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1381 sequences

• A173018 → reverse (shift +1) → θ+1
  1 · 0, 2 · 0, 2, 3 · 0, 2, 12, 4 … row sums 1, 2, 5, 18, 84, 480, 3240, 25200, …
  (−∞, 0] nonnegative
• A028326: Twice Pascal's triangle A007318: T(n,k) = 2*C(n,k).
  2 · 2, 2 · 2, 4, 2 · 2, 6, 6, 2 … row sums 2, 4, 8, 16, 32, 64, 128, 256, …
  A028326 (−∞, 0) nonnegative rational roots
• A154986: Triangle T(n, k) = coefficients of p(x, n) where p(x,n) = (x+1)*p(x, n-1) + n*(n-1)*x*p(x, n-2), read by rows.
  1 · 1, 1 · 1, 4, 1 · 1, 11, 11, 1 … row sums 1, 2, 6, 24, 120, 720, 5040, 40320, …
  A154986 (−∞, 0) nonnegative
• A173018 → D
  1 · 4, 2 · 11, 22, 3 · 26, 132, 78, 4 … row sums 0, 0, 1, 6, 36, 240, 1800, 15120, …
  (−∞, 0] nonnegative
• A055356 → D
  1 · 4, 4 · 11, 36, 18 · 26, 196, 288, 96 … row sums 0, 0, 1, 8, 65, 606, 6527, 80364, …
  (−∞, 0] nonnegative
• A034870: Even-numbered rows of Pascal's triangle.
  1 · 1, 2, 1 · 1, 4, 6, 4, 1 · 1, 6, 15, 20, 15, 6, 1 … row sums 1, 4, 16, 64, 256, 1024, 4096, 16384, …
  A034870 (−∞, −1] nonnegative rational roots
• type_b_eulerian → γ (scale 1/4) → D+1
  1 · 1 · 2, 1 · 6, 5 … row sums 1, 1, 3, 11, 52, 300, 2040, 15960, …
  (−∞, 0] nonnegative
• basis-map coefficients of A113214, shifted → θ+1
  1 · -1, -2 · 1, 4, 3 · -1, -6, -9, -4 … row sums 1, -3, 8, -20, 48, -112, 256, -576, …
  (−∞, 0] rational roots
• A038207 → θ+1
  1 · 2, 2 · 4, 8, 3 · 8, 24, 18, 4 … row sums 1, 4, 15, 54, 189, 648, 2187, 7290, …
  (−∞, 0] nonnegative rational roots
• A046716 → D
  1 · 3, 2 · 6, 16, 3 · 10, 58, 72, 4 … row sums 0, 1, 5, 25, 144, 961, 7313, 62525, …
  (−∞, 0] nonnegative
• A249248 → D
  3 · 7, 6 · 12, 44, 9 · 18, 138, 120, 12 … row sums 0, 3, 13, 65, 288, 1325, 6073, 28563, …
  (−∞, 0] nonnegative
• delannoy → x ↦ x/(x+1)
  1 · 1, 2 · 1, 5, 5 · 1, 8, 18, 12 … row sums 1, 3, 11, 39, 139, 495, 1763, 6279, …
  [−1, 0] nonnegative
• A094816 → θ+1
  1 · 1, 2 · 1, 6, 3 · 1, 16, 18, 4 … row sums 1, 3, 10, 39, 181, 995, 6386, 47075, …
  (−∞, 0] nonnegative
• A099097 → x ↦ x−2
  1 · -6, 3 · 34, -35, 9 · -192, 300, -156, 27 … row sums 1, -3, 8, -21, 55, -144, 377, -987, …
  (14/9, 2]
• A334218 → D+1
  1 · 1 · 2, 2 · 3, 9, 3 … row sums 1, 1, 4, 15, 72, 420, 2880, 22680, …
