Sequences

• A038271 → basis A013611 → θ+1
  1 · 12, 40 · 144, 960, 1200 … Σ 1, 52, 2304, 94208, 3670016, 138412032, …
  (−∞, 0]nonnegativerational roots
• A123519 → (θ+1)²
  1, 24, 36 · 1, 48, 180, 128 · 1, 80, 540, 896, 400 … Σ 61, 357, 1917, 9717, 47249, 222633, …
  (−∞, 0]nonnegative
• A103633: Triangle read by rows: triangle of repeated stepped binomial coefficients.
  1 · 0, 1 · 0, 1, 1 · 0, 0, 1, 1 … Σ 1, 1, 2, 2, 4, 4, 8, 8, …
  (−∞, 0]nonnegativerational roots
• A027465 → D → basis A013611
  1 · 8, 8 · 48, 96, 48 · 256, 768, 768, 256 … Σ 0, 1, 16, 192, 2048, 20480, 196608, …
  (−∞, 0]nonnegativerational roots
• A132440 → θ+1 → basis A013609
  1 · 4, 8 · 9, 36, 36 · 16, 96, 192, 128 … Σ 0, 1, 12, 81, 432, 2025, 8748, 35721, …
  (−∞, 0]nonnegativerational roots
• A257617 → D+1
  1 · 4, 2 · 40, 44, 4 · 396, 1164, 412, 8 … Σ 1, 6, 88, 1980, 59400, 2217600, …
  (−∞, 0]nonnegative
• A269939 → (θ+1)²
  1 · 0, 4 · 0, 4, 27 · 0, 4, 90, 240 … Σ 1, 4, 31, 334, 4534, 73868, 1401068, …
  (−∞, 0]nonnegative
• A152198 → basis A013610 → D
  3 · 3 · 12, 18 · 12, 18 … Σ 0, 0, 3, 3, 30, 30, 225, 225, …
  (−∞, 0]nonnegativerational roots
• A113214 → θ+1 → reverse
  1 · 2, 2 · 3, 6 · 4, 12, 4 … Σ 1, 4, 9, 20, 40, 78, 147, 272, …
  (−∞, 0]nonnegative
• A207824 → basis A008277
  1 · 6, 1 · 35, 13, 1 · 204, 125, 21, 1 … Σ 1, 7, 49, 351, 2578, 19439, 150631, …
  (−∞, 0]nonnegative
• A172431 → basis A013610 → basis A008277
  1 · 9, 6 · 65, 111, 27 · 441, 1464, 846, 108 … Σ 1, 15, 203, 2859, 43090, 697428, …
  (−∞, 0]nonnegative
• A267482 → x ↦ x+1
  1 · 2, 1 · 1, 3, 1 · -1, 3, 4, 1 … Σ 1, 3, 5, 7, 9, 11, 13, 15, …
  (−3, 1)
• A124848 → basis A013610
  1 · 5, 12 · 19, 84, 90 · 63, 396, 810, 540 … Σ 1, 17, 193, 1809, 15105, 116625, …
  (−∞, 0]nonnegative
• A008288 → basis A013609 → x ↦ x/(x+1)
  1 · 2, 4 · 5, 20, 19 · 12, 72, 140, 88 … Σ 1, 6, 44, 312, 2224, 15840, 112832, …
  [−1, 0]nonnegative
• A144699: Triangle of 5-Eulerian numbers.
