Sequences

• 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
• 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]
• 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
• 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
• A169803 → D
  1 · 2 · 3, 2 · 4, 6 … Σ 0, 1, 2, 5, 10, 20, 38, 71, …
  (−∞, 0]nonnegative
• A113413 → basis A007318
  1 · 3, 1 · 7, 6, 1 · 17, 23, 9, 1 … Σ 1, 4, 14, 50, 178, 634, 2258, 8042, …
  (−∞, −1]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, …
  (−∞, 0]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
• A081581 → basis A007318
  1 · 2, 1 · 10, 10, 1 · 32, 48, 18, 1 … Σ 1, 3, 21, 99, 549, 2835, 15093, 79299, …
  (−∞, −1]nonnegative
• A091044 → Veronese 2 (j=1)
  2 · 10 · 28, 4 · 60, 60 … Σ 0, 2, 10, 32, 120, 512, 2080, 8192, …
  (−∞, 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
• A380860: Triangle read by rows: T(n,m) (0<=m<=n) = number of positive n-digit numbers that have exactly m copies of a specific, previously selected positive ba…
  1 · 8, 1 · 72, 17, 1 · 648, 225, 26, 1 … Σ 1, 9, 90, 900, 9000, 90000, 900000, …
  (−∞, 0)nonnegativerational roots
• A026374 → x ↦ x+1
  1 · 2, 1 · 5, 5, 1 · 10, 15, 7, 1 … Σ 1, 3, 11, 33, 121, 363, 1331, 3993, …
  (−∞, −1]nonnegative
• A038326 → basis A013611
  1 · 23, 48 · 529, 2208, 2304 … Σ 1, 71, 5041, 357911, 25411681, …
  (−∞, 0]nonnegativerational roots
• A033282 → D+1
  1 · 3, 2 · 6, 15, 5 · 10, 51, 63, 14 … Σ 1, 5, 26, 138, 743, 4043, 22180, …
  (−∞, 0]nonnegative
• A145596 → x ↦ x+1
  1 · 4, 2 · 14, 14, 3 · 48, 72, 32, 4 … Σ 1, 6, 31, 156, 785, 3978, 20335, …
  (−∞, −1]nonnegative
• A154986 → basis A007318
  1 · 2, 1 · 6, 6, 1 · 24, 36, 14, 1 … Σ 1, 3, 13, 75, 537, 4611, 46053, 525483, …
  (−∞, −1]nonnegative
• A008277: Triangle of Stirling numbers of the second kind, S2(n,k), n >= 1, 1 <= k <= n.
  1 · 1, 1 · 1, 3, 1 · 1, 7, 6, 1 … Σ 1, 2, 5, 15, 52, 203, 877, 4140, …
  (−∞, 0)nonnegative
• A249250 → reverse
  1 · 3, 1 · 3, 6, 1 · 3, 15, 9, 1 … Σ 1, 4, 10, 28, 76, 208, 568, 1552, …
  (−∞, 0]nonnegative
• basis-map coefficients of Square array of binomial coefficients T(n,k) = binomial(n,k), n >= 0, k >= 0, read by downward antidiagonals. shifted by x -> -x + 0
  1 · 0, -1 · 0, 0, 1 · 0, 0, 0, -1 … Σ 1, -1, 1, -1, 1, -1, 1, -1, …
  [−1, 0]rational roots
• A038329 → basis A013610
  225, 270, 81 · 3375, 6075, 3645, 729 … Σ 576, 13824, 331776, 7962624, 191102976, …
  (−∞, 0]nonnegativerational roots
• A163626 → Pₙ + Pₙ₊₁
  2, -1 · 2, -4, 2 · 2, -10, 14, -6 … Σ 1, 0, 0, 0, 0, 0, 0, 0, …
  (−∞, ∞)
• A304236 → D+1
  1 · 1 · 4, 3 · 7, 6 … Σ 1, 1, 7, 13, 46, 106, 301, 739, …
  (−∞, 0]nonnegative
• A177267: Triangle read by rows: T(n,k) is the number of permutations of {1,2,...,n} having genus k (see first comment for definition of genus).
