Sequences

• A013622 → basis A008288
  1 · 8, 5 · 64, 105, 25 · 512, 1435, 850, 125 … Σ 1, 13, 194, 2922, 44036, 663668, …
  [−3−2√2, −3+2√2]nonnegative
• A132774 → D
  3 · 4, 10 · 0, 12, 21 · 0, 0, 24, 36 … Σ 0, 3, 14, 33, 60, 95, 138, 189, …
  (−∞, 0]nonnegativerational roots
• A130123 → D
  2 · 0, 8 · 0, 0, 24 · 0, 0, 0, 64 … Σ 0, 2, 8, 24, 64, 160, 384, 896, …
  (−∞, 0]nonnegativerational roots
• A207606 → reverse
  2, 7, 4 · 2, 11, 16, 5 · 2, 15, 36, 30, 6 … Σ 13, 34, 89, 233, 610, 1597, 4181, …
  (−∞, 0]nonnegative
• A123160: Triangle read by rows: T(n,k) = n!*(n+k-1)!/((n-k)!*(n-1)!*(k!)^2) for 0 <= k <= n, with T(0,0) = 1.
  1 · 1, 1 · 1, 4, 3 · 1, 9, 18, 10 … Σ 1, 2, 8, 38, 192, 1002, 5336, 28814, …
  (−∞, 0)nonnegative
• A059473 → Veronese 2 (j=1)
  2 · 10 · 32, 8 · 88, 88 … Σ 0, 2, 10, 40, 176, 792, 3528, 15680, …
  (−∞, 0]nonnegative
• A372873: Triangle read by rows: T(n,k) is the number of flattened Catalan words of length n with exactly k runs of descents.
  1 · 0, 2 · 0, 1, 4 · 0, 0, 6, 8 … Σ 1, 2, 5, 14, 41, 122, 365, 1094, …
  (−∞, 0]nonnegative
• A145596 → θ+1
  1 · 2, 4 · 3, 16, 9 · 4, 40, 60, 16 … Σ 1, 6, 28, 120, 495, 2002, 8008, 31824, …
  (−∞, 0]nonnegative
• A008459 → x ↦ x/(x+1)
  1 · 1, 2 · 1, 6, 6 · 1, 12, 30, 20 … Σ 1, 3, 13, 63, 321, 1683, 8989, 48639, …
  [−1, 0]nonnegative
• A078812 → Veronese 2
  1 · 2 · 3, 1 · 4, 6 … Σ 1, 2, 4, 10, 27, 72, 189, 494, …
  (−∞, 0]nonnegative
• A099040 → basis A013609
  1 · 2, 4 · 6, 20, 16 · 16, 80, 128, 64 … Σ 1, 6, 42, 288, 1980, 13608, 93528, …
  (−∞, 0]nonnegative
• A350512: Triangle read by rows with T(n,0) = 1 for n >= 0 and T(n,k) = binomial(n-1,k-1)*(2*k*(n-k) + n)/k for 0 < k <= n.
  1 · 1, 1 · 1, 4, 1 · 1, 7, 7, 1 … Σ 1, 2, 6, 16, 40, 96, 224, 512, …
  (−∞, 0)nonnegative
• A180047: Coefficient triangle of the numerators of the (n-th convergents to) the continued fraction w/(1 + w/(2 + w/(3 + w/(...)))).
  0, 1 · 0, 2 · 0, 6, 1 · 0, 24, 6 … Σ 0, 1, 2, 7, 30, 157, 972, 6961, …
  (−∞, 0]nonnegative
• A201637 → Pₙ + Pₙ₊₁
  2 · 2, 2 · 2, 10, 6 · 2, 30, 64, 24 … Σ 2, 4, 18, 120, 1050, 11340, 145530, …
  (−∞, ∞)nonnegative
• A056939 → x ↦ x+1
  1 · 2, 1 · 6, 6, 1 · 22, 33, 13, 1 … Σ 1, 3, 13, 69, 417, 2763, 19609, 146793, …
  (−∞, −1]nonnegative
• A207823 → Veronese 2 (j=1)
  1 · 8 · 46, 1 · 232, 16 … Σ 0, 1, 8, 47, 248, 1248, 6136, 29809, …
  (−∞, 0]nonnegative
• A126351 → θ+1
  1 · 1, 4 · 1, 10, 12 · 1, 18, 57, 32 … Σ 1, 5, 23, 108, 534, 2803, 15623, 92249, …
  (−∞, 0]nonnegative
• A081581 → γ
  1 · 1 · 1, 6 · 1, 12 … Σ 1, 1, 7, 13, 55, 133, 463, 1261, …
  (−∞, 0]nonnegative
• A169803: Triangle read by rows: T(n,k) = binomial(n+1-k,k) (n >= 0, 0 <= k <= n).