  1 · 1, 5 · 1, 16, 25 · 1, 39, 171, 125 … Σ 1, 6, 42, 336, 3024, 30240, 332640, …
  (−∞, 0)nonnegative
• A085881 → basis A013610
  1 · 2, 3 · 12, 36, 27 · 120, 540, 810, 405 … Σ 1, 5, 75, 1875, 65625, 2953125, …
  [−1, 0]nonnegativerational roots
• delannoy → θ+1
  1 · 1, 2 · 1, 6, 3 · 1, 10, 15, 4 … Σ 1, 3, 10, 30, 87, 245, 676, 1836, …
  (−∞, 0]nonnegative
• A038331 → basis A013611 → D+1
  969, 1480, 400 · 22253, 58140, 44400, 8000 … Σ 2849, 132793, 5926401, 256760057, …
  (−∞, 0]nonnegativerational roots
• A028246 → D
  1 · 3, 4 · 7, 24, 18 · 15, 100, 180, 96 … Σ 0, 1, 7, 49, 391, 3601, 37927, 451249, …
  (−∞, 0]nonnegative
• A052553 → basis A013609 → D+1
  1 · 1 · 4, 2 · 7, 4 … Σ 1, 1, 6, 11, 37, 84, 233, 565, …
  (−∞, 0]nonnegative
• A280580: Triangle read by rows: T(n,k) = binomial(2*n,2*k)*binomial(2*n-2*k,n-k)/(n+1-k) for 0<=k<=n.
  1 · 1, 1 · 2, 6, 1 · 5, 30, 15, 1 … Σ 1, 2, 9, 51, 323, 2188, 15511, 113634, …
  (−∞, 0)nonnegative
• A091044 → basis A013611 → D+1
  1 · 12, 8 · 80, 160, 48 · 448, 1664, 1408, 256 … Σ 1, 20, 288, 3776, 47360, 577536, …
  (−∞, 0]nonnegative
• A286718 → basis A013609 → (θ+1)²
  1 · 2, 8 · 10, 56, 36 · 80, 528, 540, 128 … Σ 1, 10, 102, 1276, 19372, 348384, …
  (−∞, 0]nonnegative
• A257617 → D
  2 · 36, 8 · 388, 776, 24 · 3676, 24832, 11028, 64 … Σ 0, 2, 44, 1188, 39600, 1584000, …
  (−∞, 0]nonnegative
• A081580 → basis A013611 → θ+1
  1 · 2, 8 · 9, 72, 48 · 28, 336, 768, 256 … Σ 1, 10, 129, 1388, 14837, 152526, …
  (−∞, 0]nonnegative
• A109692 → x ↦ x/(x+1)
  1 · 1, 2 · 1, 6, 8 · 1, 12, 44, 48 … Σ 1, 3, 15, 105, 945, 10395, 135135, …
  [−1, 0]nonnegativerational roots
• A054142 → Veronese 2 → D
  1 · 6 · 15, 2 · 28, 30 … Σ 0, 0, 1, 6, 17, 58, 188, 570, …
  (−∞, 0]nonnegative
• A134309 → D
  1 · 0, 4 · 0, 0, 12 · 0, 0, 0, 32 … Σ 0, 1, 4, 12, 32, 80, 192, 448, …
  (−∞, 0]nonnegativerational roots
• A153518 → basis A013610
  2 · 10, 15 · 50, 150, 18 · 250, 1125, 1161, 54 … Σ 2, 25, 218, 2590, 17310, 138350, …
  (−∞, 0]nonnegative
• A199478 → D
  1 · 3 · 5, 4 · 7, 16 … Σ 1, 3, 9, 23, 57, 135, 313, 711, …
  (−∞, 0]nonnegative
• type_b_eulerian → θ+1
  1 · 1, 2 · 1, 12, 3 · 1, 46, 69, 4 … Σ 1, 3, 16, 120, 1152, 13440, 184320, …
  (−∞, 0]nonnegative
• A225476 → D+1
  1 · 2, 1 · 5, 8, 2 · 14, 49, 36, 6 … Σ 1, 3, 15, 105, 933, 10023, 126195, …
  (−∞, 0]nonnegative
• A063967 → θ+1
  1 · 1, 2 · 2, 6, 3 · 3, 14, 15, 4 … Σ 1, 3, 11, 36, 116, 364, 1124, 3424, …
