Sequences

• A030528 → (θ+1)²
  1 · 1, 4 · 0, 8, 9 · 0, 4, 27, 16 … Σ 1, 5, 17, 47, 116, 266, 579, 1213, …
  (−∞, 0]nonnegative
• A352880 → reverse → x ↦ x/(x+1)
  8 · 18, 30 · 32, 128, 112 · 50, 350, 700, 420 … Σ 8, 48, 272, 1520, 8472, 47264, 264224, …
  [−1, 0]nonnegative
• A084534 → reverse
  1 · 2, 1 · 2, 4, 1 · 2, 9, 6, 1 … Σ 1, 3, 7, 18, 47, 123, 322, 843, …
  (−∞, 0]nonnegative
• A094262 → D
  2, 2 · 6, 24, 30, 12 · 14, 122, 372, 524, 350, 90 … Σ 0, 4, 72, 1472, 36480, 1078528, …
  (−∞, 0]nonnegative
• A152198 → x ↦ x+1 → (θ+1)²
  1 · 1 · 2, 4 · 2, 4 … Σ 1, 1, 6, 6, 29, 29, 126, 126, …
  (−∞, 0]nonnegative
• A086645 → basis A013609 → x ↦ x/(x+1)
  1 · 2, 4 · 8, 32, 28 · 32, 192, 360, 208 … Σ 1, 6, 68, 792, 9232, 107616, 1254464, …
  [−1, 0]nonnegative
• A132200: Numbers in (4,4)-Pascal triangle .
  1 · 4, 4 · 4, 8, 4 · 4, 12, 12, 4 … Σ 1, 8, 16, 32, 64, 128, 256, 512, …
  (−∞, 0)nonnegativerational roots
• A038338 → basis A013610 → D
  1728, 2592 · 62208, 186624, 139968 … Σ 4320, 388800, 31104000, 2332800000, …
  (−∞, 0]nonnegativerational roots
• basis-map coefficients of A026729 → basis A013610 → (θ+1)²
  1 · 1, 12 · 1, 24, 81 · 1, 36, 243, 432 … Σ 1, 13, 106, 712, 4288, 24064, 128512, …
  (−∞, 0]nonnegative
• A304236 → basis A013610 → D+1
  1 · 1 · 13, 9 · 25, 18 … Σ 1, 1, 22, 43, 424, 1165, 7882, 26191, …
  (−∞, 0]nonnegative
• A130534 → Pₙ + Pₙ₊₁
  2, 1 · 3, 4, 1 · 8, 14, 7, 1 · 30, 61, 41, 11, 1 … Σ 3, 8, 30, 144, 840, 5760, 45360, …
  (−∞, ∞)nonnegativerational roots
• A081577 → basis A013610 → D
  3 · 18, 18 · 72, 180, 81 · 264, 1044, 1134, 324 … Σ 0, 3, 36, 333, 2766, 21591, 162072, …
  (−∞, 0]nonnegative
• A111006 → θ+1
  1 · 0, 2 · 0, 2, 6 · 0, 0, 6, 12 … Σ 1, 2, 8, 18, 48, 110, 260, 586, …
  (−∞, 0]nonnegative
• basis-map coefficients of A030528, shifted → basis A013610 → basis A013610
  1 · -4, -9 · 16, 72, 81 · -64, -432, -972, -729 … Σ 1, -13, 169, -2197, 28561, -371293, …
  (−∞, 0]rational roots
• A103327 → x ↦ x+1 → x ↦ x/(x+1)
  1 · 4, 5 · 16, 44, 29 · 64, 272, 376, 169 … Σ 1, 9, 89, 881, 8721, 86329, 854569, …
  [−1, 0]nonnegative
• A103327 → basis A013610 → D
  3 · 36, 18 · 240, 432, 81 · 1344, 4320, 3240, 324 … Σ 0, 3, 54, 753, 9228, 105183, 1145922, …
  (−∞, 0]nonnegative
• A269944 → basis A013609 → basis A013609
  1 · 3, 4 · 12, 28, 16 · 84, 244, 224, 64 … Σ 1, 7, 56, 616, 9856, 226688, 7254016, …
