Sequences

• A104684 → D → θ+1
  1 · 6, 4 · 30, 48, 9 · 140, 360, 180, 16 … Σ 0, 1, 10, 87, 696, 5265, 38298, 270655, …
  (−∞, 0]nonnegative
• A055151 → basis A007318 → D+1
  1 · 1 · 3, 1 · 7, 3 … Σ 1, 1, 4, 10, 35, 111, 386, 1324, …
  (−∞, 0]nonnegative
• A094816 → x ↦ x+1 → reverse
  1 · 1, 2 · 1, 5, 5 · 1, 9, 23, 16 … Σ 1, 3, 11, 49, 261, 1631, 11743, 95901, …
  (−∞, 0]nonnegative
• A143491 → x ↦ x/(x+1)
  6, 17, 12 · 24, 98, 133, 60 … Σ 35, 315, 3465, 45045, 675675, 11486475, …
  [−1, 0]nonnegativerational roots
• A094638 → basis A013609 → basis A013611
  1 · 4, 8 · 28, 120, 128 · 280, 1872, 4160, 3072 … Σ 1, 12, 276, 9384, 422280, 23647680, …
  (−∞, 0]nonnegativerational roots
• A124038 → D+1
  1 · -1, 1 · -3, 0, 1 · 0, -6, 1, 1 … Σ 1, 0, -2, -4, -3, 2, 7, 6, …
  (−∞, ∞)
• A108838 → x ↦ x+1
  2 · 5, 2 · 14, 12, 2 · 42, 56, 21, 2 … Σ 2, 7, 28, 121, 550, 2591, 12536, 61921, …
  (−∞, −1]nonnegative
• A038301 → x ↦ x+1 → x ↦ x+1
  961, 682, 121 · 29791, 31713, 11253, 1331 … Σ 1764, 74088, 3111696, 130691232, …
  (−∞, −1]nonnegativerational roots
• A132774 → Veronese 2 (j=1) → x ↦ x+1
  3 · 4 · 7, 7 · 8, 8 … Σ 0, 3, 4, 14, 16, 44, 48, 120, …
  (−∞, −1]nonnegativerational roots
• A159854 → θ+1
  0, 0, 3 · 0, 0, 3, 4 · 0, 0, 3, 8, 5 … Σ 3, 7, 16, 36, 80, 176, 384, 832, …
  (−∞, 0]nonnegativerational roots
• A207606 → Veronese 2 (j=1)
  7 · 16, 2 · 30, 15 · 50, 64, 2 … Σ 7, 18, 45, 116, 304, 798, 2091, 5474, …
  (−∞, 0]nonnegative
• A110441 → basis A007318 → reverse
  1 · 1, 4 · 1, 8, 14 · 1, 12, 44, 48 … Σ 1, 5, 23, 105, 479, 2185, 9967, 45465, …
  (−1, 0]nonnegative
• A059344 → basis A007318 → basis A013609
  1 · 1 · 5, 4 · 13, 12 … Σ 1, 1, 9, 25, 241, 1041, 10681, 60649, …
  (−∞, 0]nonnegative
• A207607 → basis A013609 → basis A007318
  1 · 7, 4 · 34, 34, 8 · 163, 234, 108, 16 … Σ 1, 11, 76, 521, 3571, 24476, 167761, …
  (−∞, 0]nonnegative
• A085478 → basis A013611 → basis A013611
  1 · 1 · 6, 16 · 41, 208, 256 … Σ 1, 1, 22, 505, 11593, 266134, 6109489, …
  (−∞, 0]nonnegative
• A086645 → basis A007318 → θ+1
  1 · 2, 2 · 8, 16, 3 · 32, 96, 54, 4 … Σ 1, 4, 27, 186, 1253, 8288, 54047, …
  (−∞, 0]nonnegative
• basis-map coefficients of A112227 → basis A008277 → x ↦ x/(x+1)
  1, 5, 5 · 1, 10, 23, 15 · 1, 19, 76, 109, 52 … Σ 11, 49, 257, 1539, 10299, 75905, …
  [−1, 0]nonnegative
• A110441 → basis A013609 → reverse
  1 · 2, 4 · 4, 16, 14 · 8, 48, 88, 48 … Σ 1, 6, 34, 192, 1084, 6120, 34552, …
  (−∞, 0]nonnegative
• basis-map coefficients of Triangle read by rows, n>=1, 1<=k<=n, T(n,k) = k*binomial(n,k)^2/(n-k+1).
