Sequences

• A038291 → basis A013610
  1 · 10, 3 · 100, 60, 9 · 1000, 900, 270, 27 … Σ 1, 13, 169, 2197, 28561, 371293, …
  (−∞, 0]nonnegativerational roots
• A104556: Matrix inverse of triangle A001497 of Bessel polynomials, read by rows; essentially the same as triangle A096713 of modified Hermite polynomials.
  1 · -1, 1 · 0, -3, 1 · 0, 3, -6, 1 … Σ 1, 0, -2, -2, 6, 16, -20, -132, …
  [0, ∞)
• A091044 → ⊙ C(n+2,k+1) → γ
  1 · 1 · 1, 3 · 1, 11 … Σ 1, 1, 4, 12, 53, 221, 1055, 5055, …
  (−∞, 0]nonnegative
• A099040 → x ↦ x−12
  1 · -24, 2 · 552, -94, 4 · -12672, 3264, -280, 8 … Σ 1, -22, 462, -9680, 202796, -4248552, …
  (10, 12]
• A048993 → θ+1
  1 · 0, 2 · 0, 2, 3 · 0, 2, 9, 4 … Σ 1, 2, 5, 15, 52, 203, 877, 4140, …
  (−∞, 0]nonnegative
• A290595 → Pₙ + Pₙ₊₁
  2, 2 · 5, 21, 4 · 32, 241, 151, 8 … Σ 4, 30, 432, 8910, 238140, 7807590, …
  (−∞, ∞)nonnegative
• A008288 → (θ+1)²
  1 · 1, 4 · 1, 12, 9 · 1, 20, 45, 16 … Σ 1, 5, 22, 82, 283, 923, 2892, 8788, …
  (−∞, 0]nonnegative
• A038220 → basis A008277
  1 · 5, 2 · 25, 24, 4 · 125, 218, 84, 8 … Σ 1, 7, 53, 435, 3865, 37039, 381037, …
  (−∞, 0]nonnegative
• A102547 → reverse → basis A013611
  1, 4 · 1, 8, 16 · 1, 12, 48, 64 … Σ 5, 25, 125, 750, 4375, 25000, 143750, …
  (−∞, 0]nonnegative
• A272866 → basis A013610
  1 · 5, 15, 9 · 25, 150, 315, 270, 81 … Σ 1, 29, 841, 24389, 707281, 20511149, …
  (−∞, 0]nonnegative
• A153649: Triangle T(n, k) = T(n-1, k) + T(n-1, k-1) + (j+1)*prime(j)*T(n-2, k-1) with j=4, read by rows.
  2 · 7, 7 · 2, 94, 2 · 2, 341, 341, 2 … Σ 2, 14, 98, 686, 4802, 33614, 235298, …
  (−∞, 0)nonnegative
• A274498 → D+1
  1 · 3 · 9, 6 · 27, 18 … Σ 1, 3, 15, 45, 189, 567, 2187, 6561, …
  (−∞, 0]nonnegativerational roots
• A013612 → Pₙ + Pₙ₊₁
  2, 25, 100, 125 · 2, 35, 225, 625, 625 … Σ 252, 1512, 9072, 54432, 326592, …
  (−∞, ∞)nonnegativerational roots
• A038335 → basis A007318
  1 · 21, 9 · 441, 378, 81 · 9261, 11907, 5103, 729 … Σ 1, 30, 900, 27000, 810000, 24300000, …
  (−∞, 0]nonnegativerational roots
• A035607 → D
  2 · 4, 4 · 6, 16, 6 · 8, 36, 36, 8 … Σ 0, 0, 2, 8, 28, 88, 262, 752, …
  (−∞, 0]nonnegative
• basis-map coefficients of A371080, shifted → basis A008277
  1 · 1, 1 · 4, 6, 1 · 28, 52, 15, 1 … Σ 1, 2, 11, 96, 1141, 17126, 310207, …
  (−∞, 0]nonnegative
• A108838 → basis A013609
  2 · 5, 4 · 14, 24, 8 · 42, 112, 84, 16 … Σ 2, 9, 46, 254, 1476, 8893, 55046, …
  (−∞, 0]nonnegative
• A048993 → (θ+1)²