  (−∞, 0]nonnegative
• A178822 → basis A013609 → D+1
  1 · 24, 12 · 252, 336, 84 · 1792, 4032, 2688, 448 … Σ 1, 36, 672, 8960, 96768, 903168, …
  (−∞, 0]nonnegativerational roots
• A038207 → Pₙ + Pₙ₊₁
  3, 1 · 6, 5, 1 · 12, 16, 7, 1 · 24, 44, 30, 9, 1 … Σ 4, 12, 36, 108, 324, 972, 2916, 8748, …
  (−∞, ∞)nonnegativerational roots
• A125092 → reverse → x ↦ x+1
  1 · 5, 1 · 18, 10, 1 · 56, 54, 15, 1 … Σ 1, 6, 29, 126, 513, 1998, 7533, 27702, …
  (−∞, −1]nonnegative
• A178821 → basis A013611 → θ+1
  1 · 10, 40 · 60, 480, 720 · 280, 3360, 10080, 8960 … Σ 1, 50, 1260, 22680, 332640, 4245696, …
  (−∞, 0]nonnegativerational roots
• A038305 → basis A013609 → D
  156, 72 · 3042, 2808, 648 · 52728, 73008, 33696, 5184 … Σ 228, 6498, 164616, 3909630, 89139564, …
  (−∞, 0]nonnegativerational roots
• A249248 → x ↦ x/(x+1)
  1 · 1, 4 · 1, 9, 11 · 1, 15, 49, 38 … Σ 1, 5, 21, 103, 519, 2793, 15645, 91623, …
  [−1, 0]nonnegative
• A027467 → basis A013609 → x ↦ x/(x+1)
  1 · 16, 18 · 256, 576, 324 · 4096, 13824, 15552, 5832 … Σ 1, 34, 1156, 39304, 1336336, 45435424, …
  [−1, 0]nonnegativerational roots
• A131431 → (θ+1)² → reverse
  1 · 16 · 63 · 160 … Σ 1, 16, 63, 160, 325, 576, 931, 1408, …
  (−∞, 0]nonnegativerational roots
• A113214 → basis A008277
  1 · 3, 1 · 4, 6, 1 · 7, 21, 10, 1 … Σ 1, 4, 11, 39, 152, 660, 3131, 16078, …
  (−∞, 0]nonnegative
• basis-map coefficients of A021012 → basis A008277 → x ↦ x/(x+1)
  1 · -1, -2 · 2, 10, 10 · -6, -60, -138, -90 … Σ 1, -3, 22, -294, 6168, -184680, …
  [−1, 0]
• A038279: Triangle whose (i,j)-th entry is binomial(i,j)*8^(i-j)*1^j.
  1 · 8, 1 · 64, 16, 1 · 512, 192, 24, 1 … Σ 1, 9, 81, 729, 6561, 59049, 531441, …
  (−∞, −1]nonnegativerational roots
• A124038 → x ↦ x+1
  1 · -1, 1 · -2, 0, 1 · -1, -3, 1, 1 … Σ 1, 0, -1, -2, -3, -4, -5, -6, …
  (−3, 2)
• A049029 → Pₙ + Pₙ₊₁
  6, 1 · 50, 16, 1 · 630, 270, 31, 1 … Σ 7, 67, 932, 16867, 374887, 9868532, …
  (−∞, ∞)nonnegative
• A074246 → x ↦ x+1
  1 · 5, 2 · 26, 18, 3 · 154, 142, 42, 4 … Σ 1, 7, 47, 342, 2754, 24552, 241128, …
  (−∞, −1]nonnegative
• A038208 → Veronese 2 (j=1) → D+1
  2 · 8 · 32, 8 · 128, 64 … Σ 0, 2, 8, 40, 192, 896, 4096, 18432, …
  (−∞, 0]nonnegative
• A001263 → basis A013611 → θ+1
  1 · 2, 8 · 5, 40, 48 · 14, 168, 432, 256 … Σ 1, 10, 93, 870, 8266, 79636, 775765, …
  (−∞, 0]nonnegative
• A143494 → x ↦ x+1
  1 · 3, 1 · 10, 7, 1 · 37, 40, 12, 1 … Σ 1, 4, 18, 90, 494, 2946, 18926, 130066, …
  (−∞, −1]nonnegative