Sequences

• A133080 → D
  1 · 0, 2 · 0, 2, 3 · 0, 0, 0, 4 … Σ 0, 1, 2, 5, 4, 9, 6, 13, …
  (−∞, 0]nonnegativerational roots
• A358735 → basis A013609
  1 · 2, 2 · 7, 16, 8 · 33, 120, 136, 48 … Σ 1, 4, 31, 337, 4687, 79342, 1582153, …
  (−∞, 0]nonnegative
• A344565 → θ+1
  3 · 15, 30 · 45, 180, 135 · 105, 630, 945, 420 … Σ 3, 45, 360, 2100, 10080, 42336, 161280, …
  (−∞, 0]nonnegativerational roots
• A160562: Triangle of scaled central factorial numbers, T(n,k) = A008958(n,n-k).
  1 · 1, 1 · 1, 10, 1 · 1, 91, 35, 1 … Σ 1, 2, 12, 128, 1872, 37600, 990784, …
  (−∞, 0]nonnegative
• A196347 → γ
  1 · 1 · 2 · 6 … Σ 1, 1, 2, 6, 24, 120, 720, 5040, …
  (−∞, 0]nonnegativerational roots
• A007318 → ×(−(1/2)n+(1/2)n²) → x ↦ x+1
  4, 4, 1 · 24, 36, 18, 3 · 96, 192, 144, 48, 6 … Σ 0, 0, 9, 81, 486, 2430, 10935, 45927, …
  (−∞, −1]nonnegativerational roots
• A134082: Triangle read by rows, (n-1) zeros followed by (2n, 1).
  1 · 2, 1 · 0, 4, 1 · 0, 0, 6, 1 … Σ 1, 3, 5, 7, 9, 11, 13, 15, …
  (−∞, 0]nonnegativerational roots
• A292219: Triangle read by rows. A generalization of unsigned Lah numbers, called L[4,3].
  1 · 6, 1 · 60, 20, 1 · 840, 420, 42, 1 … Σ 1, 7, 81, 1303, 26785, 669351, …
  (−∞, 0)nonnegative
• A038324 → basis A007318
  1 · 21, 10 · 441, 420, 100 · 9261, 13230, 6300, 1000 … Σ 1, 31, 961, 29791, 923521, 28629151, …
  (−∞, 0]nonnegativerational roots
• A102365 → Pₙ + Pₙ₊₁
  2 · 2, 1 · 2, 6, 1 · 2, 23, 16, 1 … Σ 2, 3, 9, 42, 261, 2013, 18504, 197277, …
  (−∞, ∞)nonnegative
• A033282: Triangle read by rows: T(n, k) is the number of diagonal dissections of a convex n-gon into k+1 regions.
  1 · 1, 2 · 1, 5, 5 · 1, 9, 21, 14 … Σ 1, 3, 11, 45, 197, 903, 4279, 20793, …
  (−1, 0)nonnegative
• A089627 → θ+1
  1 · 1 · 1, 4 · 1, 12 … Σ 1, 1, 5, 13, 43, 131, 411, 1275, …
  (−∞, 0]nonnegative
• A136572 → basis A008277
  1 · 1, 1 · 2, 6, 2 · 6, 42, 36, 6 … Σ 1, 2, 10, 90, 1248, 24360, 631440, …
  (−∞, 0]nonnegative
• A054142: Triangular array binomial(2*n-k, k), k=0..n, n >= 0.
  1 · 1, 1 · 1, 3, 1 · 1, 5, 6, 1 … Σ 1, 2, 5, 13, 34, 89, 233, 610, …
  (−∞, 0)nonnegative
• A028246: Triangular array a(n,k) = (1/k)*Sum_{i=0..k} (-1)^(k-i)*binomial(k,i)*i^n; n >= 1, 1 <= k <= n, read by rows.
