Sequences

3,043 sequences

• A028326 → Veronese 2
  2 · 2 · 2, 2 · 2, 6 … row sums 2, 2, 4, 8, 16, 32, 64, 128, …
  (−∞, 0] 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
• A007318 → D → Veronese 2
  1 · 2 · 3, 3 · 4, 12 … row sums 0, 1, 2, 6, 16, 40, 96, 224, …
  (−∞, 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
• A038323 → Pₙ + Pₙ₊₁
  12, 9 · 132, 207, 81 · 1452, 3465, 2754, 729 … row sums 21, 420, 8400, 168000, 3360000, …
  (−∞, ∞) nonnegative rational roots
• 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
• A114687 → basis A013609
  1 · 3, 4 · 11, 28, 16 · 45, 168, 192, 64 … row sums 1, 7, 55, 469, 4237, 39907, 387739, …
  (−∞, 0] nonnegative
• basis-map coefficients of A112227 → basis A013611
  1, 8, 16 · 1, 12, 48, 64 · 1, 16, 96, 256, 256 … row sums 25, 125, 625, 3125, 15625, 78125, …
  (−∞, 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
• A257621 → γ
  1 · 3 · 9, 24 · 27, 312 … row sums 1, 3, 33, 339, 5409, 95427, 2087937, …
  (−∞, 0] nonnegative
• A166340 → Pₙ + Pₙ₊₁
  2, 27, 20, 1 · 2, 61, 133, 43, 1 … row sums 50, 240, 1400, 9600, 75600, 672000, …
  (−∞, ∞) nonnegative
• A038334 → basis A013611
  400, 1280, 1024 · 8000, 38400, 61440, 32768 … row sums 2704, 140608, 7311616, 380204032, …
  (−∞, 0] nonnegative rational roots
• A038320 → basis A008277
  289, 240, 36 · 4913, 7254, 2484, 216 … row sums 565, 14867, 419161, 12640799, …
  (−∞, 0] nonnegative
• A144439: Triangle T(n, k) = (m*(n-k) + 1)*T(n-1, k-1) + (m*(k-1) + 1)*T(n-1, k) + j*T(n-2, k-1), where T(n, 1) = T(n, n) = 1, m = 2, and j = 2, read by rows.
  1 · 1, 1 · 1, 8, 1 · 1, 31, 31, 1 … row sums 1, 2, 10, 64, 532, 5448, 66440, 941056, …
  A144439 (−∞, 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
• A028338 → x ↦ −2x−1 (shift -1) → Pₙ + Pₙ₊₁
  1, 1 · 0, 0, 1 · 0, 1, -2, 1 · 0, -4, 8, -5, 1 … row sums 2, 1, 0, 0, 0, 0, 0, 0, …
  (−∞, ∞) rational roots
• A102662: Triangle read by rows: T(1,1)=1,T(2,1)=1,T(2,2)=3, T(k-1,r-1)+T(k-1,r)+T(k-2,r-1).
  1 · 1, 3 · 1, 5, 3 · 1, 7, 11, 3 … row sums 1, 4, 9, 22, 53, 128, 309, 746, …
  A102662 (−∞, 0) nonnegative
• A091042 → basis A013611
  1 · 4, 12 · 16, 80, 80 · 64, 448, 896, 448 … row sums 1, 16, 176, 1856, 19456, 203776, …
  (−∞, 0] nonnegative
• A297191: Irregular triangle read by rows formed by taking every other row of the Delannoy array (A008288) regarded as a triangle.
  basis-map coefficients of A297191, shifted → basis A008288
  1 · 1, 3, 1 · 1, 7, 13, 7, 1 … row sums 1, 5, 29, 169, 985, 5741, 33461, …
  A297191 [−3−2√2, −3+2√2] nonnegative
• A008955 → Pₙ + Pₙ₊₁
  2, 1 · 2, 6, 4 · 2, 19, 53, 36 · 2, 44, 322, 856, 576 … row sums 3, 12, 110, 1800, 45900, 1679600, …
  (−∞, ∞) nonnegative rational roots
• 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
• A008292 → Pₙ + Pₙ₊₁
  2, 1 · 2, 5, 1 · 2, 15, 12, 1 · 2, 37, 77, 27, 1 … row sums 3, 8, 30, 144, 840, 5760, 45360, …
  (−∞, ∞) 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
• A026374 → basis A013610
  1 · 2, 3 · 5, 15, 9 · 10, 45, 63, 27 … row sums 1, 5, 29, 145, 841, 4205, 24389, …
  (−∞, 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
• A013610 → Veronese 2 (j=1)
  3 · 6 · 9, 27 · 12, 108 … row sums 0, 3, 6, 36, 120, 528, 2016, 8256, …
  (−∞, 0] nonnegative
• A038281 → Pₙ + Pₙ₊₁
  576, 624, 225, 27 · 4608, 6720, 3672, 891, 81 … row sums 1452, 15972, 175692, 1932612, 21258732, …
  (−∞, ∞) nonnegative rational roots
• 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
• A038226 → basis A013609
  121, 352, 256 · 1331, 5808, 8448, 4096 … row sums 729, 19683, 531441, 14348907, …
  (−∞, 0] nonnegative rational roots
• A249251 → basis A013609
  1 · 4, 6 · 13, 36, 24 · 43, 174, 228, 96 … row sums 1, 10, 73, 541, 4006, 29665, 219673, …
  (−∞, 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, …
  (−∞, ∞)
• A038226 → basis A008277
  121, 240, 64 · 1331, 5528, 3648, 512 … row sums 425, 11019, 324241, 10631107, …
  (−∞, 0] nonnegative
• 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
• A001263 → basis A013610
  1 · 2, 3 · 5, 15, 9 · 14, 63, 81, 27 … row sums 1, 5, 29, 185, 1257, 8925, 65445, …
  (−∞, 0] nonnegative
• 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
• A038277 → basis A013611
  1 · 18, 44 · 324, 1584, 1936 … row sums 1, 62, 3844, 238328, 14776336, …
  (−∞, 0] nonnegative rational roots
• A038329 → basis A013611
  225, 360, 144 · 3375, 8100, 6480, 1728 … row sums 729, 19683, 531441, 14348907, …
  (−∞, 0] nonnegative rational roots