Sequences

3,043 sequences

• A099097 → Veronese 2 (j=1)
  3 · 1 · 0, 27 · 0, 27 … row sums 0, 3, 1, 27, 27, 252, 406, 2457, …
  (−∞, 0] nonnegative
• A027465 → x ↦ x/(x+1)
  1 · 3, 4 · 9, 24, 16 · 27, 108, 144, 64 … row sums 1, 7, 49, 343, 2401, 16807, 117649, …
  [−1, 0] nonnegative rational roots
• A318772 → basis A013609
  1 · 1 · 1 · 1 … row sums 1, 1, 1, 1, 10, 19, 28, 37, …
  (−∞, 0] nonnegative
• A147716 → basis A008277
  1 · 15, 1 · 225, 31, 1 · 3375, 721, 48, 1 … row sums 1, 16, 257, 4145, 67140, 1092427, …
  (−∞, 0] nonnegative
• A318772 → basis A007318
  1 · 1 · 1 · 1 … row sums 1, 1, 1, 1, 7, 13, 19, 25, …
  (−∞, −1] nonnegative
• A088996 → basis A013610
  1 · 1, 3 · 3, 15, 18 · 15, 102, 225, 162 … row sums 1, 4, 36, 504, 9576, 229824, 6664896, …
  (−∞, 0] nonnegative rational roots
• A114687 → reverse
  1 · 2, 1 · 4, 6, 1 · 8, 24, 12, 1 … row sums 1, 3, 11, 45, 197, 903, 4279, 20793, …
  (−∞, 0] nonnegative
• A078812 → D
  1 · 4, 2 · 10, 12, 3 · 20, 42, 24, 4 … row sums 0, 1, 6, 25, 90, 300, 954, 2939, …
  (−∞, 0] nonnegative
• A099097 → x ↦ x−10
  1 · -30, 3 · 890, -179, 9 · -26400, 7980, -804, 27 … row sums 1, -27, 720, -19197, 511839, -13646880, …
  (86/9, 10]
• A143491 → basis A007318
  12, 7, 1 · 60, 47, 12, 1 · 360, 342, 119, 18, 1 … row sums 20, 120, 840, 6720, 60480, 604800, …
  (−∞, 0] nonnegative rational roots
• A091044 → Veronese 2
  1 · 2 · 3, 3 · 4, 28 … row sums 1, 2, 6, 32, 136, 512, 2016, 8192, …
  (−∞, 0] nonnegative
• A103327 → basis A008277
  1 · 4, 1 · 16, 13, 1 · 64, 105, 27, 1 … row sums 1, 5, 30, 197, 1399, 10664, 86651, …
  (−∞, 0] nonnegative
• A317496 → basis A013610
  1 · 1 · 1 · 4, 9 … row sums 1, 1, 1, 13, 25, 37, 193, 493, …
  (−∞, 0] nonnegative
• A051339: Generalized Stirling number triangle of first kind read by rows: T(n, k) = [x^k] Product_{m=1..n} (x - m - r), with r = 6.
  A028338 → x ↦ −2x+13
  1 · -7, 1 · 56, -15, 1 · -504, 191, -24, 1 … row sums 1, -6, 42, -336, 3024, -30240, 332640, …
  A051339 [13/2, ∞) rational roots
• A038208 → Veronese 2
  1 · 2 · 4, 4 · 8, 24 … row sums 1, 2, 8, 32, 128, 512, 2048, 8192, …
  (−∞, 0] nonnegative
• A023531 → D → Veronese 2 (j=1)
  2 · 0, 4 · 0, 0, 6 · 0, 0, 0, 8 … row sums 0, 0, 2, 0, 4, 0, 6, 0, …
  (−∞, 0] nonnegative rational roots
• A122431 → reverse
  1, 3, 3, 1 · 1, 3, 3, 1 · 1, 3, 3, 1 · 1, 3, 3, 1 … row sums 8, 8, 8, 8, 8, 8, 8, 8, …
  (−∞, 0] nonnegative rational roots
• A060187: Triangle read by rows: Eulerian numbers of type B, T(n,k) (1 <= k <= n) given by T(n, 1) = T(n,n) = 1, otherwise T(n, k) = (2*n - 2*k + 1)*T(n-1, k-1) + (2*k - 1)*T(n-1, k).
