Sequences

• A062145 → reverse
  1 · 4, 1 · 10, 10, 1 · 20, 45, 18, 1 … Σ 1, 5, 21, 84, 330, 1287, 5005, 19448, …
  (−∞, 0]nonnegative
• A013610 → θ+1
  1 · 1, 6 · 1, 12, 27 · 1, 18, 81, 108 … Σ 1, 7, 40, 208, 1024, 4864, 22528, …
  (−∞, 0]nonnegativerational roots
• A081578 → D
  1 · 5, 2 · 9, 18, 3 · 13, 66, 39, 4 … Σ 0, 1, 7, 30, 122, 455, 1641, 5740, …
  (−∞, 0]nonnegative
• type_b_eulerian → γ (scale 1/4) → x ↦ x+1
  1 · 1 · 2, 1 · 6, 5 … Σ 1, 1, 3, 11, 57, 361, 2763, 24611, …
  (−∞, −1]nonnegative
• A060187 → γ
  1 · 1 · 1, 4 · 1, 20 … Σ 1, 1, 5, 21, 153, 1209, 12285, 140589, …
  (−∞, 0]nonnegative
• A178820 → basis A007318
  1 · 8, 4 · 40, 40, 10 · 160, 240, 120, 20 … Σ 1, 12, 90, 540, 2835, 13608, 61236, …
  (−∞, −1]nonnegativerational roots
• A145596 → D+1
  1 · 4, 2 · 11, 14, 3 · 24, 60, 32, 4 … Σ 1, 6, 28, 120, 495, 2002, 8008, 31824, …
  (−∞, 0]nonnegative
• A249139 → D
  1 · 2 · 7, 2 · 16, 6 … Σ 0, 1, 2, 9, 22, 68, 174, 475, …
  (−∞, 0]nonnegative
• A249248 → θ+1
  1 · 1, 6 · 1, 14, 9 · 1, 24, 66, 12 … Σ 1, 7, 24, 103, 419, 1815, 7970, 36277, …
  (−∞, 0]nonnegative
• A008971: Triangle read by rows: T(n,k) is the number of permutations of [n] with k increasing runs of length at least 2.
  type_b_eulerian → γ (scale 1/4)
  1 · 1 · 1, 1 · 1, 5 … Σ 1, 1, 2, 6, 24, 120, 720, 5040, …
  (−∞, 0]nonnegative
• basis-map coefficients of A297191, shifted → D+1
  1 · 0, 2, 1 · 0, 0, 0, 4, 1 · 0, 0, 0, 0, 0, 6, 1 … Σ 1, 3, 5, 7, 9, 11, 13, 15, …
  (−∞, 0]nonnegativerational roots
• A099040 → D
  2 · 2, 8 · 0, 16, 24 · 0, 8, 72, 64 … Σ 0, 2, 10, 40, 144, 488, 1592, 5056, …
  (−∞, 0]nonnegative
• A108838 → basis A013611
  2 · 5, 8 · 14, 48, 32 · 42, 224, 336, 128 … Σ 2, 13, 94, 730, 5956, 50357, 437318, …
  (−∞, 0]nonnegative
• A110441 → basis A008277
  1 · 4, 1 · 14, 9, 1 · 48, 57, 15, 1 … Σ 1, 5, 24, 121, 647, 3668, 21997, …
  (−∞, 0]nonnegative
• A026729 → Veronese 2
  1 · 0, 1 · 0, 2 · 0, 1, 1 … Σ 1, 0, 1, 2, 2, 4, 7, 10, …
  (−∞, 0]nonnegative
• A125662 → (θ+1)²
  1 · 3, 4 · 8, 24, 9 · 21, 100, 81, 16 … Σ 1, 7, 41, 218, 1091, 5237, 24379, …
  (−∞, 0]nonnegative
• A099040 → D+1
  1 · 2, 2 · 2, 10, 4 · 0, 16, 32, 8 … Σ 1, 4, 16, 56, 188, 608, 1920, 5952, …
  (−∞, 0]nonnegative
• A249248: Triangular array: row n gives the coefficients of the polynomial p(n,x) defined in Comments.
