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1381 sequences

• A023531 → (1/2)D²+2D+1 → x ↦ x/(x+1)
  1 · 2, 3 · 1, 6, 6 · 0, 3, 12, 10 … row sums 1, 5, 13, 25, 41, 61, 85, 113, …
  [−1, 0] nonnegative
• A104684 → basis A007318
  1 · 3, 1 · 13, 8, 1 · 63, 57, 15, 1 … row sums 1, 4, 22, 136, 886, 5944, 40636, …
  (−∞, −1] nonnegative
• A318773: Triangle T(n,k) = 3*T(n-1,k) + T(n-4,k-1) for k = 0..floor(n/4), with T(0,0) = 1 and T(n,k) = 0 for n or k < 0, read by rows.
  A318772 → x ↦ (1/243)x
  1 · 3 · 9 · 27 … row sums 1, 3, 9, 27, 82, 249, 756, 2295, …
  A318773 (−∞, 0] nonnegative
• A008292 → γ (shift +1) → θ+1
  1 · 1 · 1, 4 · 1, 16 … row sums 1, 1, 5, 17, 93, 513, 3477, 25569, …
  (−∞, 0] nonnegative
• A126351 → D+1
  1 · 3, 2 · 6, 13, 4 · 10, 47, 43, 8 … row sums 1, 5, 23, 108, 534, 2803, 15623, 92249, …
  (−∞, 0] nonnegative
• A178820 → x ↦ x/(x+1)
  1 · 4, 8 · 10, 40, 40 · 20, 120, 240, 160 … row sums 1, 12, 90, 540, 2835, 13608, 61236, …
  [−1, 0] nonnegative rational roots
• A100861 → reverse → x ↦ x+1
  1 · 1, 1 · 2, 3, 1 · 4, 9, 6, 1 … row sums 1, 2, 6, 20, 76, 312, 1384, 6512, …
  (−∞, −1] nonnegative
• A173018 → (θ+1)²
  1 · 1 · 1, 4 · 1, 16, 9 … row sums 1, 1, 5, 26, 160, 1140, 9240, 84000, …
  (−∞, 0] nonnegative
• A132393 → (θ+1)²
  1 · 0, 4 · 0, 4, 9 · 0, 8, 27, 16 … row sums 1, 4, 13, 51, 244, 1392, 9260, 70508, …
  (−∞, 0] nonnegative
• A059344 → ⊙ 1/k! (shift -1) → x ↦ x+1
  1 · 1 · 3, 2 · 7, 6 … row sums 1, 1, 5, 13, 49, 161, 581, 2045, …
  (−∞, −1] nonnegative
• A132393 → D+1
  1 · 1, 1 · 1, 3, 1 · 2, 8, 6, 1 … row sums 1, 2, 5, 17, 74, 394, 2484, 18108, …
  (−∞, 0] nonnegative
• A341287: Triangle read by rows: T(n,k) = Sum_{i=0..n-1} binomial(n-1, i)*T(n-1-i,k-1) - Sum_{i=1..n-1} binomial(n-1,i)*T(n-1-i,k) for 1 <= k <= n+1 with T(0,1) = 1 (and T(n,k) = 0 otherwise).