  5, 1 · 14, 10 · 42, 70, 8 · 132, 420, 168 … Σ 6, 24, 120, 720, 5040, 40320, 362880, …
  (−∞, 0)nonnegative
• A114656 → basis A013611
  1 · 3, 4 · 11, 32, 16 · 45, 204, 240, 64 … Σ 1, 7, 59, 553, 5541, 58107, 629799, …
  (−∞, 0]nonnegative
• A093375 → D+1
  1 · 3, 1 · 7, 6, 1 · 13, 21, 9, 1 … Σ 1, 4, 14, 44, 128, 352, 928, 2368, …
  (−∞, 0]nonnegative
• A099093 → D
  3 · 3, 18 · 0, 36, 81 · 0, 18, 243, 324 … Σ 0, 3, 21, 117, 585, 2754, 12474, 54999, …
  (−∞, 0]nonnegative
• A091044 → basis A013609
  1 · 4, 4 · 16, 32, 12 · 64, 192, 160, 32 … Σ 1, 8, 60, 448, 3344, 24960, 186304, …
  (−∞, 0]nonnegative
• A013612 → basis A008277
  36, 85, 25 · 216, 1115, 825, 125 … Σ 146, 2281, 40791, 816926, 18036311, …
  (−∞, 0]nonnegative
• A091044 → basis A007318
  1 · 4, 2 · 16, 16, 3 · 64, 96, 40, 4 … Σ 1, 6, 35, 204, 1189, 6930, 40391, …
  (−∞, −1]nonnegative
• A054142 → Veronese 2 (j=1)
  1 · 3 · 5, 1 · 7, 10 … Σ 0, 1, 3, 6, 17, 45, 116, 305, …
  (−∞, 0]nonnegative
• A154986 → basis A013609
  1 · 2, 2 · 6, 12, 4 · 24, 72, 56, 8 … Σ 1, 4, 22, 160, 1432, 15328, 190192, …
  (−∞, 0]nonnegative
• A008303: Triangle read by rows: T(n,k) (n >= 1, 0 <= k <= ceiling(n/2)-1) = number of permutations of [n] with k peaks.
  A008292 → γ (scale 1/4) (shift +1)
  1 · 2 · 4, 2 · 8, 16 … Σ 1, 2, 6, 24, 120, 720, 5040, 40320, …
  (−∞, 0]nonnegative
• A060920 → D+1
  1 · 3, 1 · 10, 7, 1 · 33, 38, 12, 1 … Σ 1, 4, 18, 84, 390, 1784, 8042, 35804, …
  (−∞, ∞)nonnegative
• A038231: Triangle whose (i,j)-th entry is binomial(i,j)*4^(i-j).
  1 · 4, 1 · 16, 8, 1 · 64, 48, 12, 1 … Σ 1, 5, 25, 125, 625, 3125, 15625, 78125, …
  (−∞, −1]nonnegativerational roots
• A038291: Triangle whose (i,j)-th entry is binomial(i,j)*9^(i-j)*1^j.
  1 · 9, 1 · 81, 18, 1 · 729, 243, 27, 1 … Σ 1, 10, 100, 1000, 10000, 100000, …
  (−∞, 0)nonnegativerational roots
• A102662 → basis A013609
  1 · 4, 6 · 9, 22, 12 · 22, 76, 80, 24 … Σ 1, 10, 43, 202, 937, 4354, 20227, …
  (−∞, 0]nonnegative
• A021010: Triangle of coefficients of Laguerre polynomials L_n(x) (powers of x in decreasing order).
  A144084 → x ↦ −x (shift -1)
  1 · -1, 1 · 1, -4, 2 · -1, 9, -18, 6 … Σ 1, 0, -1, -4, -15, -56, -185, -204, …
  [0, ∞)
• A013611 → basis A013611
  1 · 5, 16 · 25, 160, 256 · 125, 1200, 3840, 4096 … Σ 1, 21, 441, 9261, 194481, 4084101, …
  (−∞, 0]nonnegativerational roots
• A125092 → D
  4 · 8, 18 · 12, 54, 48 · 16, 108, 192, 100 … Σ 0, 4, 26, 114, 416, 1360, 4128, 11872, …
  (−∞, 0]nonnegative
• A038328 → basis A008277
  196, 60, 4 · 2744, 1352, 192, 8 … Σ 260, 4296, 72256, 1238368, 21646912, …
  (−∞, 0]nonnegative
• A137320 → reverse
  1 · 2 · 4, 2 · 8, 12, 4 … Σ 1, 2, 6, 24, 120, 720, 5040, 40320, …
  (−∞, 0]nonnegativerational roots
• A100861 → (θ+1)²
  1 · 1 · 1, 4 · 1, 12 … Σ 1, 1, 5, 13, 52, 176, 706, 2710, …
  (−∞, 0]nonnegative
• A126216 → D
  1 · 5, 2 · 21, 18, 3 · 84, 112, 42, 4 … Σ 0, 1, 7, 42, 242, 1375, 7773, 43876, …
  (−∞, 0]nonnegative
• A103406 → D+1
  1 · 3, 2 · 5, 10, 3 · 7, 24, 21, 4 … Σ 1, 5, 18, 56, 160, 432, 1120, 2816, …
  (−∞, 0]nonnegative