Sequences

3,043 sequences

• A028338 → x ↦ −2x+9 → Pₙ + Pₙ₊₁
  -4, 1 · 25, -10, 1 · -180, 96, -17, 1 … row sums -3, 16, -100, 720, -5880, 53760, …
  (−∞, ∞) rational roots
• A123519 → basis A013611
  11, 56, 64 · 41, 304, 704, 512 … row sums 131, 1561, 18601, 221651, 2641211, …
  (−∞, 0] nonnegative
• A122431 → Veronese 2
  1, 3 · 0, 3, 1 · 0, 1, 3 · 0, 0, 3, 1 … row sums 4, 4, 4, 4, 4, 4, 4, 4, …
  (−∞, 0] nonnegative rational roots
• 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
• A121574 → basis A008277
  1 · 3, 1 · 10, 8, 1 · 33, 47, 14, 1 … row sums 1, 4, 19, 95, 506, 2862, 17143, 108398, …
  (−∞, 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
• A027465 → Veronese 2
  1 · 3 · 9, 1 · 27, 9 … row sums 1, 3, 10, 36, 136, 528, 2080, 8256, …
  (−∞, 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
• A030528 → basis A013609
  1 · 2, 2 · 3, 8, 4 · 5, 20, 24, 8 … row sums 1, 4, 15, 57, 216, 819, 3105, 11772, …
  (−∞, 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
• A038319 → basis A008277
  256, 185, 25 · 4096, 5165, 1575, 125 … row sums 466, 10961, 273631, 7247476, 203358371, …
  (−∞, 0] nonnegative
• A038338 → basis A008277
  576, 720, 144 · 13824, 32832, 15552, 1728 … row sums 1440, 63936, 3131136, 167712768, …
  (−∞, 0] nonnegative
• 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
• A052553 → basis A013610
  1 · 1 · 2, 3 · 3, 6 … row sums 1, 1, 5, 9, 29, 65, 181, 441, …
  (−∞, 0] nonnegative
• 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
• A099040 → basis A013610
  1 · 2, 6 · 6, 30, 36 · 16, 120, 288, 216 … row sums 1, 8, 72, 640, 5696, 50688, 451072, …
  (−∞, 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
• A133087 → basis A013610
  1 · 3, 3 · 4, 12, 9 · 12, 48, 63, 27 … row sums 1, 6, 25, 150, 625, 3750, 15625, 93750, …
  (−∞, 0] nonnegative rational roots
• A099093 → basis A008277
  1 · 3, 3 · 12, 30, 9 · 45, 243, 180, 27 … row sums 1, 6, 51, 495, 5472, 67392, 911655, …
  (−∞, 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
• A118933 → basis A013611
  1 · 1 · 1 · 1 … row sums 1, 1, 1, 1, 31, 151, 451, 1051, …
  (−∞, 0] nonnegative
• A272866 → basis A013611
  1 · 5, 20, 16 · 25, 200, 560, 640, 256 … row sums 1, 41, 1681, 68921, 2825761, 115856201, …
  (−∞, 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
• A091044 → basis A013610
  1 · 4, 6 · 16, 48, 27 · 64, 288, 360, 108 … row sums 1, 10, 91, 820, 7381, 66430, 597871, …
  (−∞, 0] nonnegative
• Triangle read by rows, related to number of permutations of [n] with 0 successions and k rises.
  1, 7, 1 · 1, 21, 21, 1 · 1, 51, 161, 51, 1 … row sums 9, 44, 265, 1854, 14833, 133496, …
  (−∞, 0) nonnegative
• 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
• A013622 → basis A013609
  1 · 8, 10 · 64, 160, 100 · 512, 1920, 2400, 1000 … row sums 1, 18, 324, 5832, 104976, 1889568, …
  (−∞, 0] nonnegative rational roots
• 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
• A178822 → Veronese 2
  1 · 6 · 21, 21 · 56, 168 … row sums 1, 6, 42, 224, 1008, 4032, 14784, …
  (−∞, 0] nonnegative
• A008292 → γ
  1 · 1 · 1, 2 · 1, 8 … row sums 1, 1, 3, 9, 39, 189, 1107, 7281, …
  (−∞, 0] nonnegative
• A144084 → Pₙ + Pₙ₊₁
  2, 1 · 2, 5, 2 · 2, 13, 20, 6 · 2, 25, 90, 102, 24 … row sums 3, 9, 41, 243, 1755, 14873, 144249, …
  (−∞, ∞) nonnegative
• A249250 → basis A013609
  1 · 4, 6 · 10, 24, 12 · 28, 96, 96, 24 … row sums 1, 10, 46, 244, 1252, 6472, 33400, …
  (−∞, 0] nonnegative
• 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
• A145597 → basis A013609
  1 · 6, 6 · 27, 54, 24 · 110, 330, 300, 80 … row sums 1, 12, 105, 820, 6081, 43932, 313012, …
  (−∞, 0] nonnegative
• A126351: Triangle read by rows: matrix product of the Stirling numbers of the second kind with the binomial coefficients.
  1 · 1, 2 · 1, 5, 4 · 1, 9, 19, 8 … row sums 1, 3, 10, 37, 151, 674, 3263, 17007, …
  A126351 (−∞, 0) nonnegative
• A046716 → D
  1 · 3, 2 · 6, 16, 3 · 10, 58, 72, 4 … row sums 0, 1, 5, 25, 144, 961, 7313, 62525, …
  (−∞, 0] nonnegative
• A142461 → Pₙ + Pₙ₊₁
  2, 1 · 2, 15, 1 · 2, 125, 112, 1 … row sums 3, 18, 240, 4704, 120960, 3843840, …
  (−∞, ∞) 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]
• A081578 → basis A013611
  1 · 2, 4 · 7, 28, 16 · 20, 120, 192, 64 … row sums 1, 6, 51, 396, 3141, 24786, 195831, …
  (−∞, 0] nonnegative
• A334218 → D+1
  1 · 1 · 2, 2 · 3, 9, 3 … row sums 1, 1, 4, 15, 72, 420, 2880, 22680, …
  (−∞, 0] nonnegative
• A011973 → x ↦ x+2 (shift +1) → basis A008277
  1 · 4, 1 · 7, 2 · 19, 10, 1 … row sums 1, 5, 9, 30, 68, 200, 503, 1426, …
  (−∞, 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
• A081580 → Veronese 2
  1 · 1 · 1, 1 · 1, 13 … row sums 1, 1, 2, 14, 63, 171, 532, 2044, …
  (−∞, 0] nonnegative
• A038334 → basis A008277
  400, 384, 64 · 8000, 13952, 5376, 512 … row sums 848, 27840, 989440, 37927936, …
  (−∞, 0] nonnegative
• A142462: 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 = 7.
  1 · 1, 1 · 1, 16, 1 · 1, 143, 143, 1 … row sums 1, 2, 18, 288, 6624, 198720, 7352640, …
  A142462 (−∞, 0) nonnegative