  A023531 → basis A341287
  1 · 0, 1 · -1, 1, 1 · -1, -2, 3, 1 … row sums 1, 1, 1, 1, 1, 1, 1, 1, …
  A341287 (−∞, 1]
• A116412 → basis A007318
  1 · 4, 1 · 13, 8, 1 · 43, 42, 12, 1 … row sums 1, 5, 22, 98, 436, 1940, 8632, 38408, …
  (−∞, −1] nonnegative
• A008292 → γ (shift +1) → D+1
  1 · 1 · 3, 2 · 9, 8 … row sums 1, 1, 5, 17, 93, 513, 3477, 25569, …
  (−∞, 0] nonnegative
• A011973 → (θ+1)²
  1 · 1 · 1, 4 · 1, 8 … row sums 1, 1, 5, 9, 22, 44, 91, 179, …
  (−∞, 0] nonnegative
• A062264 → θ+1
  1 · 1, 10 · 1, 24, 45 · 1, 42, 189, 140 … row sums 1, 11, 70, 372, 1815, 8437, 38038, …
  (−∞, 0] nonnegative
• A062145 → x ↦ x+1
  1 · 5, 4 · 21, 30, 10 · 84, 168, 105, 20 … row sums 1, 9, 61, 377, 2241, 13073, 75517, …
  (−∞, −1] nonnegative
• A159854 → (θ+1)²
  0, 0, 9 · 0, 0, 9, 16 · 0, 0, 9, 32, 25 … row sums 9, 25, 66, 168, 416, 1008, 2400, 5632, …
  (−∞, 0] nonnegative
• A137320 → D
  2 · 2, 8 · 4, 24, 24 · 12, 88, 144, 64 … row sums 0, 2, 10, 52, 308, 2088, 16056, 138528, …
  (−∞, 0] nonnegative
• A064861 → reverse
  2, 3, 1 · 4, 8, 5, 1 · 4, 12, 13, 6, 1 … row sums 6, 18, 36, 108, 216, 648, 1296, 3888, …
  (−∞, 0] nonnegative rational roots
• A055356 → (θ+1)²
  1 · 1 · 1, 4 · 1, 16, 18 … row sums 1, 1, 5, 35, 303, 3123, 37349, 508547, …
  (−∞, 0] nonnegative
• A141611: Triangle read by rows: T(n, k) = (n-k+1)*(k+1)*binomial(n, k).
  A007318 → −D²+(−1+n)D+1+n
  1 · 2, 2 · 3, 8, 3 · 4, 18, 18, 4 … row sums 1, 4, 14, 44, 128, 352, 928, 2368, …
  A141611 (−∞, 0] nonnegative
• A081581 → θ+1
  1 · 1, 2 · 1, 16, 3 · 1, 30, 45, 4 … row sums 1, 3, 20, 80, 372, 1540, 6496, 26496, …
  (−∞, 0] nonnegative
• A086645 → (θ+1)²
  1 · 1, 4 · 1, 24, 9 · 1, 60, 135, 16 … row sums 1, 5, 34, 212, 1216, 6592, 34304, …
  (−∞, 0] nonnegative
• A060920 → (θ+1)²
  1 · 2, 4 · 5, 20, 9 · 13, 80, 81, 16 … row sums 1, 6, 34, 190, 1026, 5342, 26962, …
  (−∞, ∞) nonnegative
• A039755 → θ+1
  1 · 1, 2 · 1, 8, 3 · 1, 26, 27, 4 … row sums 1, 3, 12, 58, 324, 2044, 14320, 109960, …
  (−∞, 0] nonnegative
• A059473 → D+1
  1 · 4, 2 · 14, 18, 4 · 40, 96, 56, 8 … row sums 1, 6, 36, 200, 1068, 5544, 28192, …
  (−∞, 0] nonnegative
• A059344 → ⊙ 1/k! (shift -1) → (θ+1)²
  1 · 1 · 1, 8 · 1, 24 … row sums 1, 1, 9, 25, 103, 351, 1251, 4299, …
  (−∞, 0] nonnegative
• A001263 → D+1
  1 · 2, 1 · 4, 5, 1 · 7, 18, 9, 1 … row sums 1, 3, 10, 35, 126, 462, 1716, 6435, …
  (−∞, 0] nonnegative
• A008278 → x ↦ x+1 (shift +1) → x ↦ x+1
  1 · 3, 1 · 11, 7, 1 · 49, 46, 13, 1 … row sums 1, 4, 19, 109, 742, 5815, 51193, …
  (−∞, −1] nonnegative
• A128099 → D+1
  1 · 1 · 3, 2 · 5, 4 … row sums 1, 1, 5, 9, 25, 53, 125, 273, …
  (−∞, 0] nonnegative
• A143685 → θ+1
  1 · 1, 2 · 1, 22, 3 · 1, 42, 63, 4 … row sums 1, 3, 26, 110, 615, 2821, 13828, 63756, …
  (−∞, 0] nonnegative
• A008292 → γ (scale 1/4) → D+1
  1 · 2 · 6, 2 · 24, 16 … row sums 1, 2, 8, 40, 240, 1680, 13440, 120960, …
  (−∞, 0] nonnegative
• A013611 → (θ+1)²
  1 · 1, 16 · 1, 32, 144 · 1, 48, 432, 1024 … row sums 1, 17, 177, 1505, 11425, 80625, 540625, …
  (−∞, 0] nonnegative
• A053117 → D+1
  1 · 2, 2 · -1, 8, 4 · -4, -4, 24, 8 … row sums 1, 4, 11, 24, 45, 76, 119, 176, …
  (−∞, ∞)
• A010054 → reverse → D
  3 · 0, 12 · 0, 0, 30 · 0, 0, 0, 60 … row sums 0, 3, 12, 30, 60, 105, 168, 252, …
  (−∞, 0] nonnegative rational roots
• A055151: Triangular array of Motzkin polynomial coefficients.