  1 · 0, 2 · -3, 3, 3 · 0, -12, 12, 4 … Σ 1, 2, 3, 4, 5, 6, 7, 8, …
  (−∞, 1]
• A178820 → basis A013610 → basis A008277
  1 · 20, 12 · 250, 390, 90 · 2500, 7740, 4320, 540 … Σ 1, 32, 730, 15100, 305900, 6258616, …
  (−∞, 0]nonnegative
• A142461: 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 = …
  1 · 1, 1 · 1, 14, 1 · 1, 111, 111, 1 … Σ 1, 2, 16, 224, 4480, 116480, 3727360, …
  (−∞, 0)nonnegative
• A207824 → basis A013610 → D+1
  1 · 9, 3 · 71, 54, 9 · 522, 642, 243, 27 … Σ 1, 12, 134, 1434, 14905, 151668, …
  (−∞, 0]nonnegative
• A131222 → basis A013609
  1 · 1, 2 · 4, 10, 4 · 24, 70, 48, 8 … Σ 1, 3, 18, 150, 1584, 20160, 299520, …
  (−∞, 0]nonnegative
• A144436 → D+1
  1 · 2, 1 · 9, 10, 1 · 24, 69, 26, 1 … Σ 1, 3, 20, 120, 840, 6552, 56896, …
  (−∞, 0]nonnegative
• narayana → basis A007318 → θ+1
  1 · 2, 2 · 5, 10, 3 · 14, 42, 27, 4 … Σ 1, 4, 18, 87, 439, 2278, 12052, 64669, …
  (−∞, 0]nonnegative
• A081577 → x ↦ x+1
  1 · 2, 1 · 6, 6, 1 · 16, 24, 10, 1 … Σ 1, 3, 13, 51, 205, 819, 3277, 13107, …
  (−∞, −1]nonnegative
• A154228 → basis A008277
  1 · 2, 1 · 18, 19, 1 · 96, 195, 53, 1 … Σ 1, 3, 38, 345, 6674, 117814, 3414011, …
  (−∞, 0]nonnegative
• A091042 → Veronese 2 (j=1)
  3 · 10 · 21, 7 · 36, 84 … Σ 0, 3, 10, 28, 120, 528, 2080, 8128, …
  (−∞, 0]nonnegative
• A011973 → basis A013609 → basis A013611
  1 · 1 · 4, 8 · 7, 16 … Σ 1, 1, 12, 23, 155, 408, 2113, 6601, …
  (−∞, 0]nonnegative
• A104684 → basis A013611 → reverse
  1 · 4, 3 · 16, 32, 13 · 64, 240, 228, 63 … Σ 1, 7, 61, 595, 6145, 65527, 712909, …
  (−∞, 0]nonnegative
• A169803 → D
  1 · 2 · 3, 2 · 4, 6 … Σ 0, 1, 2, 5, 10, 20, 38, 71, …
  (−∞, 0]nonnegative
• A113413 → x ↦ x+1
  1 · 3, 1 · 7, 6, 1 · 17, 23, 9, 1 … Σ 1, 4, 14, 50, 178, 634, 2258, 8042, …
  (−∞, −1]nonnegative
• A088996 → basis A013611 → θ+1
  1 · 1, 8 · 3, 40, 96 · 15, 272, 1200, 1536 … Σ 1, 9, 139, 3023, 84489, 2880281, …
  (−∞, 0]nonnegative
• A120909 → Veronese 2
  3 · 3 · 3, 12 · 3, 36 … Σ 3, 3, 15, 39, 123, 363, 1095, 3279, …
  (−∞, 0]nonnegative
• A038303 → basis A013610
  1 · 11, 3 · 121, 66, 9 · 1331, 1089, 297, 27 … Σ 1, 14, 196, 2744, 38416, 537824, …
  (−∞, −1]nonnegativerational roots
