 16 … Σ 1, 5, 22, 104, 531, 2897, 16787, …
  (−∞, 0]nonnegative
• A105070 → D+1
  1 · 2 · 5, 2 · 12, 8 … Σ 1, 2, 7, 20, 57, 158, 431, 1160, …
  (−∞, 0]nonnegative
• A008277 → θ+2 (shift +1) → D
  3 · 9, 8 · 21, 48, 15 · 45, 200, 150, 24 … Σ 0, 3, 17, 84, 419, 2183, 11990, 69541, …
  (−∞, 0]nonnegative
• A132393 → basis A013610 → x ↦ x/(x+1)
  1 · 1, 4 · 2, 13, 20 · 6, 51, 138, 120 … Σ 1, 5, 35, 315, 3465, 45045, 675675, …
  [−1, 0]nonnegativerational roots
• A113413 → basis A013611 → reverse
  1 · 4, 3 · 16, 24, 7 · 64, 144, 92, 17 … Σ 1, 7, 47, 317, 2137, 14407, 97127, …
  (−∞, 0]nonnegative
• A136572 → (θ+1)² → (θ+1)²
  1 · 0, 16 · 0, 0, 162 · 0, 0, 0, 1536 … Σ 1, 16, 162, 1536, 15000, 155520, …
  (−∞, 0]nonnegativerational roots
• A367270 → x ↦ x+1
  1 · 1 · 3, 2 · 10, 12, 3 … Σ 1, 1, 5, 25, 129, 681, 3653, 19825, …
  (−∞, −1]nonnegative
• A253284 → D
  2 · 18, 24 · 144, 480, 360 · 1200, 7200, 12600, 6720 … Σ 0, 2, 42, 984, 27720, 928080, 36202320, …
  (−∞, 0]nonnegative
• A207824: Triangle of coefficients of Chebyshev's S(n,x+5) polynomials (exponents of x in increasing order).
  1 · 5, 1 · 24, 10, 1 · 115, 73, 15, 1 … Σ 1, 6, 35, 204, 1189, 6930, 40391, …
  (−7, −3)nonnegative
• A081579 → basis A013609 → basis A007318
  1 · 4, 2 · 28, 24, 4 · 160, 208, 80, 8 … Σ 1, 6, 56, 456, 3856, 32256, 270656, …
  (−∞, −1]nonnegative
• A052553 → basis A013610 → D
  3 · 6 · 15, 18 · 30, 54 … Σ 0, 0, 3, 6, 33, 84, 303, 834, …
  (−∞, 0]nonnegative
• A008292 → D → x ↦ x+1
  1 · 6, 2 · 36, 28, 3 · 240, 300, 90, 4 … Σ 0, 1, 8, 67, 634, 6793, 81780, 1095967, …
  (−∞, −1]nonnegative
• A013620 → basis A013610 → (θ+1)²
  1 · 5, 36 · 25, 360, 729 · 125, 2700, 10935, 11664 … Σ 1, 41, 1114, 25424, 525280, 10169264, …
  (−∞, 0]nonnegative
• A327997 → x ↦ x+1 → D
  1 · 9, 2 · 65, 30, 3 · 452, 322, 66, 4 … Σ 0, 1, 11, 98, 844, 7449, 69183, 685026, …
  (−∞, 0]nonnegative
• A207607 → basis A013609 → reverse
  1 · 4, 3 · 8, 18, 8 · 16, 60, 66, 21 … Σ 1, 7, 34, 163, 781, 3742, 17929, 85903, …
  (−∞, 0]nonnegative
• A001263: Triangle of Narayana numbers T(n,k) = C(n-1,k-1)*C(n,k-1)/k with 1 <= k <= n, read by rows. Also called the Catalan triangle.
  1 · 1, 1 · 1, 3, 1 · 1, 6, 6, 1 … Σ 1, 2, 5, 14, 42, 132, 429, 1430, …
  (−∞, 0)nonnegative
• A038255 → θ+1
  1 · 6, 2 · 36, 24, 3 · 216, 216, 54, 4 … Σ 1, 8, 63, 490, 3773, 28812, 218491, …
  (−∞, 0]nonnegativerational roots
• A038220 → Veronese 2 (j=1) → θ+1
  2 · 12 · 54, 16 · 216, 192 … Σ 0, 2, 12, 70, 408, 2346, 13284, 74222, …
  (−∞, 0]nonnegative
• A103327: Triangle read by rows: T(n,k) = binomial(2n+1, 2k+1).
  1 · 3, 1 · 5, 10, 1 · 7, 35, 21, 1 … Σ 1, 4, 16, 64, 256, 1024, 4096, 16384, …
  (−∞, 0)nonnegative
• A122542 → basis A013610 → reverse
  1 · 3, 1 · 9, 12, 3 · 27, 63, 39, 7 … Σ 1, 4, 24, 136, 776, 4424, 25224, …
  (−∞, 0]nonnegative
• A107131 → D+1
  1 · 1, 1 · 1, 3, 1 · 0, 6, 6, 1 … Σ 1, 2, 5, 13, 35, 96, 267, 750, …
  (−∞, 0]nonnegative
• A094638 → D+1 → θ+1
  1 · 2, 2 · 4, 14, 6 · 7, 56, 87, 24 … Σ 1, 4, 24, 174, 1430, 13040, 130592, …
  (−∞, 0]nonnegative
• A007318 → −D²+(−1+n)D+1+n → x ↦ x+1 → reverse
  1 · 2, 4 · 3, 14, 14 · 4, 30, 66, 44 … Σ 1, 6, 31, 144, 621, 2538, 9963, 37908, …
  (−∞, 0]nonnegative
• A103633 → basis A007318 → D
  1 · 3, 2 · 5, 8, 3 · 12, 26, 18, 4 … Σ 0, 1, 5, 16, 60, 156, 540, 1296, …
  (−∞, 0]nonnegativerational roots
• A130534 → basis A008277 → D
  1 · 6, 2 · 36, 24, 3 · 240, 240, 60, 4 … Σ 0, 1, 8, 63, 544, 5225, 55656, 653023, …
  (−∞, 0]nonnegative
• A026729 → θ+1 → D
  2 · 2, 6 · 0, 12, 12 · 0, 6, 36, 20 … Σ 0, 2, 8, 24, 62, 146, 324, 688, …
  (−∞, 0]nonnegative
• A106246 → D+1 → (θ+1)²
  1 · 3, 4 · 5, 24, 9 · 3, 60, 81, 16 … Σ 1, 7, 38, 160, 535, 1481, 3532, 7498, …
  (−∞, 0]nonnegative
• A144084 → D+1
  1 · 2, 1 · 5, 8, 2 · 10, 45, 36, 6 … Σ 1, 3, 15, 97, 753, 6771, 68983, 783945, …
  (−∞, 0]nonnegative
• A075498 → x ↦ x+1
  1 · 4, 1 · 19, 11, 1 · 109, 102, 21, 1 … Σ 1, 5, 31, 233, 2047, 20417, 226711, …
  (−∞, −1]nonnegative
• A136572 → D → (θ+1)²
  1 · 0, 16 · 0, 0, 162 · 0, 0, 0, 1536 … Σ 0, 1, 16, 162, 1536, 15000, 155520, …
  (−∞, 0]nonnegativerational roots