  narayana → γ (shift +1)
  1 · 1 · 1, 1 · 1, 3 … row sums 1, 1, 2, 4, 9, 21, 51, 127, …
  A055151 (−∞, 0] nonnegative
• A145597 → θ+1
  1 · 3, 6 · 6, 30, 18 · 10, 90, 135, 40 … row sums 1, 9, 54, 275, 1287, 5733, 24752, …
  (−∞, 0] nonnegative
• A001263 → θ+1
  1 · 1, 2 · 1, 6, 3 · 1, 12, 18, 4 … row sums 1, 3, 10, 35, 126, 462, 1716, 6435, …
  (−∞, 0] nonnegative
• A113413 → reverse
  1 · 1, 2 · 1, 4, 2 · 1, 6, 8, 2 … row sums 1, 3, 7, 17, 41, 99, 239, 577, …
  (−∞, 0] nonnegative
• A039757: Triangle of coefficients in expansion of (x-1)*(x-3)*(x-5)*...*(x-(2*n-1)).
  A028338 → x ↦ −x (shift -1)
  1 · -1, 1 · 3, -4, 1 · -15, 23, -9, 1 … row sums 1, 0, 0, 0, 0, 0, 0, 0, …
  A039757 [0, ∞) rational roots
• A008292 → γ (scale 1/2) (shift +1) → x ↦ x+1
  1 · 1 · 2, 1 · 5, 4 … row sums 1, 1, 3, 9, 39, 189, 1107, 7281, …
  (−∞, −1] nonnegative
• A106246: Number triangle T(n,k)=C(n,k)C(2,n-k).
  A023531 → (1/2)D²+2D+1
  1 · 2, 1 · 1, 4, 1 · 0, 3, 6, 1 … row sums 1, 3, 6, 10, 15, 21, 28, 36, …
  A106246 (−∞, 0] nonnegative
• A008278 → x ↦ x/(x+1)
  1 · 1, 2 · 1, 5, 5 · 1, 9, 22, 15 … row sums 1, 3, 11, 47, 227, 1215, 7107, 44959, …
  [−1, 0] nonnegative
• A207823 → (θ+1)²
  1 · 4, 4 · 15, 32, 9 · 56, 184, 108, 16 … row sums 1, 8, 56, 364, 2255, 13504, 78841, …
  (−∞, 0] nonnegative
• A007318 → 2θ+1 → θ+1
  1 · 1, 6 · 1, 12, 15 · 1, 18, 45, 28 … row sums 1, 7, 28, 92, 272, 752, 1984, 5056, …
  (−∞, 0] nonnegative
• A039755 → D
  1 · 4, 2 · 13, 18, 3 · 40, 116, 48, 4 … row sums 0, 1, 6, 34, 208, 1396, 10232, 81320, …
  (−∞, 0] nonnegative
• A099040 → x ↦ x−9
  1 · -18, 2 · 306, -70, 4 · -5184, 1800, -208, 8 … row sums 1, -16, 240, -3584, 53504, -798720, …
  (7, 9]
• A007318 → 2θ+1 → D
  3 · 6, 10 · 9, 30, 21 · 12, 60, 84, 36 … row sums 0, 3, 16, 60, 192, 560, 1536, 4032, …
  (−∞, 0] nonnegative rational roots
• A249250 → D+1
  1 · 4, 3 · 7, 12, 3 · 10, 39, 24, 3 … row sums 1, 7, 22, 76, 244, 772, 2392, 7312, …
  (−∞, 0] nonnegative