Sequences

• narayana → basis A013609 → D
  2 · 10, 8 · 42, 72, 24 · 168, 448, 336, 64 … Σ 0, 2, 18, 138, 1016, 7380, 53358, …
  (−∞, 0]nonnegative
• A038338 → basis A013610 → (θ+1)²
  576, 6912, 11664 · 13824, 248832, 839808, 746496 … Σ 19152, 1848960, 162259200, 13374720000, …
  (−∞, 0]nonnegative
• A350512 → basis A013611
  1 · 2, 4 · 6, 24, 16 · 16, 96, 160, 64 … Σ 1, 6, 46, 336, 2376, 16416, 111456, …
  (−∞, 0]nonnegative
• A257609 → γ
  1 · 2 · 4, 8 · 8, 64 … Σ 1, 2, 12, 72, 624, 6048, 70848, 931968, …
  (−∞, 0]nonnegative
• A113953 → basis A007318 → D
  1 · 4, 2 · 11, 14, 3 · 30, 56, 30, 4 … Σ 0, 1, 6, 28, 120, 480, 1856, 6976, …
  (−∞, 0]nonnegative
• A038329 → basis A013611 → x ↦ x+1
  729, 648, 144 · 19683, 26244, 11664, 1728 … Σ 1521, 59319, 2313441, 90224199, …
  (−∞, −1]nonnegativerational roots
• A038207 → (θ+1)²
  1 · 2, 4 · 4, 16, 9 · 8, 48, 54, 16 … Σ 1, 6, 29, 126, 513, 1998, 7533, 27702, …
  (−∞, 0]nonnegative
• A166344 → x ↦ x+1
  8, 8, 1 · 32, 48, 18, 1 · 160, 320, 198, 38, 1 … Σ 17, 99, 717, 6219, 62877, 726219, …
  (−∞, −1]nonnegative
• A094638 → basis A013610 → θ+1
  1 · 2, 6 · 6, 42, 54 · 24, 276, 783, 648 … Σ 1, 8, 102, 1731, 36447, 914562, …
  (−∞, 0]nonnegative
• A166962: Triangle T(n,k) read by rows: T(n,1) = T(n,n)=1, otherwise T(n,k) = (3n-3k+1)*T(n-1,k-1) + k*(3k-2)*T(n-1,k), 1<=k<=n.
  1 · 1, 1 · 1, 12, 1 · 1, 103, 69, 1 … Σ 1, 2, 14, 174, 3322, 89756, 3211420, …
  (−∞, 0]nonnegative
• A178821 → Veronese 2 → basis A013610
  1 · 5 · 30, 45 · 140, 315 … Σ 1, 5, 75, 455, 2870, 15246, 76650, …
  (−∞, 0]nonnegative
• A123519 → basis A013610 → basis A007318
  89, 114, 36 · 881, 1668, 1044, 216 … Σ 239, 3809, 60705, 967471, 15418831, …
  (−∞, 0]nonnegative
• A027467 → basis A013611 → basis A013610
  1 · 20, 12 · 400, 480, 144 · 8000, 14400, 8640, 1728 … Σ 1, 32, 1024, 32768, 1048576, 33554432, …
  (−∞, 0]nonnegativerational roots
• A114687 → (θ+1)²
  1 · 1, 8 · 1, 24, 36 · 1, 48, 216, 128 … Σ 1, 9, 61, 393, 2481, 15473, 95677, …
  (−∞, 0]nonnegative
• A035469 → Pₙ + Pₙ₊₁
  5, 1 · 32, 13, 1 · 308, 172, 25, 1 … Σ 6, 46, 506, 7186, 124662, 2551086, …
  (−∞, ∞)nonnegative
• basis-map coefficients of A112227 → (θ+1)² → D
  0, 18 · 0, 0, 48 · 0, 0, 0, 100 · 0, 0, 0, 0, 180 … Σ 18, 48, 100, 180, 294, 448, 648, 900, …
  (−∞, 0]nonnegativerational roots
• A049444: Generalized Stirling number triangle of first kind read by rows: T(n, k) = [x^k] Product_{m=1..n} (x - m - r), with r = 1.
