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1381 sequences

• A099040 → basis A007318
  1 · 2, 2 · 6, 10, 4 · 16, 40, 32, 8 … row sums 1, 4, 20, 96, 464, 2240, 10816, 52224, …
  (−∞, −1] nonnegative
• A113953 → x ↦ x−3
  1 · -3, 1 · 3, -4, 1 · 9, 3, -5, 1 … row sums 1, -2, 0, 8, -16, 0, 64, -128, …
  (−5, 3]
• A028326 → θ+1
  2 · 2, 4 · 2, 8, 6 · 2, 12, 18, 8 … row sums 2, 6, 16, 40, 96, 224, 512, 1152, …
  (−∞, 0] nonnegative rational roots
• A063007 → θ+1
  1 · 1, 4 · 1, 12, 18 · 1, 24, 90, 80 … row sums 1, 5, 31, 195, 1221, 7593, 46915, …
  (−∞, 0] nonnegative
• A091042 → x ↦ x/(x+1)
  1 · 1, 4 · 1, 12, 16 · 1, 24, 80, 64 … row sums 1, 5, 29, 169, 985, 5741, 33461, …
  [−1, 0] nonnegative
• A178820 → θ+1
  1 · 4, 8 · 10, 40, 30 · 20, 120, 180, 80 … row sums 1, 12, 80, 400, 1680, 6272, 21504, …
  (−∞, 0] nonnegative rational roots
• A132812 → x ↦ x+1
  1 · 4, 2 · 15, 15, 3 · 56, 84, 36, 4 … row sums 1, 6, 33, 180, 985, 5418, 29953, …
  (−∞, −1] nonnegative
• A059473 → θ+1
  1 · 2, 4 · 4, 20, 12 · 8, 64, 96, 32 … row sums 1, 6, 36, 200, 1068, 5544, 28192, …
  (−∞, 0] nonnegative
• A128099 → (θ+1)²
  1 · 1 · 1, 8 · 1, 16 … row sums 1, 1, 9, 17, 61, 141, 385, 921, …
  (−∞, 0] nonnegative
• basis-map coefficients of A021012 → D+1
  1 · -1, -1 · 0, 4, 2 · 0, 0, -18, -6 … row sums 1, -2, 6, -24, 120, -720, 5040, -40320, …
  (−∞, 0] rational roots
• A007318 → 2θ+1 → (θ+1)²
  1 · 1, 12 · 1, 24, 45 · 1, 36, 135, 112 … row sums 1, 13, 70, 284, 992, 3152, 9376, 26560, …
  (−∞, 0] nonnegative
• A172431 → ⊙ C(n,k+1) (shift -1) → θ+1
  1 · 1, 2 · 1, 8, 3 · 1, 18, 30, 4 … row sums 1, 3, 12, 53, 244, 1152, 5531, 26875, …
  (−∞, 0] nonnegative
• A082985 → x ↦ x+1
  1 · 4, 3 · 11, 15, 5 · 29, 56, 35, 7 … row sums 1, 7, 31, 127, 511, 2047, 8191, 32767, …
  (−∞, −1] nonnegative
• 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).
  1 · 0, 2 · -2, 2, 3 · 0, -8, 8, 4 … row sums 1, 2, 3, 4, 5, 6, 7, 8, …
  (−∞, 1]
• A038220: Triangle whose (i,j)-th entry is binomial(i,j)*3^(i-j)*2^j.