  1 · 1, 1 · 1, 2 · 1, 3, 1 … Σ 1, 2, 3, 5, 8, 13, 21, 34, …
  (−∞, 0)nonnegative
• A081579 → D+1
  1 · 2, 1 · 7, 8, 1 · 12, 33, 14, 1 … Σ 1, 3, 16, 60, 240, 896, 3328, 12096, …
  (−∞, 0]nonnegative
• A113953 → basis A008277
  1 · 1, 1 · 3, 5, 1 · 5, 19, 10, 1 … Σ 1, 2, 9, 35, 162, 799, 4275, 24448, …
  (−∞, 0]nonnegative
• A056242 → (θ+1)²
  1 · 1, 8 · 1, 20, 36 · 1, 36, 144, 128 … Σ 1, 9, 57, 309, 1530, 7134, 31864, …
  (−∞, 0]nonnegative
• A166972: Triangle T(n,k) read by rows: T(n,k) = (n-k+1)*T(n-1,k-1) + (3*k-2)*k*T(n-1,k), initialized by T(n,1) = T(n,n) = 1.
  1 · 1, 1 · 1, 10, 1 · 1, 83, 41, 1 … Σ 1, 2, 12, 126, 1902, 39852, 1092924, …
  (−∞, 0]nonnegative
• A154986 → basis A013610
  1 · 2, 3 · 6, 18, 9 · 24, 108, 126, 27 … Σ 1, 5, 33, 285, 3009, 37845, 550305, …
  (−∞, 0]nonnegative
• A013620: Triangle of coefficients in expansion of (2+3x)^n.
  1 · 2, 3 · 4, 12, 9 · 8, 36, 54, 27 … Σ 1, 5, 25, 125, 625, 3125, 15625, 78125, …
  (−∞, 0)[−1, 0]nonnegative+1
• A122848 → D+1
  1 · 1, 1 · 1, 3, 1 · 0, 6, 6, 1 … Σ 1, 2, 5, 13, 38, 116, 382, 1310, …
  (−∞, 0]nonnegative
• A290315 → Pₙ + Pₙ₊₁
  2, 2 · 2, 18, 12 · 2, 82, 296, 120 … Σ 4, 32, 500, 11200, 325156, 11580128, …
  (−∞, ∞)nonnegative
• A143491 → basis A013609
  12, 14, 4 · 60, 94, 48, 8 · 360, 684, 476, 144, 16 … Σ 30, 210, 1680, 15120, 151200, 1663200, …
  (−∞, 0]nonnegativerational roots
• A030528 → Veronese 2
  1 · 1 · 0, 1 · 0, 3 … Σ 1, 1, 1, 3, 4, 6, 11, 17, …
  (−∞, 0]nonnegative
• A144436 → γ
  1 · 1 · 1, 6 · 1, 20 … Σ 1, 1, 7, 21, 115, 585, 3727, 25549, …
  (−∞, 0]nonnegative
• A126216: Triangle read by rows: T(n,k) is the number of Schroeder paths of semilength n containing exactly k peaks but no peaks at level one (n >= 1; 0 <= k <=…
  1 · 2, 1 · 5, 5, 1 · 14, 21, 9, 1 … Σ 1, 3, 11, 45, 197, 903, 4279, 20793, …
  (−∞, −1]nonnegative
• A124932 → x ↦ x/(x+1)
  1 · 2, 5 · 3, 15, 18 · 4, 30, 72, 56 … Σ 1, 7, 36, 162, 675, 2673, 10206, 37908, …
  [−1, 0]nonnegativerational roots
• A008459 → x ↦ x+1
  1 · 2, 1 · 6, 6, 1 · 20, 30, 12, 1 … Σ 1, 3, 13, 63, 321, 1683, 8989, 48639, …
  (−∞, −1]nonnegative
• A128100 → D
  1 · 2 · 5, 2 · 10, 6 … Σ 0, 0, 1, 2, 7, 16, 41, 94, …
  (−∞, 0]nonnegative