• A034870 → θ+1
  1 · 1, 4, 3 · 1, 8, 18, 16, 5 … Σ 1, 8, 48, 256, 1280, 6144, 28672, …
  (−∞, 0]nonnegativerational roots
• A089231 → θ+1
  1 · 1, 4 · 1, 12, 18 · 1, 24, 108, 96 … Σ 1, 5, 31, 229, 1961, 19081, 207775, …
  (−∞, 0]nonnegative
• basis-map coefficients of A026729 → (θ+1)² → basis A013609
  1 · 4, 8 · 9, 36, 36 · 16, 96, 192, 128 … Σ 1, 12, 81, 432, 2025, 8748, 35721, …
  (−∞, 0]nonnegativerational roots
• A038322 → basis A013609 → θ+1
  1 · 19, 32 · 361, 1216, 768 … Σ 1, 51, 2345, 101675, 4244625, …
  (−∞, 0]nonnegativerational roots
• A081581 → basis A007318
  1 · 2, 1 · 10, 10, 1 · 32, 48, 18, 1 … Σ 1, 3, 21, 99, 549, 2835, 15093, 79299, …
  (−∞, −1]nonnegative
• A038207 → basis A008277 → D
  1 · 7, 2 · 37, 24, 3 · 175, 194, 54, 4 … Σ 0, 1, 9, 64, 427, 2821, 18890, 129683, …
  (−∞, 0]nonnegative
• A143494 → reverse → D
  2 · 5, 8 · 9, 38, 24 · 14, 110, 195, 64 … Σ 0, 2, 13, 71, 383, 2129, 12360, 75242, …
  (−∞, 0]nonnegative
• A038336 → basis A013609 → basis A007318
  1764, 1680, 400 · 74088, 105840, 50400, 8000 … Σ 3844, 238328, 14776336, 916132832, …
  (−∞, −1]nonnegativerational roots
• A008277 → D → D
  2 · 12, 6 · 50, 60, 12 · 180, 390, 180, 20 … Σ 0, 0, 2, 18, 122, 770, 4832, 30940, …
  (−∞, 0]nonnegative
• A091044 → Veronese 2 (j=1)
  2 · 10 · 28, 4 · 60, 60 … Σ 0, 2, 10, 32, 120, 512, 2080, 8192, …
  (−∞, 0]nonnegative
• A257609 → (θ+1)²
  1 · 2, 8 · 4, 64, 36 · 8, 352, 792, 128 … Σ 1, 10, 104, 1280, 18240, 295680, …
  (−∞, 0]nonnegative
• A111049: Triangle T(n,k), 0 <= k <= n, read by rows, given by [1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...] DELTA [1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...] w…
  1 · 1, 1 · 1, 3, 2 · 1, 6, 9, 4 … Σ 1, 2, 6, 20, 72, 272, 1056, 4160, …
  (−∞, 0)nonnegativerational roots
• A085880 → D+1
  1 · 2, 1 · 6, 8, 2 · 20, 45, 30, 5 … Σ 1, 3, 16, 100, 672, 4704, 33792, …
  (−∞, 0]nonnegativerational roots
• A185410 → reverse → (θ+1)²
  1 · 0, 4 · 0, 8, 9 · 0, 16, 90, 16 … Σ 1, 4, 17, 122, 1173, 13920, 195405, …
  (−∞, 0]nonnegative
• A132393 → D+1 → basis A013610
  1 · 2, 3 · 5, 15, 9 · 17, 69, 81, 27 … Σ 1, 5, 29, 194, 1478, 12664, 120696, …
  (−∞, 0]nonnegative