  1 · -2, 1 · 6, -5, 1 · -24, 26, -9, 1 … Σ 1, -1, 2, -6, 24, -120, 720, -5040, …
  [3/2, ∞)rational roots
• A143683 → x ↦ x/(x+1)
  1 · 1, 2 · 1, 12, 12 · 1, 22, 60, 40 … Σ 1, 3, 25, 123, 769, 4275, 25129, …
  [−1, 0]nonnegative
• A052553 → D+1
  1 · 1 · 2, 1 · 3, 2 … Σ 1, 1, 3, 5, 10, 18, 33, 59, …
  (−∞, 0]nonnegative
• A011973 → basis A013611 → D
  4 · 8 · 20, 32 · 40, 96 … Σ 0, 0, 4, 8, 52, 136, 560, 1624, …
  (−∞, 0]nonnegative
• A193722 → basis A008277
  1 · 3, 2 · 12, 23, 6 · 48, 197, 129, 18 … Σ 1, 5, 41, 392, 4271, 51989, 696506, …
  (−∞, 0]nonnegative
• A200536 → basis A013610 → basis A013609
  1 · 45, 114, 72 · 2025, 10260, 19476, 16416, 5184 … Σ 1, 231, 53361, 12326391, 2847396321, …
  (−∞, 0]nonnegativerational roots
• A201637 → reverse (shift +1) → x ↦ x+1
  1 · 1, 1 · 3, 4, 1 · 15, 25, 11, 1 … Σ 1, 2, 8, 52, 472, 5504, 78416, 1320064, …
  (−∞, −1]nonnegative
• A038338 → basis A013610 → D+1
  2304, 4320, 1296 · 76032, 248832, 233280, 46656 … Σ 7920, 604800, 44064000, 3110400000, …
  (−∞, 0]nonnegativerational roots
• basis-map coefficients of A026729, shifted → (θ+1)² → basis A008277
  1 · -4, -4 · 9, 27, 9 · -16, -112, -96, -16 … Σ 1, -8, 45, -240, 1300, -7308, 42973, …
  (−∞, 0]
• A225469 → (θ+1)²
  1 · 3, 4 · 9, 40, 9 · 27, 316, 189, 16 … Σ 1, 7, 58, 548, 5792, 67728, 868000, …
  (−∞, 0]nonnegative
• A094638 → D → basis A013610
  1 · 7, 12 · 46, 174, 162 · 326, 1974, 3942, 2592 … Σ 0, 1, 19, 382, 8834, 235239, 7134045, …
  (−∞, 0]nonnegative
• A081577 → basis A013609 → θ+1
  1 · 2, 4 · 6, 24, 12 · 16, 96, 120, 32 … Σ 1, 6, 42, 264, 1620, 9672, 56712, …
  (−∞, 0]nonnegative
• A286718: Triangle read by rows: T(n, k) is the Sheffer triangle ((1 - 3*x)^(-1/3), (-1/3)*log(1 - 3*x)). A generalized Stirling1 triangle.
