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1381 sequences

• A007318 → ×(1+2n+n²) → D+1
  1 · 8, 4 · 27, 36, 9 · 64, 144, 96, 16 … row sums 1, 12, 72, 320, 1200, 4032, 12544, …
  (−∞, 0] nonnegative rational roots
• A086645 → D+1
  1 · 2, 1 · 7, 8, 1 · 16, 45, 18, 1 … row sums 1, 3, 16, 80, 384, 1792, 8192, 36864, …
  (−∞, 0] nonnegative
• A008278 → x ↦ x+1 (shift +1) → reverse
  1 · 1, 2 · 1, 5, 5 · 1, 10, 23, 15 … row sums 1, 3, 11, 49, 257, 1539, 10299, 75905, …
  (−∞, 0] nonnegative
• A099097 → x ↦ x−15
  1 · -45, 3 · 2010, -269, 9 · -89775, 18045, -1209, 27 … row sums 1, -42, 1750, -72912, 3037804, …
  (131/9, 15]
• A113214 → D
  1 · 3, 2 · 2, 8, 3 · 0, 10, 15, 4 … row sums 0, 1, 5, 13, 29, 60, 118, 225, …
  (−∞, 0] nonnegative
• A274496 → (θ+1)²
  1 · 2 · 2, 8 · 4, 16 … row sums 1, 2, 10, 20, 72, 144, 448, 896, …
  (−∞, 0] nonnegative
• A008277 → x ↦ x+1
  1 · 2, 1 · 5, 5, 1 · 15, 22, 9, 1 … row sums 1, 3, 11, 47, 227, 1215, 7107, 44959, …
  (−∞, −1] nonnegative
• A113953 → x ↦ x−4
  1 · -4, 1 · 8, -6, 1 · 0, 16, -8, 1 … row sums 1, -3, 3, 9, -45, 81, 27, -567, …
  (−4, 4]
• A120909 → x ↦ x/(x+1)
  3 · 3, 9 · 3, 18, 27 · 3, 27, 81, 81 … row sums 3, 12, 48, 192, 768, 3072, 12288, …
  [−1, 0] nonnegative rational roots
• A099097 → reverse
  1 · 3 · 9, 1 · 27, 6 … row sums 1, 3, 10, 33, 109, 360, 1189, 3927, …
  (−∞, 0] nonnegative
• A130850: Triangle read by rows, 0 <= k <= n, T(n,k) = Sum_{j=0..n} A(n,j)*binomial(n-j,k) where A(n,j) are the Eulerian numbers A173018.
  A028246 → reverse
  1 · 1, 1 · 2, 3, 1 · 6, 12, 7, 1 … row sums 1, 2, 6, 26, 150, 1082, 9366, 94586, …
  A130850 (−∞, −1] nonnegative
• A027465 → θ+1
  1 · 3, 2 · 9, 12, 3 · 27, 54, 27, 4 … row sums 1, 5, 24, 112, 512, 2304, 10240, 45056, …
  (−∞, 0] nonnegative rational roots
• A099097 → D
  3 · 1, 18 · 0, 12, 81 · 0, 2, 81, 324 … row sums 0, 3, 19, 93, 407, 1674, 6618, 25455, …
  (−∞, 0] nonnegative
• A094816 → (θ+1)²
  1 · 1, 4 · 1, 12, 9 · 1, 32, 54, 16 … row sums 1, 5, 22, 103, 543, 3273, 22512, …
  (−∞, 0] nonnegative
• A063007: T(n,k) = binomial(n,k)*binomial(n+k,k), 0 <= k <= n, triangle read by rows.