  1 · 3, 2 · 9, 12, 4 · 27, 54, 36, 8 … row sums 1, 5, 25, 125, 625, 3125, 15625, 78125, …
  A038220 (−∞, −1] nonnegative rational roots
• A081578 → D+1
  1 · 2, 1 · 6, 7, 1 · 10, 27, 12, 1 … row sums 1, 3, 14, 50, 183, 637, 2188, 7380, …
  (−∞, 0] nonnegative
• A123519 → θ+1
  1, 12, 12 · 1, 24, 60, 32 · 1, 40, 180, 224, 80 … row sums 25, 117, 525, 2289, 9773, 41065, …
  (−∞, 0] nonnegative
• A039991 → D
  0, -2 · 0, -6 · 0, -16, 0, 4 · 0, -40, 0, 20 … row sums 0, 0, -2, -6, -12, -20, -30, -42, …
  (−∞, ∞)
• A113953 → x ↦ x/(x+1)
  1 · 0, 1 · 0, 2, 3 · 0, 0, 4, 5 … row sums 1, 1, 5, 9, 29, 65, 181, 441, …
  [−1, 0] nonnegative
• A007318 → D → (θ+1)²
  1 · 2, 8 · 3, 24, 27 · 4, 48, 108, 64 … row sums 0, 1, 10, 54, 224, 800, 2592, 7840, …
  (−∞, 0] nonnegative
• A038220 → θ+1
  1 · 3, 4 · 9, 24, 12 · 27, 108, 108, 32 … row sums 1, 7, 45, 275, 1625, 9375, 53125, …
  (−∞, 0] nonnegative rational roots
• A013609 → (θ+1)²
  1 · 1, 8 · 1, 16, 36 · 1, 24, 108, 128 … row sums 1, 9, 53, 261, 1161, 4833, 19197, …
  (−∞, 0] nonnegative
• A060920 → θ+1
  1 · 2, 2 · 5, 10, 3 · 13, 40, 27, 4 … row sums 1, 4, 18, 84, 390, 1784, 8042, 35804, …
  (−∞, ∞) nonnegative
• A063007 → x ↦ x+1
  1 · 3, 2 · 13, 18, 6 · 63, 132, 90, 20 … row sums 1, 5, 37, 305, 2641, 23525, 213445, …
  (−2, −1) nonnegative
• A056939: Array read by antidiagonals: number of antichains (or order ideals) in the poset 3*m*n or plane partitions with rows <= m, columns <= n and entries <= 3.
  A108838 → ⊙ C(n+1,k+1) (shift +1)
  1 · 1, 1 · 1, 4, 1 · 1, 10, 10, 1 … row sums 1, 2, 6, 22, 92, 422, 2074, 10754, …
  A056939 (−∞, 0] nonnegative
• A347823: Triangle read by rows: T(n,k) = (n+k+1)*binomial(n,k), 0 <= k <= n.
  A007318 → θ+1+n
  1 · 2, 3 · 3, 8, 5 · 4, 15, 18, 7 … row sums 1, 5, 16, 44, 112, 272, 640, 1472, …
  A347823 (−∞, 0] nonnegative rational roots
• A113953 → basis A007318
  1 · 1, 1 · 3, 4, 1 · 5, 11, 7, 1 … row sums 1, 2, 8, 24, 80, 256, 832, 2688, …
  (−∞, −1] nonnegative
• A122076 → D+1
  2 · 5, 2 · 15, 12, 2 · 48, 60, 21, 2 … row sums 2, 7, 29, 131, 601, 2735, 12293, 54619, …
  (−∞, ∞) nonnegative
• basis-map coefficients of A145596 → D+1
  1 · 2, 2 · 0, 8, 3 · -8, 8, 20, 4 … row sums 1, 4, 11, 24, 45, 76, 119, 176, …
  (−∞, ∞)
• A099093 → reverse
  1 · 3 · 9, 3 · 27, 18 … row sums 1, 3, 12, 45, 171, 648, 2457, 9315, …
  (−∞, 0] nonnegative
• A178821 → D+1
  1 · 10, 5 · 45, 60, 15 · 140, 315, 210, 35 … row sums 1, 15, 120, 700, 3360, 14112, 53760, …
  (−∞, 0] nonnegative rational roots
• A108838 → ⊙ C(n+2,k+1) (shift +2)