  1 · 1, 1 · 1, 3, 2 · 1, 7, 12, 6 … Σ 1, 2, 6, 26, 150, 1082, 9366, 94586, …
  [−1, 0)nonnegative
• A106246 → D+1
  1 · 3, 1 · 5, 6, 1 · 3, 15, 9, 1 … Σ 1, 4, 12, 28, 55, 96, 154, 232, …
  (−∞, 0]nonnegative
• A161198 → basis A013609
  1 · 3, 4 · 15, 32, 16 · 105, 284, 240, 64 … Σ 1, 7, 63, 693, 9009, 135135, 2297295, …
  (−∞, 0]nonnegativerational roots
• A102547 → reverse
  0, 1 · 0, 0, 1 · 0, 0, 0, 1 · 0, 0, 0, 1, 1 … Σ 1, 1, 1, 2, 3, 4, 6, 9, …
  (−∞, 0]nonnegative
• A088996 → basis A007318
  1 · 1, 1 · 3, 5, 2 · 15, 34, 25, 6 … Σ 1, 2, 10, 80, 880, 12320, 209440, …
  (−∞, 0]nonnegativerational roots
• A026374 → x ↦ x/(x+1)
  1 · 1, 2 · 1, 5, 5 · 1, 7, 15, 10 … Σ 1, 3, 11, 33, 121, 363, 1331, 3993, …
  [−1, 0]nonnegative
• A156289: Triangle read by rows: T(n,k) is the number of end rhyme patterns of a poem of an even number of lines (2n) with 1<=k<=n evenly rhymed sounds.
  1 · 1, 3 · 1, 15, 15 · 1, 63, 210, 105 … Σ 1, 4, 31, 379, 6556, 150349, 4373461, …
  (−∞, 0]nonnegative
• A081578 → x ↦ x/(x+1)
  1 · 1, 2 · 1, 7, 7 · 1, 12, 30, 20 … Σ 1, 3, 15, 63, 279, 1215, 5319, 23247, …
  [−1, 0]nonnegative
• A111125 → x ↦ x+1
  1 · 4, 1 · 11, 7, 1 · 29, 31, 10, 1 … Σ 1, 5, 19, 71, 265, 989, 3691, 13775, …
  (−5, −1)nonnegative
• A152842 → x ↦ x+1
  1 · 4, 3 · 8, 10, 3 · 32, 64, 42, 9 … Σ 1, 7, 21, 147, 441, 3087, 9261, 64827, …
  (−∞, −1]nonnegativerational roots
• A038255 → basis A013610
  1 · 7, 3 · 49, 42, 9 · 343, 441, 189, 27 … Σ 1, 10, 100, 1000, 10000, 100000, …
  (−∞, 0]nonnegativerational roots
• A100862 → θ+1
  1 · 1, 2 · 1, 6, 3 · 1, 12, 18, 4 … Σ 1, 3, 10, 35, 129, 497, 1996, 8325, …
  (−∞, 0]nonnegative
• A038338 → basis A013610
  576, 1728, 1296 · 13824, 62208, 93312, 46656 … Σ 3600, 216000, 12960000, 777600000, …
  (−∞, 0]nonnegativerational roots
• basis-map coefficients of A030528, shifted → reverse
  1 · -1 · 1 · -1 … Σ 1, -1, 1, -1, 1, -1, 1, -1, …
  (−∞, 0]rational roots
• delannoy → (θ+1)²
  1 · 1, 4 · 1, 12, 9 · 1, 20, 45, 16 … Σ 1, 5, 22, 82, 283, 923, 2892, 8788, …
  (−∞, 0]nonnegative
• Triangle T(n, k) read by rows: Row n gives the coefficients of the even powers in Product_{t=1..n}(2*x - (2*t - 1))*Product_{t=1..n}(2*x + (2*t - 1)).
  16, -40, 9 · 64, -560, 1036, -225 … Σ -15, 315, -14175, 1091475, -127702575, …
  [0, ∞)rational roots
• A114655 → Pₙ + Pₙ₊₁
  6, 2 · 12, 14, 2 · 24, 60, 26, 2 … Σ 8, 28, 112, 484, 2200, 10364, 50144, …
  (−∞, ∞)nonnegative
• A137338 → D
  1 · -3, 2 · 6, -12, 3 · -9, 52, -30, 4 … Σ 0, 1, -1, -3, 17, -57, 179, -631, …
  (−∞, ∞)
• A038763: Triangular matrix arising in enumeration of catafusenes, read by rows.