  (−∞, 0] nonnegative
• A008277 → (θ+1)²
  1 · 1, 4 · 1, 12, 9 · 1, 28, 54, 16 … row sums 1, 5, 22, 99, 471, 2386, 12867, 73681, …
  (−∞, 0] nonnegative
• A013611 → θ+1
  1 · 1, 8 · 1, 16, 48 · 1, 24, 144, 256 … row sums 1, 9, 65, 425, 2625, 15625, 90625, …
  (−∞, 0] nonnegative rational roots
• A039991 → D+1
  1 · 1 · 2, -2, -1 · 4, -6, -3 … row sums 1, 1, -1, -5, -11, -19, -29, -41, …
  (−∞, ∞)
• A008277 → θ+1 → D
  2 · 6, 6 · 14, 36, 12 · 30, 150, 120, 20 … row sums 0, 2, 12, 62, 320, 1712, 9604, 56674, …
  (−∞, 0] nonnegative
• A132393 → D
  1 · 1, 2 · 2, 6, 3 · 6, 22, 18, 4 … row sums 0, 1, 3, 11, 50, 274, 1764, 13068, …
  (−∞, 0] nonnegative
• A081579 → basis A007318
  1 · 2, 1 · 8, 8, 1 · 24, 36, 14, 1 … row sums 1, 3, 17, 75, 361, 1683, 7937, 37275, …
  (−∞, −1] nonnegative
• A039756 → x ↦ x+1
  1 · 2, 1 · 6, 6, 1 · 24, 38, 16, 1 … row sums 1, 3, 13, 79, 601, 5339, 53861, 607527, …
  (−∞, −1] nonnegative
• A172431 → ⊙ C(n,k+1) (shift -1) → D
  1 · 4, 2 · 9, 20, 3 · 16, 84, 60, 4 … row sums 0, 1, 6, 32, 164, 830, 4184, 21077, …
  (−∞, 0] nonnegative
• A008278 → x ↦ x+1 (shift +1) → D
  1 · 5, 2 · 23, 20, 3 · 109, 152, 57, 4 … row sums 0, 1, 7, 46, 322, 2427, 19645, 170236, …
  (−∞, 0] nonnegative
• A069138: Triangle formed by multiplying Stirling numbers of 2nd kind S2(n,m) (A008277) by m+1.
  A008277 → θ+2 (shift +1)
  2 · 2, 3 · 2, 9, 4 · 2, 21, 24, 5 … row sums 2, 5, 15, 52, 203, 877, 4140, 21147, …
  A069138 (−∞, 0] nonnegative
• A099097 → x ↦ x−8
  1 · -24, 3 · 568, -143, 9 · -13440, 5088, -642, 27 … row sums 1, -21, 434, -8967, 185269, -3827880, …
  (68/9, 8]
• A102547: Triangle read by rows, formed from antidiagonals of the antidiagonals (A011973) of Pascal's triangle (A007318).
  1 · 1 · 1 · 1, 1 … row sums 1, 1, 1, 2, 3, 4, 6, 9, …
  A102547 (−∞, 0] nonnegative
• type_b_eulerian → γ (scale 1/4) → θ+1
  1 · 1 · 1, 2 · 1, 10 … row sums 1, 1, 3, 11, 52, 300, 2040, 15960, …
  (−∞, 0] nonnegative
• A128099 → x ↦ x+1
  1 · 1 · 3, 2 · 5, 4 … row sums 1, 1, 5, 9, 29, 65, 181, 441, …
  (−∞, −1] nonnegative
• A051379: Generalized Stirling number triangle of first kind read by rows: T(n, k) = [x^k] Product_{m=1..n} (x - m - r), with r = 7.