  1 · 1, 2 · 1, 6, 6 · 1, 12, 30, 20 … row sums 1, 3, 13, 63, 321, 1683, 8989, 48639, …
  A063007 (−1, 0) nonnegative
• A008292 → γ (scale 1/4) → x ↦ x+1
  1 · 2 · 6, 2 · 24, 16 … row sums 1, 2, 8, 40, 256, 1952, 17408, 177280, …
  (−∞, −1] nonnegative
• A152842 → θ+1
  1 · 1, 6 · 1, 8, 9 · 1, 14, 45, 36 … row sums 1, 7, 18, 96, 224, 1088, 2432, 11264, …
  (−∞, 0] nonnegative
• A007318 → basis A049020 → x ↦ x/(x+1)
  1 · 2, 3 · 5, 15, 11 · 15, 67, 98, 47 … row sums 1, 5, 31, 227, 1897, 17693, 181351, …
  [−1, 0] nonnegative
• A172431 → x ↦ x/(x+1)
  1 · 1, 3 · 1, 6, 8 · 1, 9, 25, 21 … row sums 1, 4, 15, 56, 209, 780, 2911, 10864, …
  [−1, 0] nonnegative
• A272866 → D+1
  1 · 4, 5, 1 · 7, 28, 29, 10, 1 … row sums 1, 10, 75, 500, 3125, 18750, 109375, …
  (−∞, 0] nonnegative
• basis-map coefficients of Triangle read by rows: T(n,k) = binomial(k,n-k). shifted by x -> -x + 0
  1 · 0, -1 · 0, 0, 1 · 0, 0, 0, -1 … row sums 1, -1, 1, -1, 1, -1, 1, -1, …
  [−1, 0] rational roots
• A007318 → ×(1+(3/2)n+(1/2)n²) → D
  3 · 12, 12 · 30, 60, 30 · 60, 180, 180, 60 … row sums 0, 3, 24, 120, 480, 1680, 5376, 16128, …
  (−∞, 0] nonnegative rational roots
• A123519 → x ↦ x+1
  11, 14, 4 · 41, 76, 44, 8 · 153, 372, 324, 120, 16 … row sums 29, 169, 985, 5741, 33461, 195025, …
  (−3, −1) nonnegative
• A173018 → reverse (shift +1) → D+1
  1 · 1, 1 · 1, 3, 1 · 1, 9, 7, 1 … row sums 1, 2, 5, 18, 84, 480, 3240, 25200, …
  (−∞, 0] nonnegative
• A172431 → ⊙ C(n,k+1) (shift -1) → x ↦ x/(x+1)
  1 · 1, 2 · 1, 6, 6 · 1, 12, 31, 21 … row sums 1, 3, 13, 65, 353, 2023, 12041, 73713, …
  [−1, 0] nonnegative
• A094638 → (θ+1)²
  1 · 1, 4 · 1, 12, 18 · 1, 24, 99, 96 … row sums 1, 5, 31, 220, 1756, 15596, 152804, …
  (−∞, 0] nonnegative
• A008277 → θ+2 (shift +1) → θ+1
  2 · 2, 6 · 2, 18, 12 · 2, 42, 72, 20 … row sums 2, 8, 32, 136, 622, 3060, 16130, 90688, …
  (−∞, 0] nonnegative
• A103327 → θ+1
  1 · 3, 2 · 5, 20, 3 · 7, 70, 63, 4 … row sums 1, 5, 28, 144, 704, 3328, 15360, 69632, …
  (−∞, 0] nonnegative
• A114655 → x ↦ x/(x+1)
  2 · 4, 6 · 8, 28, 22 · 16, 96, 168, 90 … row sums 2, 10, 58, 370, 2514, 17850, 130890, …
  [−1, 0] nonnegative
• A122542 → x ↦ x/(x+1)
  1 · 0, 1 · 0, 2, 3 · 0, 2, 8, 7 … row sums 1, 1, 5, 17, 61, 217, 773, 2753, …
  [−1, 0] nonnegative
• A007318 → D+1 → x ↦ x+1
  1 · 3, 1 · 8, 6, 1 · 20, 24, 9, 1 … row sums 1, 4, 15, 54, 189, 648, 2187, 7290, …
  (−∞, −1] nonnegative rational roots
• A089627: T(n,k) = binomial(n,2*k)*binomial(2*k,k) for 0 <= k <= n, triangle read by rows.