  (−∞, 0]nonnegativerational roots
• A123519 → reverse → x ↦ x+1
  11, 8, 1 · 41, 47, 15, 1 · 153, 240, 126, 24, 1 … Σ 20, 104, 544, 2848, 14912, 78080, …
  (−∞, −1]nonnegative
• A013612 → x ↦ x+1 → reverse
  25, 60, 36 · 125, 450, 540, 216 … Σ 121, 1331, 14641, 161051, 1771561, …
  (−∞, 0]nonnegativerational roots
• A039756 → D
  1 · 4, 2 · 9, 26, 3 · 16, 116, 120, 4 … Σ 0, 1, 6, 38, 256, 1844, 14296, 119160, …
  (−∞, 0]nonnegative
• A085881 → basis A007318 → D+1
  1 · 3, 1 · 24, 18, 3 · 300, 360, 135, 15 … Σ 1, 4, 45, 810, 19845, 612360, 22733865, …
  (−∞, 0]nonnegativerational roots
• A391045 → reverse
  1 · 1, 1 · 1, 4, 1 · 1, 10, 9, 1 … Σ 1, 2, 6, 21, 80, 322, 1347, 5798, …
  (−∞, 0]nonnegative
• delannoy → basis A013609 → basis A013611
  1 · 4, 8 · 19, 72, 64 · 88, 496, 896, 512 … Σ 1, 12, 155, 1992, 25609, 329220, …
  (−∞, 0]nonnegative
• A135065 → basis A008277
  1 · 8, 4 · 36, 45, 9 · 128, 304, 144, 16 … Σ 1, 12, 90, 592, 3775, 24264, 159887, …
  (−∞, 0]nonnegative
• narayana → basis A013611
  1 · 2, 4 · 5, 20, 16 · 14, 84, 144, 64 … Σ 1, 6, 41, 306, 2426, 20076, 171481, …
  (−∞, 0]nonnegative
• A121314: Triangle T(n,k), 0 <= k <= n, read by rows given by [0, 1, 0, 0, 0, 0, ...] DELTA [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, ...] where DELTA is the operator defi…
  1 · 0, 1 · 0, 1, 1 · 0, 1, 3, 1 … Σ 1, 1, 2, 5, 13, 34, 89, 233, …
  (−∞, 0]nonnegative
• A281000 → reverse
  1 · 1, 3 · 1, 10, 10 · 1, 21, 70, 35 … Σ 1, 4, 21, 127, 835, 5798, 41835, …
  (−∞, 0]nonnegative
• A038326 → x ↦ x+1 → (θ+1)²
  1 · 23, 48 · 529, 2208, 1296 … Σ 1, 71, 4033, 205415, 9791425, …
  (−∞, 0]nonnegative
• A038326 → basis A013609
  1 · 23, 24 · 529, 1104, 576 … Σ 1, 47, 2209, 103823, 4879681, …
  (−∞, 0]nonnegativerational roots
• A142460 → θ+1
  1 · 1, 2 · 1, 24, 3 · 1, 166, 249, 4 … Σ 1, 3, 28, 420, 8568, 219912, 6785856, …
  (−∞, 0]nonnegative
• A038333 → basis A013611
  361, 1064, 784 · 6859, 30324, 44688, 21952 … Σ 2209, 103823, 4879681, 229345007, …
  (−∞, 0]nonnegativerational roots
• A299989 → (θ+1)²
  0, 4 · 0, 12, 36, 16 · 0, 36, 216, 352, 200, 36 … Σ 4, 64, 840, 9920, 109568, 1155072, …
  (−∞, 0]nonnegative
• A232535 → basis A008277
  1 · 3, 2 · 12, 17, 3 · 48, 121, 49, 4 … Σ 1, 5, 32, 222, 1655, 13169, 111169, …
  (−∞, 0]nonnegative
• A078812 → basis A013609 → basis A013610