  1 · 1, 1 · 1, 6, 1 · 1, 23, 23, 1 … row sums 1, 2, 8, 48, 384, 3840, 46080, 645120, …
  A060187 (−∞, 0) nonnegative
• A227450 → x ↦ x+1
  2 · 6, 4 · 22, 28, 8 · 94, 172, 96, 16 … row sums 2, 10, 58, 378, 2714, 21178, 177818, …
  (−∞, −1] nonnegative
• basis-map coefficients of Square array of binomial coefficients T(n,k) = binomial(n,k), n >= 0, k >= 0, read by downward antidiagonals.
  1 · 0, 1 · 0, 0, 1 · 0, 0, 0, 1 … row sums 1, 1, 1, 1, 1, 1, 1, 1, …
  [−1, 0] [0, ∞) nonnegative rational roots
• A059473: Triangle T(n, k) is coefficient of z^n*w^k in 1/(1 - 2*z - 2*w - 2*z*w) read by rows in order 00, 10, 01, 20, 11, 02, ...
  1 · 2, 2 · 4, 10, 4 · 8, 32, 32, 8 … row sums 1, 4, 18, 80, 356, 1584, 7048, 31360, …
  A059473 (−∞, 0) nonnegative
• A122542 → Veronese 2
  1 · 0, 1 · 0, 4 · 0, 8, 1 … row sums 1, 0, 1, 4, 9, 20, 49, 120, …
  (−∞, 0] nonnegative
• A132440: Infinitesimal Pascal matrix: generator (lower triangular matrix representation) of the Pascal matrix, the classical operator xDx, iterated Laguerre transforms, associated matrices of the lis…
  A023531 → D
  1 · 0, 2 · 0, 0, 3 · 0, 0, 0, 4 … row sums 0, 1, 2, 3, 4, 5, 6, 7, …
  A132440 (−∞, 0] nonnegative rational roots
• A290319 → basis A007318
  1 · 2, 1 · 12, 8, 1 · 120, 92, 18, 1 … row sums 1, 3, 21, 231, 3465, 65835, 1514205, …
  (−∞, 0] nonnegative rational roots
• A026374 → basis A008277
  1 · 2, 1 · 5, 6, 1 · 10, 23, 10, 1 … row sums 1, 3, 12, 44, 210, 922, 5108, 26068, …
  (−∞, 0] nonnegative
• A143683: Pascal-(1,8,1) array.
  1 · 1, 1 · 1, 10, 1 · 1, 19, 19, 1 … row sums 1, 2, 12, 40, 176, 672, 2752, 10880, …
  A143683 (−∞, 0) nonnegative
• A123519 → basis A008288
  11, 18, 4 · 41, 112, 60, 8 · 153, 592, 548, 168, 16 … row sums 33, 221, 1477, 9865, 65885, 440025, …
  [−3−2√2, −3+2√2] nonnegative
• A008292 → γ (shift +1) → D
  2 · 8 · 22, 32 · 52, 272 … row sums 0, 0, 2, 8, 54, 324, 2370, 18288, …
  (−∞, 0] nonnegative
• A152828 → basis A013609
  1 · 1 · 1 · 2, 2 … row sums 1, 1, 1, 4, 4, 4, 16, 16, …
  (−∞, 0] nonnegative rational roots
• A334218 → D
  2 · 3, 6 · 4, 32, 12 · 5, 110, 165, 20 … row sums 0, 0, 2, 9, 48, 300, 2160, 17640, …
  (−∞, 0] nonnegative
• A013620 → Pₙ + Pₙ₊₁
  3, 3 · 6, 15, 9 · 12, 48, 63, 27 … row sums 6, 30, 150, 750, 3750, 18750, 93750, …
  (−∞, ∞) nonnegative rational roots
• A013613 → basis A013611
  1 · 7, 24 · 49, 336, 576 · 343, 3528, 12096, 13824 … row sums 1, 31, 961, 29791, 923521, 28629151, …
  (−∞, 0] nonnegative rational roots
• basis-map coefficients of A026729, shifted → basis A013610