  1 · 1, 3 · 1, 7, 3 · 1, 12, 22, 3 … Σ 1, 4, 11, 38, 131, 490, 1897, 7714, …
  (−∞, 0)nonnegative
• chebyshev_t → x ↦ x+1
  1 · 1, 1 · 1, 4, 2 · 1, 9, 12, 4 … Σ 1, 2, 7, 26, 97, 362, 1351, 5042, …
  (−2, 0)nonnegative
• A038220 → Veronese 2
  1 · 3 · 9, 4 · 27, 36 … Σ 1, 3, 13, 63, 313, 1563, 7813, 39063, …
  (−∞, 0]nonnegative
• A143495 → x ↦ x/(x+1)
  1 · 3, 4 · 9, 25, 17 · 27, 118, 167, 77 … Σ 1, 7, 51, 389, 3121, 26423, 236403, …
  [−1, 0]nonnegative
• basis-map coefficients of A scaled Hermite triangle.
  0, 0, 1 · 0, 0, 0, 1 · 0, 0, 0, 0, 1 … Σ 1, 1, 1, 1, 1, 1, 1, 1, …
  [−1, 0]nonnegativerational roots
• A038327 → basis A008277
  1 · 13, 1 · 169, 27, 1 · 2197, 547, 42, 1 … Σ 1, 14, 197, 2787, 39652, 567515, …
  (−∞, 0]nonnegative
• A008955 → basis A013610
  1 · 2, 3 · 10, 39, 36 · 100, 660, 1413, 972 … Σ 1, 5, 85, 3145, 204425, 20646925, …
  (−∞, 0]nonnegativerational roots
• A147716 → basis A013611
  1 · 15, 4 · 225, 120, 16 · 3375, 2700, 720, 64 … Σ 1, 19, 361, 6859, 130321, 2476099, …
  (−∞, 0]nonnegativerational roots
• A038334 → basis A013610
  400, 960, 576 · 8000, 28800, 34560, 13824 … Σ 1936, 85184, 3748096, 164916224, …
  (−∞, 0]nonnegativerational roots
• A145324 → Pₙ + Pₙ₊₁
  2, 2 · 2, 7, 6 · 2, 14, 32, 24 · 2, 23, 97, 178, 120 … Σ 4, 15, 72, 420, 2880, 22680, 201600, …
  (−∞, ∞)nonnegativerational roots
• A178822 → D+1
  1 · 12, 6 · 63, 84, 21 · 224, 504, 336, 56 … Σ 1, 18, 168, 1120, 6048, 28224, 118272, …
  (−∞, 0]nonnegativerational roots
• A137320: Coefficients of raising factorial polynomials, T(n,k) = [x^k] p(x, n) where p(x, n) = (m*x + n - 1)*p(x, n - 1) with p[x, 0] = 1, p[x, -1] = 0, p[x, 1…
  1 · 0, 2 · 0, 2, 4 · 0, 4, 12, 8 … Σ 1, 2, 6, 24, 120, 720, 5040, 40320, …
  (−∞, 0]nonnegativerational roots
• A104684 → basis A013609
  1 · 3, 2 · 13, 16, 4 · 63, 114, 60, 8 … Σ 1, 5, 33, 245, 1921, 15525, 127905, …
  (−∞, 0]nonnegative
• A056242 → Veronese 2
  1 · 1 · 1, 4 · 1, 16 … Σ 1, 1, 5, 17, 58, 198, 676, 2308, …
  (−∞, 0]nonnegative
• A122542 → D+1
  1 · 1, 1 · 2, 4, 1 · 2, 10, 7, 1 … Σ 1, 2, 7, 20, 57, 158, 431, 1160, …
  (−∞, 0]nonnegative
• A039756 → D+1
  1 · 2, 1 · 5, 6, 1 · 10, 35, 16, 1 … Σ 1, 3, 12, 62, 372, 2492, 18384, 147800, …
  (−∞, 0]nonnegative
• A119808: Triangle read by rows: T(n,k) is the number of ternary words of length n having k runs of consecutive 0's (0<=k<=ceiling(n/2)).