  1 · 1, 1 · 4, 5, 1 · 28, 39, 12, 1 … Σ 1, 2, 10, 80, 880, 12320, 209440, …
  (−∞, −1]nonnegativerational roots
• A109692 → basis A007318
  1 · 2, 1 · 8, 10, 3 · 48, 100, 68, 15 … Σ 1, 3, 21, 231, 3465, 65835, 1514205, …
  (−∞, −1]nonnegativerational roots
• A028338 → basis A013609 → (θ+1)²
  1 · 2, 8 · 8, 48, 36 · 48, 352, 432, 128 … Σ 1, 10, 92, 960, 11584, 160384, 2517248, …
  (−∞, 0]nonnegative
• A102547 → reverse → basis A013610
  1, 3 · 1, 6, 9 · 1, 9, 27, 27 · 2, 21, 81, 135, 81 … Σ 4, 16, 64, 320, 1536, 7168, 33792, …
  (−∞, 0]nonnegative
• A132393 → basis A013610 → reverse
  1 · 3, 1 · 9, 9, 2 · 27, 54, 33, 6 … Σ 1, 4, 20, 120, 840, 6720, 60480, …
  (−∞, 0]nonnegativerational roots
• A038319 → basis A013611 → basis A013610
  1296, 4320, 3600 · 46656, 233280, 388800, 216000 … Σ 9216, 884736, 84934656, 8153726976, …
  (−∞, 0]nonnegativerational roots
• A008292 → γ (shift +1) → x ↦ x+1 → D
  2 · 8 · 54, 32 · 324, 272 … Σ 0, 0, 2, 8, 86, 596, 6258, 60144, …
  (−∞, 0]nonnegative
• A257610 → γ
  1 · 2 · 4, 12 · 8, 108 … Σ 1, 2, 16, 116, 1348, 17228, 276004, …
  (−∞, 0]nonnegative
• A056242 → D+1
  1 · 3, 2 · 6, 13, 4 · 10, 41, 40, 8 … Σ 1, 5, 23, 99, 408, 1632, 6388, 24596, …
  (−∞, 0]nonnegative
• A059344 → basis A013610 → basis A008277
  1 · 1 · 9, 6 · 25, 18 … Σ 1, 1, 15, 43, 781, 3621, 77731, 494215, …
  (−∞, 0]nonnegative
• A391403 → x ↦ x+1 → (θ+1)²
  1 · 1 · 3, 8 · 7, 24 … Σ 1, 1, 11, 31, 169, 641, 2891, 11831, …
  (−∞, 0]nonnegative
• A145596 → x ↦ x+1 → θ+1
  1 · 4, 4 · 14, 28, 9 · 48, 144, 96, 16 … Σ 1, 8, 51, 304, 1765, 10128, 57799, …
  (−∞, 0]nonnegative
• A028326 → basis A007318 → basis A013611
  2 · 6, 8 · 18, 48, 32 · 54, 216, 288, 128 … Σ 2, 14, 98, 686, 4802, 33614, 235298, …
  (−∞, 0]nonnegativerational roots
• A029618: Numbers in (3,2)-Pascal triangle (by row).
  1 · 3, 2 · 3, 5, 2 · 3, 8, 7, 2 … Σ 1, 5, 10, 20, 40, 80, 160, 320, …
  (−∞, 0)nonnegativerational roots
• Triangle read by rows: (i,j)-th entry is binomial(i,j)*3^(i-j)*8^j.
  9, 48, 64 · 27, 216, 576, 512 … Σ 121, 1331, 14641, 161051, 1771561, …
  (−∞, 0)nonnegativerational roots
• delannoy → basis A013609 → x ↦ x/(x+1)
  1 · 2, 4 · 5, 20, 19 · 12, 72, 140, 88 … Σ 1, 6, 44, 312, 2224, 15840, 112832, …
  [−1, 0]nonnegative
• A038324 → basis A013609 → basis A013609
  1 · 41, 40 · 1681, 3280, 1600 … Σ 1, 81, 6561, 531441, 43046721, …
  (−∞, 0]nonnegativerational roots
• A178821 → basis A013611 → reverse
  1 · 20, 10 · 240, 240, 60 · 2240, 3360, 1680, 280 … Σ 1, 30, 540, 7560, 90720, 979776, …
  (−∞, −1]nonnegativerational roots
• A178822 → Veronese 2 (j=1) → (θ+1)²
  6 · 42 · 168, 224 · 504, 2016 … Σ 0, 6, 42, 392, 2520, 13608, 64680, …
  (−∞, 0]nonnegative
• A085880 → basis A013609 → basis A013610
  1 · 4, 6 · 32, 96, 72 · 320, 1440, 2160, 1080 … Σ 1, 10, 200, 5000, 140000, 4200000, …
  (−∞, 0]nonnegativerational roots
• A102662 → reverse
  1 · 3, 1 · 3, 5, 1 · 3, 11, 7, 1 … Σ 1, 4, 9, 22, 53, 128, 309, 746, …
  (−∞, 0]nonnegative
• A027467 → x ↦ x+1 → θ+1
  1 · 16, 2 · 256, 64, 3 · 4096, 1536, 144, 4 … Σ 1, 18, 323, 5780, 103173, 1837462, …
  (−∞, 0]nonnegativerational roots