  A059344 → ⊙ 1/k! (shift -1)
  1 · 1 · 1, 2 · 1, 6 … row sums 1, 1, 3, 7, 19, 51, 141, 393, …
  A089627 (−∞, 0] nonnegative
• A026729 → D+1
  1 · 1, 1 · 1, 3, 1 · 0, 4, 5, 1 … row sums 1, 2, 5, 10, 20, 38, 71, 130, …
  (−∞, 0] nonnegative
• A121574 → (θ+1)²
  1 · 2, 4 · 4, 20, 9 · 8, 64, 72, 16 … row sums 1, 6, 33, 160, 726, 3144, 13159, 53652, …
  (−∞, 0] nonnegative
• A054142 → reverse
  1 · 1, 1 · 1, 3, 1 · 1, 6, 5, 1 … row sums 1, 2, 5, 13, 34, 89, 233, 610, …
  (−∞, 0] nonnegative
• A099093 → x ↦ x−6
  1 · -18, 3 · 306, -105, 9 · -5184, 2700, -468, 27 … row sums 1, -15, 210, -2925, 40725, -567000, …
  (14/3, 6]
• A091044 → (θ+1)²
  1 · 2, 8 · 3, 40, 27 · 4, 112, 252, 64 … row sums 1, 10, 70, 432, 2464, 13312, 69120, …
  (−∞, 0] nonnegative
• A100861 → D
  1 · 3 · 6, 6 · 10, 30 … row sums 0, 0, 1, 3, 12, 40, 150, 546, …
  (−∞, 0] nonnegative
• A207607 → D+1
  1 · 3, 2 · 6, 9, 2 · 10, 27, 15, 2 … row sums 1, 5, 17, 54, 166, 499, 1475, 4303, …
  (−∞, 0] nonnegative
• A169803 → θ+1
  1 · 1, 2 · 1, 4 · 1, 6, 3 … row sums 1, 3, 5, 10, 18, 33, 59, 105, …
  (−∞, 0] nonnegative
• A091042 → D
  3 · 10, 10 · 21, 70, 21 · 36, 252, 252, 36 … row sums 0, 3, 20, 112, 576, 2816, 13312, 61440, …
  (−∞, 0] nonnegative
• A094638: Triangle read by rows: T(n,k) = |s(n,n+1-k)|, where s(n,k) are the signed Stirling numbers of the first kind A008276 (1 <= k <= n; in other words, the unsigned Stirling numbers of the first …
  1 · 1, 1 · 1, 3, 2 · 1, 6, 11, 6 … row sums 1, 2, 6, 24, 120, 720, 5040, 40320, …
  A094638 (−∞, 0) nonnegative rational roots
• narayana → x ↦ x/(x+1)
  1 · 1, 2 · 1, 5, 5 · 1, 9, 21, 14 … row sums 1, 3, 11, 45, 197, 903, 4279, 20793, …
  [−1, 0] nonnegative
• A078812 → x ↦ x/(x+1)
  1 · 2, 3 · 3, 10, 8 · 4, 22, 38, 21 … row sums 1, 5, 21, 85, 341, 1365, 5461, 21845, …
  [−1, 0) nonnegative
• A116414 → θ+1
  1 · 4, 2 · 13, 16, 3 · 40, 84, 36, 4 … row sums 1, 6, 32, 164, 819, 4012, 19363, 92352, …
  (−∞, 0] nonnegative
• A304236 → basis A007318
  1 · 1 · 4, 3 · 7, 6 … row sums 1, 1, 7, 13, 55, 133, 463, 1261, …
  (−∞, −1] nonnegative
• A007318 → ⊙ C(n+1,k+1) (shift +2) → reverse
  8 · 18, 12 · 32, 64, 16 · 50, 200, 150, 20 … row sums 8, 30, 112, 420, 1584, 6006, 22880, …
  (−∞, 0] nonnegative
• A026374 → D
  1 · 3, 2 · 4, 8, 3 · 6, 22, 18, 4 … row sums 0, 1, 5, 15, 50, 125, 375, 875, …
  (−∞, 0] nonnegative
• A007318 → ×(1+2n+n²) → (θ+1)²
  1 · 4, 16 · 9, 72, 81 · 16, 192, 432, 256 … row sums 1, 20, 162, 896, 4000, 15552, 54880, …
  (−∞, 0] nonnegative
• A026374: Triangular array T read by rows: T(n,0) = T(n,n) = 1 for all n >= 0, T(n,k) = T(n-1,k-1) + T(n-1,k) for odd n and 1< = k <= n-1, T(n,k) = T(n-1,k-1) + T(n-1,k) + T(n-2,k-1) for even n and 1 …
  1 · 1, 1 · 1, 3, 1 · 1, 4, 4, 1 … row sums 1, 2, 5, 10, 25, 50, 125, 250, …
  A026374 (−∞, 0] nonnegative