  1 · 1, 1 · 1, 4, 3 · 1, 7, 15, 9 … Σ 1, 2, 8, 32, 128, 512, 2048, 8192, …
  (−∞, 0)nonnegativerational roots
• A134082 → (θ+1)²
  1 · 2, 4 · 0, 16, 9 · 0, 0, 54, 16 … Σ 1, 6, 25, 70, 153, 286, 481, 750, …
  (−∞, 0]nonnegativerational roots
• Triangle whose (i,j)-th entry is binomial(i,j)*12^(i-j)*8^j.
  144, 192, 64 · 1728, 3456, 2304, 512 … Σ 400, 8000, 160000, 3200000, 64000000, …
  (−∞, 0)nonnegativerational roots
• A152198 → D
  1 · 1 · 2, 2 · 2, 2 … Σ 0, 0, 1, 1, 4, 4, 12, 12, …
  (−∞, 0]nonnegativerational roots
• Stirling2 triangle with scaled diagonals (powers of 8).
  64, 24, 1 · 512, 448, 48, 1 · 4096, 7680, 1600, 80, 1 … Σ 89, 1009, 13457, 210105, 3747753, …
  (−∞, 0)nonnegative
• A038331 → basis A013609
  289, 340, 100 · 4913, 8670, 5100, 1000 … Σ 729, 19683, 531441, 14348907, …
  (−∞, 0]nonnegativerational roots
• A133080 → (θ+1)²
  1 · 1, 4 · 0, 0, 9 · 0, 0, 9, 16 … Σ 1, 5, 9, 25, 25, 61, 49, 113, …
  (−∞, 0]nonnegativerational roots
• A100861 → θ+1
  1 · 1 · 1, 2 · 1, 6 … Σ 1, 1, 3, 7, 22, 66, 226, 778, …
  (−∞, 0]nonnegative
• A172431 → θ+1
  1 · 1, 4 · 1, 8, 9 · 1, 12, 30, 16 … Σ 1, 5, 18, 59, 185, 564, 1685, 4957, …
  (−∞, 0]nonnegative
• A063007 → D
  2 · 6, 12 · 12, 60, 60 · 20, 180, 420, 280 … Σ 0, 2, 18, 132, 900, 5910, 37926, …
  (−∞, 0]nonnegative
• A274496 → Veronese 2 (j=1)
  2 · 4 · 8 · 16 … Σ 0, 0, 2, 4, 8, 16, 32, 64, …
  (−∞, 0]nonnegative
• A173018 → reverse (shift +1) → (θ+1)²
  1 · 0, 4 · 0, 4, 9 · 0, 4, 36, 16 … Σ 1, 4, 13, 56, 304, 1980, 15000, 129360, …
  (−∞, 0]nonnegative
• A081582 → Veronese 2
  1 · 1 · 1, 1 · 1, 17 … Σ 1, 1, 2, 18, 99, 275, 900, 4068, …
  (−∞, 0]nonnegative
• A133087 → basis A013609
  1 · 3, 2 · 4, 8, 4 · 12, 32, 28, 8 … Σ 1, 5, 16, 80, 256, 1280, 4096, 20480, …
  (−∞, 0]nonnegativerational roots
• A253284: Triangle read by rows, T(n,k) = (k+1)*(n+1)!*(n+k)!/((k+1)!^2*(n-k)!) with n >= 0 and 0 <= k <= n.
  1 · 2, 2 · 6, 18, 12 · 24, 144, 240, 120 … Σ 1, 4, 36, 528, 10800, 283680, 9102240, …
  (−∞, 0)nonnegative
• A282629 → Pₙ + Pₙ₊₁
  2, 3 · 2, 18, 9 · 2, 78, 117, 27 … Σ 5, 29, 224, 2075, 22133, 265274, …
  (−∞, ∞)nonnegative
• A285061 → Pₙ + Pₙ₊₁
  2, 4 · 2, 28, 16 · 2, 148, 256, 64 … Σ 6, 46, 470, 5758, 81318, 1291470, …
  (−∞, ∞)nonnegative
• A081582 → γ
  1 · 1 · 1, 7 · 1, 14 … Σ 1, 1, 8, 15, 71, 176, 673, 1905, …
  (−∞, 0]nonnegative