  1 · 5, 6 · 24, 60, 36 · 115, 438, 540, 216 … Σ 1, 11, 120, 1309, 14279, 155760, …
  (−∞, 0]nonnegative
• A128908 → basis A007318
  1 · 1, 1 · 3, 4, 1 · 8, 14, 7, 1 … Σ 1, 2, 8, 30, 112, 418, 1560, 5822, …
  (−∞, 0]nonnegative
• A126216 → D → D+1
  1 · 7, 2 · 39, 24, 3 · 196, 196, 54, 4 … Σ 0, 1, 9, 66, 450, 2955, 18963, 119812, …
  (−∞, 0]nonnegative
• A156289 → D+1
  1 · 4, 3 · 16, 45, 15 · 64, 483, 525, 105 … Σ 1, 7, 76, 1177, 24451, 650992, …
  (−∞, 0]nonnegative
• A249250 → reverse → x ↦ x+1
  1 · 4, 1 · 10, 8, 1 · 28, 36, 12, 1 … Σ 1, 5, 19, 77, 307, 1229, 4915, 19661, …
  (−∞, −1]nonnegative
• A285061 → x ↦ x+1
  1 · 5, 4 · 41, 56, 16 · 429, 796, 432, 64 … Σ 1, 9, 113, 1721, 30305, 600297, …
  (−∞, −1]nonnegative
• A090582: T(n, k) = Sum_{j=0..n-k} (-1)^j*binomial(n - k + 1, j)*(n - k + 1 - j)^n. Triangle read by rows, T(n, k) for 1 <= k <= n.
  1 · 2, 1 · 6, 6, 1 · 24, 36, 14, 1 … Σ 1, 3, 13, 75, 541, 4683, 47293, 545835, …
  (−∞, −1]nonnegative
• A178821 → basis A007318 → θ+1
  1 · 10, 10 · 60, 120, 45 · 280, 840, 630, 140 … Σ 1, 20, 225, 1890, 13230, 81648, 459270, …
  (−∞, 0]nonnegativerational roots
• A131222 → basis A008277
  1 · 1, 1 · 4, 6, 1 · 24, 48, 15, 1 … Σ 1, 2, 11, 88, 917, 11726, 177247, …
  (−∞, 0]nonnegative
• A099040 → basis A007318 → basis A008277
  1 · 4, 2 · 20, 22, 4 · 96, 192, 80, 8 … Σ 1, 6, 46, 376, 3344, 32120, 331464, …
  (−∞, 0]nonnegative
• A269945 → D
  1 · 1, 2 · 1, 10, 3 · 1, 42, 42, 4 … Σ 0, 1, 3, 14, 89, 737, 7696, 98093, …
  (−∞, 0]nonnegative
• A027466 → basis A013611 → D
  4 · 64, 32 · 768, 768, 192 · 8192, 12288, 6144, 1024 … Σ 0, 4, 96, 1728, 27648, 414720, 5971968, …
  (−∞, 0]nonnegativerational roots
• A139548 → basis A013610 → basis A013609
  1 · 50, 120, 72 · 2500, 12000, 21600, 17280, 5184 … Σ 1, 242, 58564, 14172488, 3429742096, …
  (−∞, 0]nonnegativerational roots
• A136124 → Pₙ + Pₙ₊₁
  3, 1 · 8, 6, 1 · 30, 31, 10, 1 · 144, 180, 80, 15, 1 … Σ 4, 15, 72, 420, 2880, 22680, 201600, …
  (−∞, ∞)nonnegativerational roots
• A130534 → Veronese 2 (j=1) → D
  1 · 10 · 85, 2 · 735, 42 … Σ 0, 0, 0, 1, 10, 87, 777, 7416, …
  (−∞, 0]nonnegative
• A094305 → x ↦ x/(x+1)
  1 · 3, 6 · 6, 24, 24 · 10, 60, 120, 80 … Σ 1, 9, 54, 270, 1215, 5103, 20412, …
  [−1, 0]nonnegativerational roots
• A114687 → basis A013610
  1 · 3, 6 · 11, 42, 36 · 45, 252, 432, 216 … Σ 1, 9, 89, 945, 10577, 123129, 1476841, …
  (−∞, 0]nonnegative