  1 · -1, -3 · 1, 6, 9 · -1, -9, -27, -27 … row sums 1, -4, 16, -64, 256, -1024, 4096, …
  (−∞, 0] rational roots
• A082985 → basis A008277
  1 · 4, 3 · 11, 20, 5 · 29, 98, 56, 7 … row sums 1, 7, 36, 190, 1072, 6491, 42030, …
  (−∞, 0] nonnegative
• A026374 → Veronese 2
  1 · 1 · 1, 1 · 1, 4 … row sums 1, 1, 2, 5, 13, 25, 62, 125, …
  (−∞, 0] nonnegative
• A007318 → θ+1+n → reverse
  1 · 3, 2 · 5, 8, 3 · 7, 18, 15, 4 … row sums 1, 5, 16, 44, 112, 272, 640, 1472, …
  (−∞, 0] nonnegative rational roots
• A011973 → x ↦ x−1/4 → θ+1
  1 · 2 · 3, 8 · 4, 32 … row sums 1, 2, 11, 36, 133, 454, 1551, 5192, …
  (−∞, 0] nonnegative
• A008292 → D+1
  1 · 2, 1 · 5, 6, 1 · 12, 33, 14, 1 … row sums 1, 3, 12, 60, 360, 2520, 20160, 181440, …
  (−∞, 0] nonnegative
• A034870 → basis A013610
  1 · 4, 12, 9 · 16, 96, 216, 216, 81 … row sums 1, 25, 625, 15625, 390625, 9765625, …
  (−∞, 0] nonnegative rational roots
• A088996 → basis A013609
  1 · 1, 2 · 3, 10, 8 · 15, 68, 100, 48 … row sums 1, 3, 21, 231, 3465, 65835, 1514205, …
  (−∞, 0] nonnegative rational roots
• basis-map coefficients of A113214, shifted → basis A013611
  1 · -2, -4 · 4, 16, 16 · -8, -48, -96, -64 … row sums 1, -6, 36, -216, 1296, -7776, 46656, …
  (−∞, 0] rational roots
• A081582: Pascal-(1,7,1) array.
  1 · 1, 1 · 1, 9, 1 · 1, 17, 17, 1 … row sums 1, 2, 11, 36, 149, 550, 2143, 8136, …
  A081582 (−∞, 0) nonnegative
• A008288 → 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
• basis-map coefficients of A026729 → basis A013611
  1 · 1, 4 · 1, 8, 16 · 1, 12, 48, 64 … row sums 1, 5, 25, 125, 625, 3125, 15625, 78125, …
  (−∞, 0] nonnegative rational roots
• A113953 → D
  1 · 2, 2 · 0, 8, 3 · 0, 8, 18, 4 … row sums 0, 1, 4, 11, 30, 73, 176, 407, …
  (−∞, 0] nonnegative
• A011973 → ⊙ C(n,k) → x ↦ x+1
  1 · 1 · 3, 2 · 7, 6 … row sums 1, 1, 5, 13, 49, 161, 581, 2045, …
  (−∞, −1] nonnegative
• A257609 → D (shift +2)
  11, 22, 3 · 26, 132, 78, 4 · 57, 604, 906, 228, 5 … row sums 36, 240, 1800, 15120, 141120, 1451520, …
  (−∞, 0] nonnegative
• Triangle read by rows: coefficients of a Bessel polynomial recursion: P(x, n) = 2*(n-1)*P(x, n - 1)/x - n*P(x, n - 2) with substitution x -> 1/y.
  -2, 0, 2 · 0, -11, 0, 8 · 8, 0, -74, 0, 48 … row sums 0, -3, -18, -129, -1182, -13281, …
  (−2, 2)
• A028338 → x ↦ −x+1 → Pₙ + Pₙ₊₁
  -1, 1 · 6, -5, 1 · -40, 38, -11, 1 … row sums 0, 2, -12, 90, -840, 9450, -124740, …
  (−∞, ∞) rational roots
• A102547 → reverse → θ+1
  0, 2 · 0, 0, 3 · 0, 0, 0, 4 · 0, 0, 0, 4, 5 … row sums 2, 3, 4, 9, 16, 25, 42, 70, …
  (−∞, 0] nonnegative