  1 · 0, 4 · 0, 4, 9 · 0, 4, 27, 16 … Σ 1, 4, 13, 47, 188, 825, 3937, 20270, …
  (−∞, 0]nonnegative
• A367270 → D+1
  1 · 1 · 3, 2 · 7, 12, 3 … Σ 1, 1, 5, 22, 95, 406, 1722, 7260, …
  (−∞, 0]nonnegative
• A178820 → D+1
  1 · 8, 4 · 30, 40, 10 · 80, 180, 120, 20 … Σ 1, 12, 80, 400, 1680, 6272, 21504, …
  (−∞, 0]nonnegativerational roots
• A102547 → x ↦ x+1
  1 · 1 · 1 · 2, 1 … Σ 1, 1, 1, 3, 5, 7, 13, 23, …
  (−∞, −1]nonnegative
• basis-map coefficients of A021012 → basis A013611
  1 · -1, -4 · 2, 16, 32 · -6, -72, -288, -384 … Σ 1, -5, 50, -750, 15000, -375000, …
  (−∞, 0]rational roots
• A059364 → basis A007318
  1 · 3, 1 · 15, 11, 2 · 105, 122, 47, 6 … Σ 1, 4, 28, 280, 3640, 58240, 1106560, …
  (−∞, 0]nonnegativerational roots
• A030528 → x ↦ x−15
  1 · -14, 1 · 195, -28, 1 · -2715, 586, -42, 1 … Σ 1, -13, 168, -2170, 28028, -362012, …
  (11, 15]
• A153656: Triangle T(n, k) = T(n-1, k) + T(n-1, k-1) + (2*j +3)*prime(j)*T(n-2, k-1) with j=9, read by rows.
  2 · 23, 23 · 2, 1054, 2 · 2, 12165, 12165, 2 … Σ 2, 46, 1058, 24334, 559682, 12872686, …
  (−∞, 0)nonnegative
• A274496 → D+1
  1 · 2 · 4, 2 · 8, 4 … Σ 1, 2, 6, 12, 32, 64, 160, 320, …
  (−∞, 0]nonnegativerational roots
• A173018 → D+1
  1 · 1 · 2, 1 · 5, 6, 1 … Σ 1, 1, 3, 12, 60, 360, 2520, 20160, …
  (−∞, 0]nonnegative
• A249252 → D
  4 · 8, 16 · 12, 64, 48 · 16, 144, 288, 128 … Σ 0, 4, 24, 124, 576, 2532, 10728, 44300, …
  (−∞, 0]nonnegative
• A144442 → γ
  1 · 1 · 1, 15 · 1, 115 … Σ 1, 1, 16, 116, 1951, 32946, 767576, …
  (−∞, 0]nonnegative
• A225471 → Pₙ + Pₙ₊₁
  4, 1 · 24, 11, 1 · 252, 141, 22, 1 … Σ 5, 36, 416, 6528, 129024, 3072000, …
  (−∞, ∞)nonnegativerational roots
• A193722: Triangular array: the fusion of (x+1)^n and (x+2)^n; see Comments for the definition of fusion.
  1 · 1, 2 · 1, 5, 6 · 1, 8, 21, 18 … Σ 1, 3, 12, 48, 192, 768, 3072, 12288, …
  (−∞, 0)nonnegativerational roots
• A391045 → x ↦ x+1
  1 · 2, 1 · 6, 6, 1 · 21, 32, 13, 1 … Σ 1, 3, 13, 67, 377, 2243, 13877, 88371, …
  (−∞, −1]nonnegative
• chebyshev_t → D
  1 · 0, 4 · -3, 0, 12 · 0, -16, 0, 32 … Σ 0, 1, 4, 9, 16, 25, 36, 49, …
  (−∞, ∞)
• A232535 → D+1
  1 · 3, 2 · 9, 14, 3 · 19, 68, 37, 4 … Σ 1, 5, 26, 128, 608, 2816, 12800, 57344, …
  (−∞, 0]nonnegative
• narayana → basis A007318
  1 · 2, 1 · 5, 5, 1 · 14, 21, 9, 1 … Σ 1, 3, 11, 45, 197, 903, 4279, 20793, …
  (−∞, −1]nonnegative
• A118931: Triangle, read by rows, where T(n,k) = n!/(k!*(n-3*k)!*3^k) for n>=3*k>=0.
