Sequences

3,043 sequences

• 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
• A085881 → basis A007318
  1 · 2, 1 · 12, 12, 3 · 120, 180, 90, 15 … row sums 1, 3, 27, 405, 8505, 229635, 7577955, …
  (−∞, 0] nonnegative rational roots
• A290316 → Pₙ + Pₙ₊₁
  2, 6 · 2, 54, 90 · 2, 282, 2304, 2160 … row sums 8, 146, 4748, 218906, 13035296, …
  (−∞, ∞) nonnegative
• A257614 → γ
  1 · 2 · 4, 20 · 8, 220 … row sums 1, 2, 24, 228, 3996, 75132, 1850364, …
  (−∞, 0] nonnegative
• A109692 → basis A013611
  1 · 2, 4 · 8, 40, 48 · 48, 400, 1088, 960 … row sums 1, 6, 96, 2496, 89856, 4133376, …
  (−∞, 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
• A038221 → basis A013609
  1 · 6, 6 · 36, 72, 36 · 216, 648, 648, 216 … row sums 1, 12, 144, 1728, 20736, 248832, …
  (−∞, 0] nonnegative rational roots
• 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
• A069466 → basis A008277
  1 · 4, 2 · 36, 42, 6 · 400, 860, 300, 20 … row sums 1, 6, 84, 1580, 35350, 895608, …
  (−∞, 0] nonnegative
• A102547 → basis A013611
  1 · 1 · 1 · 2, 4 … row sums 1, 1, 1, 6, 11, 16, 46, 101, …
  (−∞, 0] 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
• A122431 → basis A013610
  8, 36, 54, 27 · 8, 60, 162, 189, 81 … row sums 125, 500, 2000, 8000, 32000, 128000, …
  (−∞, 0] nonnegative rational roots
• 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
• A038231 → Veronese 2
  1 · 4 · 16, 1 · 64, 12 … row sums 1, 4, 17, 76, 353, 1684, 8177, 40156, …
  (−∞, 0] 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
• A088996 → basis A013611
  1 · 1, 4 · 3, 20, 32 · 15, 136, 400, 384 … row sums 1, 5, 55, 935, 21505, 623645, 21827575, …
  (−∞, 0] nonnegative rational roots
• A011973 → basis A013610
  1 · 1 · 2, 3 · 3, 6 … row sums 1, 1, 5, 9, 29, 65, 181, 441, …
  (−∞, 0] nonnegative
• A142460: Triangle read by rows: T(n,k) (1<=k<=n) given by T(n, 1) = T(n,n) = 1, otherwise T(n, k) = (m*n-m*k+1)*T(n-1,k-1) + (m*k-m+1)*T(n-1,k), where m = 5.
  1 · 1, 1 · 1, 12, 1 · 1, 83, 83, 1 … row sums 1, 2, 14, 168, 2856, 62832, 1696464, …
  A142460 (−∞, 0) nonnegative
• A030528 → basis A013611
  1 · 2, 4 · 3, 16, 16 · 5, 40, 96, 64 … row sums 1, 6, 35, 205, 1200, 7025, 41125, …
  (−∞, 0] nonnegative
• A033282 → basis A008277
  1 · 3, 2 · 11, 20, 5 · 45, 170, 105, 14 … row sums 1, 5, 36, 334, 3753, 49097, 728269, …
  (−∞, 0] nonnegative
• A038336 → basis A013610
  484, 1320, 900 · 10648, 43560, 59400, 27000 … row sums 2704, 140608, 7311616, 380204032, …
  (−∞, 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
• A039756 → Pₙ + Pₙ₊₁
  2, 1 · 2, 5, 1 · 2, 13, 14, 1 · 2, 25, 71, 41, 1 … row sums 3, 8, 30, 140, 764, 4736, 32728, …
  (−∞, ∞) nonnegative
• 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
• A028338 → x ↦ −2x+3 → Pₙ + Pₙ₊₁
  -1, 1 · 4, -4, 1 · -18, 21, -8, 1 … row sums 0, 1, -4, 18, -96, 600, -4320, 35280, …
  (−∞, ∞) rational roots
• 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
• A010054 → reverse → Veronese 2
  1 · 0, 7 · 0, 0, 13 · 0, 0, 0, 19 … row sums 1, 0, 7, 0, 13, 0, 19, 0, …
  (−∞, 0] nonnegative rational roots
• A249248 → basis A013610
  1 · 4, 9 · 11, 39, 27 · 38, 195, 279, 81 … row sums 1, 13, 77, 593, 4505, 36757, 309925, …
  (−∞, 0] nonnegative
• A086645 → Veronese 2 (j=1)
  1 · 6 · 15, 1 · 28, 28 … row sums 0, 1, 6, 16, 56, 256, 1056, 4096, …
  (−∞, 0] nonnegative
• A059473 → basis A008277
  1 · 4, 2 · 18, 22, 4 · 80, 184, 80, 8 … row sums 1, 6, 44, 352, 3084, 29344, 300984, …
  (−∞, 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
• A207823 → basis A013610
  1 · 5, 3 · 24, 30, 9 · 115, 219, 135, 27 … row sums 1, 8, 63, 496, 3905, 30744, 242047, …
  (−∞, 0] nonnegative
• A082985 → basis A013610
  1 · 4, 9 · 11, 45, 45 · 29, 168, 315, 189 … row sums 1, 13, 101, 701, 4693, 31021, 204101, …
  (−∞, 0] nonnegative
• A137320 → basis A013611
  1 · 2, 8 · 6, 40, 64 · 24, 208, 576, 512 … row sums 1, 10, 110, 1320, 17160, 240240, …
  (−∞, 0] nonnegative rational roots
• basis-map coefficients of A026729, shifted → basis A013609
  1 · -1, -2 · 1, 4, 4 · -1, -6, -12, -8 … row sums 1, -3, 9, -27, 81, -243, 729, -2187, …
  (−∞, 0] rational roots
• 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