Sequences

3,043 sequences

• A085478: Triangle read by rows: T(n, k) = binomial(n + k, 2*k).
  1 · 1, 1 · 1, 3, 1 · 1, 6, 5, 1 … row sums 1, 2, 5, 13, 34, 89, 233, 610, …
  A085478 (−4, 0) nonnegative
• A128099 → basis A008277
  1 · 1 · 3, 2 · 5, 4 … row sums 1, 1, 5, 9, 33, 77, 261, 705, …
  (−∞, 0] nonnegative
• A007318 → D → Veronese 2 (j=1)
  2 · 6 · 12, 4 · 20, 20 … row sums 0, 0, 2, 6, 16, 40, 96, 224, …
  (−∞, 0] nonnegative
• 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
• A318772 → basis A013610
  1 · 1 · 1 · 1 … row sums 1, 1, 1, 1, 13, 25, 37, 49, …
  (−∞, 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
• A023531 → 2D+1+2n → Veronese 2 (j=1)
  3 · 4 · 0, 7 · 0, 8 … row sums 0, 3, 4, 7, 8, 11, 12, 15, …
  (−∞, 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
• A028326 → basis A013610
  2 · 4, 6 · 8, 24, 18 · 16, 72, 108, 54 … row sums 2, 10, 50, 250, 1250, 6250, 31250, …
  (−∞, 0] nonnegative rational roots
• 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
• A038338 → γ
  144 · 1728 · 20736 · 248832 … row sums 144, 1728, 20736, 248832, 2985984, …
  (−∞, 0] nonnegative rational roots
• 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
• A110441 → basis A013609
  1 · 4, 2 · 14, 16, 4 · 48, 88, 48, 8 … row sums 1, 6, 34, 192, 1084, 6120, 34552, …
  (−∞, 0] nonnegative
• A038281: Triangle whose (i,j)-th entry is binomial(i,j)*8^(i-j)*3^j.
  64, 48, 9 · 512, 576, 216, 27 … row sums 121, 1331, 14641, 161051, 1771561, …
  A038281 (−∞, 0) nonnegative rational roots
• basis-map coefficients of A026729, shifted → Veronese 2 (j=1)
  -1 · 0, -1 · 0, 0, -1 · 0, 0, 0, -1 … row sums 0, -1, 0, -1, 0, -1, 0, -1, …
  (−∞, 0] rational roots
• 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
• A038303 → basis A013609
  1 · 11, 2 · 121, 44, 4 · 1331, 726, 132, 8 … row sums 1, 13, 169, 2197, 28561, 371293, …
  (−∞, 0] nonnegative rational roots
• 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
• A023531 → (1/2)D²+2D+1 → x ↦ x/(x+1)
  1 · 2, 3 · 1, 6, 6 · 0, 3, 12, 10 … row sums 1, 5, 13, 25, 41, 61, 85, 113, …
  [−1, 0] nonnegative
• A106800 → Pₙ + Pₙ₊₁
  2 · 2, 1 · 2, 4, 1 · 2, 9, 8, 1 … row sums 2, 3, 7, 20, 67, 255, 1080, 5017, …
  (−∞, ∞) nonnegative
• A008459 → basis A013610
  1 · 2, 3 · 6, 18, 9 · 20, 90, 108, 27 … row sums 1, 5, 33, 245, 1921, 15525, 127905, …
  (−∞, 0] nonnegative
• A104684 → basis A007318
  1 · 3, 1 · 13, 8, 1 · 63, 57, 15, 1 … row sums 1, 4, 22, 136, 886, 5944, 40636, …
  (−∞, −1] nonnegative
• A318773: Triangle T(n,k) = 3*T(n-1,k) + T(n-4,k-1) for k = 0..floor(n/4), with T(0,0) = 1 and T(n,k) = 0 for n or k < 0, read by rows.