  A028338 → x ↦ −2x+15
  1 · -8, 1 · 72, -17, 1 · -720, 242, -27, 1 … row sums 1, -7, 56, -504, 5040, -55440, 665280, …
  A051379 [15/2, ∞) rational roots
• A053123 → D+1
  1 · -1, -2 · -3, 2, 3 · -5, 14, -2, -4 … row sums 1, -3, 2, 3, -7, 4, 5, -11, …
  (−∞, ∞)
• A055356 → D+1
  1 · 1 · 2, 1 · 5, 8, 2 … row sums 1, 1, 3, 15, 101, 851, 8603, 101423, …
  (−∞, 0] nonnegative
• A113214 → x ↦ x−9
  1 · -7, 1 · 54, -15, 1 · -423, 173, -23, 1 … row sums 1, -6, 40, -272, 1856, -12672, 86528, …
  (5, 9]
• A113214 → x ↦ x−10
  1 · -8, 1 · 70, -17, 1 · -620, 222, -26, 1 … row sums 1, -7, 54, -423, 3321, -26082, 204849, …
  (6, 10]
• A145596: basis-map coefficients of Triangular array of generalized Narayana numbers: T(n, k) = 2*binomial(n + 1, k + 1)*binomial(n + 1, k - 1)/(n + 1). shifted by x -> x + 1
  1 · 2, 2 · 3, 8, 3 · 4, 20, 20, 4 … row sums 1, 4, 14, 48, 165, 572, 2002, 7072, …
  A145596 (−∞, 0) nonnegative
• A232535 → θ+1
  1 · 1, 4 · 1, 16, 9 · 1, 36, 75, 16 … row sums 1, 5, 26, 128, 608, 2816, 12800, 57344, …
  (−∞, 0] nonnegative
• A249251 → x ↦ x/(x+1)
  1 · 1, 4 · 1, 8, 13 · 1, 12, 42, 43 … row sums 1, 5, 22, 98, 436, 1940, 8632, 38408, …
  [−1, 0] nonnegative
• A007318 → ×(−(1/2)n+(1/2)n²) → x ↦ x/(x+1)
  1, 4, 4 · 3, 18, 36, 24 · 6, 48, 144, 192, 96 … row sums 0, 0, 9, 81, 486, 2430, 10935, 45927, …
  [−1, 0] nonnegative rational roots
• A038220 → (θ+1)²
  1 · 3, 8 · 9, 48, 36 · 27, 216, 324, 128 … row sums 1, 11, 93, 695, 4825, 31875, 203125, …
  (−∞, 0] nonnegative
• A152842 → D
  3 · 4, 6 · 7, 30, 27 · 8, 44, 72, 36 … row sums 0, 3, 10, 64, 160, 832, 1920, 9216, …
  (−∞, 0] nonnegative rational roots
• A011973 → x ↦ x−1/4 → D
  4 · 16 · 40, 32 · 80, 192 … row sums 0, 0, 4, 16, 72, 272, 1004, 3552, …
  (−∞, 0] nonnegative
• A033282 → D
  2 · 5, 10 · 9, 42, 42 · 14, 112, 252, 168 … row sums 0, 2, 15, 93, 546, 3140, 17901, 101675, …
  (−∞, 0] nonnegative
• basis-map coefficients of A021012 → θ+1
  1 · 0, -2 · 0, 0, 6 · 0, 0, 0, -24 … row sums 1, -2, 6, -24, 120, -720, 5040, -40320, …
  (−∞, 0] rational roots
• basis-map coefficients of A132812 → D+1
  1 · 2, 2 · 0, 9, 3 · -12, 12, 24, 4 … row sums 1, 4, 12, 28, 55, 96, 154, 232, …
  (−∞, ∞)
• A154986 → D
  1 · 4, 2 · 11, 22, 3 · 24, 140, 72, 4 … row sums 0, 1, 6, 36, 240, 1800, 15120, 141120, …
  (−∞, 0] nonnegative
• A207607 → x ↦ x/(x+1)
  1 · 1, 3 · 1, 7, 8 · 1, 12, 30, 21 … row sums 1, 4, 16, 64, 256, 1024, 4096, 16384, …
  [−1, 0) nonnegative
• A100862 → D
  1 · 3, 2 · 6, 12, 3 · 10, 42, 30, 4 … row sums 0, 1, 5, 21, 86, 355, 1497, 6475, …
  (−∞, 0] nonnegative
• A227450 → D
  4 · 12, 16 · 28, 96, 48 · 60, 400, 480, 128 … row sums 0, 4, 28, 172, 1068, 6924, 47276, …
  (−∞, 0] nonnegative
• A304236 → D
  3 · 6 · 9, 18 · 12, 54 … row sums 0, 0, 3, 6, 27, 66, 204, 522, …
  (−∞, 0] nonnegative
• A008292 → γ (shift +1) → (θ+1)²
  1 · 1 · 1, 8 · 1, 32 … row sums 1, 1, 9, 33, 233, 1433, 11289, 92097, …
  (−∞, 0] nonnegative