• A078812 → basis A013610
  1 · 3, 3 · 8, 18, 9 · 21, 75, 81, 27 … Σ 1, 6, 35, 204, 1189, 6930, 40391, …
  (−∞, 0]nonnegative
• A178821 → basis A013611
  1 · 10, 20 · 60, 240, 240 · 280, 1680, 3360, 2240 … Σ 1, 30, 540, 7560, 90720, 979776, …
  (−∞, 0]nonnegativerational roots
• A051380 → Pₙ + Pₙ₊₁
  -8, 1 · 81, -18, 1 · -900, 280, -29, 1 … Σ -7, 64, -648, 7200, -87120, 1140480, …
  (−∞, ∞)rational roots
• A120909 → θ+1
  3 · 3, 12 · 3, 24, 36 · 3, 36, 108, 96 … Σ 3, 15, 63, 243, 891, 3159, 10935, …
  (−∞, 0]nonnegativerational roots
• A001263 → basis A013609
  1 · 2, 2 · 5, 10, 4 · 14, 42, 36, 8 … Σ 1, 4, 19, 100, 562, 3304, 20071, …
  (−∞, 0]nonnegative
• A026374 → D+1
  1 · 2, 1 · 4, 5, 1 · 5, 12, 7, 1 … Σ 1, 3, 10, 25, 75, 175, 500, 1125, …
  (−∞, 0]nonnegative
• A102662 → Veronese 2
  1 · 1 · 1, 3 · 1, 11 … Σ 1, 1, 4, 12, 27, 63, 154, 374, …
  (−∞, 0]nonnegative
• A114687 → basis A008277
  1 · 3, 2 · 11, 18, 4 · 45, 140, 72, 8 … Σ 1, 5, 33, 265, 2473, 26037, 303089, …
  (−∞, 0]nonnegative
• A038301 → basis A013611
  400, 1760, 1936 · 8000, 52800, 116160, 85184 … Σ 4096, 262144, 16777216, 1073741824, …
  (−∞, 0]nonnegativerational roots
• A038322 → basis A013610
  1 · 19, 24 · 361, 912, 576 … Σ 1, 43, 1849, 79507, 3418801, 147008443, …
  (−∞, 0]nonnegativerational roots
• A169803 → Veronese 2 (j=1)
  1 · 2 · 3 · 4 … Σ 0, 1, 2, 3, 4, 6, 10, 17, …
  (−∞, 0]nonnegative
• A008277 → Pₙ + Pₙ₊₁
  2, 1 · 2, 4, 1 · 2, 10, 7, 1 · 2, 22, 31, 11, 1 … Σ 3, 7, 20, 67, 255, 1080, 5017, 25287, …
  (−∞, ∞)nonnegative
• A225468: Triangle read by rows, S_3(n, k) where S_m(n, k) are the Stirling-Frobenius subset numbers of order m; n >= 0, k >= 0.
  1 · 2, 1 · 4, 7, 1 · 8, 39, 15, 1 … Σ 1, 3, 12, 63, 405, 3024, 25515, 239355, …
  (−∞, 0)nonnegative
• A081580 → basis A013611
  1 · 2, 4 · 9, 36, 16 · 28, 168, 256, 64 … Σ 1, 6, 61, 516, 4621, 40626, 359281, …
  (−∞, 0]nonnegative
• A062190: Coefficient triangle of certain polynomials N(5; m,x).
  1 · 1, 6 · 1, 14, 21 · 1, 24, 84, 56 … Σ 1, 7, 36, 165, 715, 3003, 12376, 50388, …
  (−∞, 0)nonnegative
• A103450: A figurate number triangle read by rows.
  1 · 1, 1 · 1, 3, 1 · 1, 5, 5, 1 … Σ 1, 2, 5, 12, 28, 64, 144, 320, …
  (−∞, 0)nonnegative