  1 · 1 · 1 · 1, 2 … Σ 1, 1, 1, 3, 9, 21, 81, 351, …
  (−∞, 0]nonnegative
• A105868: Triangle read by rows, T(n,k) = C(n,k)*C(k,n-k).
  1 · 0, 1 · 0, 2, 1 · 0, 0, 6, 1 … Σ 1, 1, 3, 7, 19, 51, 141, 393, …
  (−∞, 0]nonnegative
• A207606 → basis A008277
  13, 13, 2 · 34, 63, 23, 2 · 89, 273, 176, 35, 2 … Σ 28, 122, 575, 2916, 15825, 91434, …
  (−∞, 0]nonnegative
• A096940: Pascal (1,5) triangle.
  5 · 1, 5 · 1, 6, 5 · 1, 7, 11, 5 … Σ 5, 6, 12, 24, 48, 96, 192, 384, …
  (−∞, 0)nonnegativerational roots
• A059344 → basis A013609
  1 · 1 · 3, 4 · 7, 12 … Σ 1, 1, 7, 19, 145, 601, 4951, 26587, …
  (−∞, 0]nonnegative
• A023531: a(n) = 1 if n is of the form m(m+3)/2, otherwise 0.
  1 · 0, 1 · 0, 0, 1 · 0, 0, 0, 1 … Σ 1, 1, 1, 1, 1, 1, 1, 1, …
  [−1, 0][0, ∞)nonnegative+1
• A391533 → Veronese 2 (j=1)
  4 · 8, 1 · 12, 6 · 16, 19, 1 … Σ 4, 9, 18, 36, 72, 144, 288, 576, …
  (−∞, 0]nonnegative
• A038320 → basis A007318
  289, 204, 36 · 4913, 5202, 1836, 216 … Σ 529, 12167, 279841, 6436343, 148035889, …
  (−∞, 0]nonnegativerational roots
• A257611 → γ
  1 · 3 · 9, 12 · 27, 132 … Σ 1, 3, 21, 159, 1593, 18027, 238509, …
  (−∞, 0]nonnegative
• A026729 → Veronese 2 (j=1)
  1 · 1 · 0, 1 · 0, 3 … Σ 0, 1, 1, 1, 3, 4, 6, 11, …
  (−∞, 0]nonnegative
• A051523: Generalized Stirling number triangle of first kind read by rows: T(n, k) = [x^k] Product_{m=1..n} (x - m - r), with r = 9.
  1 · -10, 1 · 110, -21, 1 · -1320, 362, -33, 1 … Σ 1, -9, 90, -990, 11880, -154440, …
  [19/2, ∞)rational roots
• A145324 → basis A013610
  1 · 3, 6 · 12, 51, 54 · 60, 399, 882, 648 … Σ 1, 9, 117, 1989, 41769, 1044225, …
  (−∞, 0]nonnegativerational roots
• A371080: Triangle read by rows: BellMatrix(Product_{p in P(n)} p), where P(n) = {k : k mod m = 1 and 1 <= k <= m*(n + 1)} and m = 3.
  1 · 0, 1 · 0, 4, 1 · 0, 28, 12, 1 … Σ 1, 1, 5, 41, 465, 6721, 117941, …
  (−∞, 0]nonnegative
• A128099 → θ+1
  1 · 1 · 1, 4 · 1, 8 … Σ 1, 1, 5, 9, 25, 53, 125, 273, …
  (−∞, 0]nonnegative
• A013610 → (θ+1)²
  1 · 1, 12 · 1, 24, 81 · 1, 36, 243, 432 … Σ 1, 13, 106, 712, 4288, 24064, 128512, …
  (−∞, 0]nonnegative