  A318772 → x ↦ (1/243)x
  1 · 3 · 9 · 27 … row sums 1, 3, 9, 27, 82, 249, 756, 2295, …
  A318773 (−∞, 0] nonnegative
• A008292 → γ (shift +1) → θ+1
  1 · 1 · 1, 4 · 1, 16 … row sums 1, 1, 5, 17, 93, 513, 3477, 25569, …
  (−∞, 0] nonnegative
• A126351 → D+1
  1 · 3, 2 · 6, 13, 4 · 10, 47, 43, 8 … row sums 1, 5, 23, 108, 534, 2803, 15623, 92249, …
  (−∞, 0] nonnegative
• A178820 → x ↦ x/(x+1)
  1 · 4, 8 · 10, 40, 40 · 20, 120, 240, 160 … row sums 1, 12, 90, 540, 2835, 13608, 61236, …
  [−1, 0] nonnegative rational roots
• A100861 → reverse → x ↦ x+1
  1 · 1, 1 · 2, 3, 1 · 4, 9, 6, 1 … row sums 1, 2, 6, 20, 76, 312, 1384, 6512, …
  (−∞, −1] nonnegative
• A085881 → basis A008277
  1 · 2, 1 · 12, 15, 3 · 120, 285, 135, 15 … row sums 1, 3, 30, 555, 15855, 636930, 33918885, …
  (−∞, 0] nonnegative
• A173018 → (θ+1)²
  1 · 1 · 1, 4 · 1, 16, 9 … row sums 1, 1, 5, 26, 160, 1140, 9240, 84000, …
  (−∞, 0] nonnegative
• A102547 → x ↦ (1/27)x → basis A013611
  1 · 3 · 9 · 28, 4 … row sums 1, 3, 9, 32, 111, 378, 1294, 4437, …
  (−∞, 0] nonnegative
• A132393 → (θ+1)²
  1 · 0, 4 · 0, 4, 9 · 0, 8, 27, 16 … row sums 1, 4, 13, 51, 244, 1392, 9260, 70508, …
  (−∞, 0] nonnegative
• A152198 → basis A008277
  1 · 1 · 2, 1 · 2, 1 … row sums 1, 1, 3, 3, 10, 10, 37, 37, …
  (−∞, 0] nonnegative
• A059344 → ⊙ 1/k! (shift -1) → x ↦ x+1
  1 · 1 · 3, 2 · 7, 6 … row sums 1, 1, 5, 13, 49, 161, 581, 2045, …
  (−∞, −1] nonnegative
• A154228 → basis A013609
  1 · 2, 2 · 18, 36, 4 · 96, 288, 200, 8 … row sums 1, 4, 58, 592, 11938, 209368, 5851432, …
  (−∞, 0] nonnegative
• A007318 → 2θ+1 → Veronese 2 (j=1)
  3 · 6 · 9, 7 · 12, 28 … row sums 0, 3, 6, 16, 40, 96, 224, 512, …
  (−∞, 0] nonnegative
• A132393 → D+1
  1 · 1, 1 · 1, 3, 1 · 2, 8, 6, 1 … row sums 1, 2, 5, 17, 74, 394, 2484, 18108, …
  (−∞, 0] nonnegative
• A132393 → basis A013611
  1 · 1, 4 · 2, 12, 16 · 6, 44, 96, 64 … row sums 1, 5, 30, 210, 1680, 15120, 151200, …
  (−∞, 0] nonnegative rational roots
• A135838 → γ
  1 · 2 · 2 · 4 … row sums 1, 2, 2, 4, 4, 8, 8, 16, …
  (−∞, 0] nonnegative rational roots
• A128813 → basis A013611
  1 · 2, 4 · 8, 40, 48 · 56, 472, 1296, 1152 … row sums 1, 6, 96, 2976, 151776, 11534976, …
  (−∞, 0] nonnegative rational roots
• A341287: Triangle read by rows: T(n,k) = Sum_{i=0..n-1} binomial(n-1, i)*T(n-1-i,k-1) - Sum_{i=1..n-1} binomial(n-1,i)*T(n-1-i,k) for 1 <= k <= n+1 with T(0,1) = 1 (and T(n,k) = 0 otherwise).
  A023531 → basis A341287
  1 · 0, 1 · -1, 1, 1 · -1, -2, 3, 1 … row sums 1, 1, 1, 1, 1, 1, 1, 1, …
  A341287 (−∞, 1]
• A027467 → Pₙ + Pₙ₊₁
  16, 1 · 240, 31, 1 · 3600, 705, 46, 1 … row sums 17, 272, 4352, 69632, 1114112, …
  (−∞, ∞) nonnegative rational roots
• A116412 → basis A007318
  1 · 4, 1 · 13, 8, 1 · 43, 42, 12, 1 … row sums 1, 5, 22, 98, 436, 1940, 8632, 38408, …
  (−∞, −1] nonnegative
• A204420: Triangle T(n,k) giving number of degree-2n permutations which decompose into exactly k cycles of even length, k=0..n.
  1 · 0, 1 · 0, 6, 3 · 0, 120, 90, 15 … row sums 1, 1, 9, 225, 11025, 893025, 108056025, …
  A204420 (−∞, 0] nonnegative rational roots
• A062196 → Pₙ + Pₙ₊₁
  2, 3 · 2, 11, 6 · 2, 23, 36, 10 · 2, 39, 120, 90, 15 … row sums 5, 19, 71, 266, 1002, 3795, 14443, …
  (−∞, ∞) nonnegative
• A257611 → Pₙ + Pₙ₊₁
  4, 3 · 12, 33, 9 · 36, 243, 222, 27 … row sums 7, 54, 528, 6240, 86400, 1370880, …
  (−∞, ∞) nonnegative