  1 · 2, 1 · 4, 5 · 8, 17, 2 … Σ 1, 3, 9, 27, 81, 243, 729, 2187, …
  (−∞, 0)nonnegative
• A274498 → basis A013609
  1 · 3 · 9, 12 · 27, 36 … Σ 1, 3, 21, 63, 441, 1323, 9261, 27783, …
  (−∞, 0]nonnegativerational roots
• A128100 → Veronese 2
  1 · 1 · 2 · 3 … Σ 1, 1, 2, 3, 6, 11, 22, 43, …
  (−∞, 0]nonnegative
• A102662 → x ↦ x+1
  1 · 4, 3 · 9, 11, 3 · 22, 38, 20, 3 … Σ 1, 7, 23, 83, 295, 1051, 3743, 13331, …
  (−∞, −1]nonnegative
• Triangle whose (i,j)-th entry is binomial(i,j)*12^(i-j)*3^j.
  144, 72, 9 · 1728, 1296, 324, 27 … Σ 225, 3375, 50625, 759375, 11390625, …
  (−∞, 0)nonnegativerational roots
• A137597 → x ↦ x+1
  1 · 3, 1 · 11, 7, 1 · 47, 43, 12, 1 … Σ 1, 4, 19, 103, 622, 4117, 29521, …
  (−∞, −1]nonnegative
• A136572 → Veronese 2 (j=1)
  1 · 0, 6 · 0, 0, 120 · 0, 0, 0, 5040 … Σ 0, 1, 0, 6, 0, 120, 0, 5040, …
  (−∞, 0]nonnegativerational roots
• A013620 → (θ+1)²
  1 · 2, 12 · 4, 48, 81 · 8, 144, 486, 432 … Σ 1, 14, 133, 1070, 7825, 53750, 353125, …
  (−∞, 0]nonnegative
• A154227 → basis A013611
  1 · 2, 4 · 10, 40, 16 · 40, 240, 352, 64 … Σ 1, 6, 66, 696, 9126, 127836, 2044656, …
  (−∞, 0]nonnegative
• A225471 → basis A007318
  1 · 4, 1 · 32, 12, 1 · 384, 176, 24, 1 … Σ 1, 5, 45, 585, 9945, 208845, 5221125, …
  (−∞, 0]nonnegativerational roots
• A391403 → D
  2 · 6 · 12, 12 · 20, 60 … Σ 0, 0, 2, 6, 24, 80, 270, 882, …
  (−∞, 0]nonnegative
• A257626: Triangle read by rows: T(n,k) = t(n-k, k); t(n,m) = f(m)*t(n-1,m) + f(n)*t(n,m-1), where f(x) = 3*x + 6.
  1 · 6, 6 · 36, 108, 36 · 216, 1404, 1404, 216 … Σ 1, 12, 180, 3240, 68040, 1632960, …
  (−∞, 0)nonnegative
• A134082 → reverse
  1 · 1, 2 · 1, 4 · 1, 6 … Σ 1, 3, 5, 7, 9, 11, 13, 15, …
  (−∞, 0]nonnegativerational roots
• A008299: Triangle T(n,k) of associated Stirling numbers of second kind, n >= 2, 1 <= k <= floor(n/2).
  1 · 1 · 1, 3 · 1, 10 … Σ 1, 1, 4, 11, 41, 162, 715, 3425, …
  (−∞, 0)nonnegative
• A116666: Triangle, row sums = number of edges in n-dimensional hypercubes.
  1 · 1, 3 · 1, 6, 5 · 1, 9, 15, 7 … Σ 1, 4, 12, 32, 80, 192, 448, 1024, …
  (−∞, 0)nonnegativerational roots
• A122542 → (θ+1)²
  1 · 0, 4 · 0, 8, 9 · 0, 8, 36, 16 … Σ 1, 4, 17, 60, 201, 640, 1969, 5896, …
  (−∞, 0]nonnegative
• A052553 → x ↦ x+1
  1 · 1 · 2, 1 · 3, 2 … Σ 1, 1, 3, 5, 11, 21, 43, 85, …
  (−∞, −1]nonnegative