  30, 120, 30 · 60, 600, 600, 60 … row sums 180, 1320, 9660, 70896, 522648, …
  (−∞, 0] nonnegative
• A052553 → D
  1 · 2 · 3, 2 · 4, 6 … row sums 0, 0, 1, 2, 5, 10, 20, 38, …
  (−∞, 0] nonnegative
• A013620 → basis A007318
  1 · 5, 3 · 25, 30, 9 · 125, 225, 135, 27 … row sums 1, 8, 64, 512, 4096, 32768, 262144, …
  (−∞, −1] nonnegative rational roots
• A038208 → (θ+1)²
  1 · 2, 8 · 4, 32, 36 · 8, 96, 216, 128 … row sums 1, 10, 72, 448, 2560, 13824, 71680, …
  (−∞, 0] nonnegative
• A152198 → (θ+1)²
  1 · 1 · 1, 4 · 1, 4 … row sums 1, 1, 5, 5, 18, 18, 56, 56, …
  (−∞, 0] nonnegative
• A272866 → x ↦ x/(x+1)
  1 · 1, 5, 5 · 1, 10, 35, 50, 25 … row sums 1, 11, 121, 1331, 14641, 161051, …
  [−1, 0] nonnegative
• A011973 → basis A007318 → (θ+1)²
  1 · 1 · 2, 4 · 3, 8 … row sums 1, 1, 6, 11, 34, 75, 190, 435, …
  (−∞, 0] nonnegative
• A143495 → reverse
  1 · 1, 3 · 1, 7, 9 · 1, 12, 37, 27 … row sums 1, 4, 17, 77, 372, 1915, 10481, 60814, …
  (−∞, 0] nonnegative
• A099040 → x ↦ x/(x+1)
  1 · 0, 2 · 0, 2, 6 · 0, 0, 8, 16 … row sums 1, 2, 8, 24, 80, 256, 832, 2688, …
  [−1, 0] nonnegative
• A081577 → θ+1
  1 · 1, 2 · 1, 8, 3 · 1, 14, 21, 4 … row sums 1, 3, 12, 40, 132, 420, 1312, 4032, …
  (−∞, 0] nonnegative
• A108838 → ⊙ C(n+1,k+1) (shift +1) → θ+1
  1 · 1, 2 · 1, 8, 3 · 1, 20, 30, 4 … row sums 1, 3, 12, 55, 276, 1477, 8296, 48393, …
  (−∞, 0] nonnegative
• A120909 → D
  6 · 12, 24 · 18, 72, 72 · 24, 144, 288, 192 … row sums 0, 6, 36, 162, 648, 2430, 8748, 30618, …
  (−∞, 0] nonnegative rational roots
• A102365 → (θ+1)²
  1 · 1 · 1, 4 · 1, 20, 9 … row sums 1, 1, 5, 30, 224, 2011, 21057, 251719, …
  (−∞, 0] nonnegative
• A033282 → x ↦ x+1
  1 · 3, 2 · 11, 15, 5 · 45, 93, 63, 14 … row sums 1, 5, 31, 215, 1597, 12425, 99955, …
  (−2, −1) nonnegative
• A100862: Triangle read by rows: T(n,k) is the number of k-matchings of the corona K'(n) of the complete graph K(n) and the complete graph K(1); in other words, K'(n) is the graph constructed from K(n…
  1 · 1, 1 · 1, 3, 1 · 1, 6, 6, 1 … row sums 1, 2, 5, 14, 43, 142, 499, 1850, …
  A100862 (−∞, 0) nonnegative
• type_b_eulerian → γ (scale 1/4) → (θ+1)²
  1 · 1 · 1, 4 · 1, 20 … row sums 1, 1, 5, 21, 118, 782, 6004, 52332, …
  (−∞, 0] nonnegative
• A081579 → x ↦ x/(x+1)
  1 · 1, 2 · 1, 8, 8 · 1, 14, 36, 24 … row sums 1, 3, 17, 75, 361, 1683, 7937, 37275, …
  [−1, 0] nonnegative
• A188440 → D+1
  1 · 1 · 3, 2 · 3, 2 … row sums 1, 1, 5, 5, 21, 21, 81, 81, …
  (−∞, 0] nonnegative rational roots
• narayana → D+1
  1 · 2, 1 · 4, 5, 1 · 7, 18, 9, 1 … row sums 1, 3, 10, 35, 126, 462, 1716, 6435, …
  (−∞, 0] nonnegative