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1381 sequences

• A207606 → θ+1
  4, 14, 6 · 5, 32, 33, 8 · 6, 60, 108, 60, 10 … row sums 24, 78, 244, 743, 2218, 6521, 18942, …
  (−∞, 0] nonnegative
• A011973 → basis A007318 → D+1
  1 · 1 · 3, 1 · 5, 2 … row sums 1, 1, 4, 7, 18, 37, 84, 179, …
  (−∞, 0] nonnegative
• A010054 → D∘x → D
  (−∞, 0] nonnegative rational roots
• A007318 → (θ+1)² → reverse
  1 · 4, 1 · 9, 8, 1 · 16, 27, 12, 1 … row sums 1, 5, 18, 56, 160, 432, 1120, 2816, …
  (−∞, 0] nonnegative
• A145597 → x ↦ x/(x+1)
  1 · 3, 6 · 6, 27, 27 · 10, 75, 165, 110 … row sums 1, 9, 60, 360, 2061, 11529, 63728, …
  [−1, 0] nonnegative
• A274498 → x ↦ x+1
  1 · 3 · 9, 6 · 27, 18 … row sums 1, 3, 15, 45, 225, 675, 3375, 10125, …
  (−∞, −1] nonnegative rational roots
• A143494 → x ↦ x/(x+1)
  1 · 2, 3 · 4, 13, 10 · 8, 43, 71, 37 … row sums 1, 5, 27, 159, 1025, 7221, 55307, …
  [−1, 0] nonnegative
• A102662 → (θ+1)²
  1 · 1, 12 · 1, 20, 27 · 1, 28, 99, 48 … row sums 1, 13, 48, 176, 591, 1895, 5858, 17614, …
  (−∞, 0] nonnegative
• A085880 → θ+1
  1 · 1, 2 · 2, 8, 6 · 5, 30, 45, 20 … row sums 1, 3, 16, 100, 672, 4704, 33792, …
  (−∞, 0] nonnegative rational roots
• A081577 → (θ+1)²
  1 · 1, 4 · 1, 16, 9 · 1, 28, 63, 16 … row sums 1, 5, 26, 108, 424, 1564, 5552, 19104, …
  (−∞, 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 A007318
  1 · 1 · 1 · 1 … row sums 1, 1, 1, 1, 7, 13, 19, 25, …
  (−∞, −1] nonnegative
• 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]
• 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
• 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
• 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
• 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
• 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
• A008292 → γ (shift +1) → D
  2 · 8 · 22, 32 · 52, 272 … row sums 0, 0, 2, 8, 54, 324, 2370, 18288, …
  (−∞, 0] nonnegative
• A334218 → D
  2 · 3, 6 · 4, 32, 12 · 5, 110, 165, 20 … row sums 0, 0, 2, 9, 48, 300, 2160, 17640, …
  (−∞, 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
• 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
• 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
• 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
• A099093 → basis A007318
  1 · 3, 3 · 12, 21, 9 · 45, 117, 99, 27 … row sums 1, 6, 42, 288, 1980, 13608, 93528, …
  (−∞, −1] nonnegative
• A113214 → (θ+1)²
  1 · 2, 4 · 0, 12, 9 · 0, 8, 36, 16 … row sums 1, 6, 21, 60, 150, 348, 763, 1608, …
  (−∞, 0] nonnegative
• A172431 → D+1
  1 · 3, 2 · 5, 10, 3 · 7, 26, 22, 4 … row sums 1, 5, 18, 59, 185, 564, 1685, 4957, …
  (−∞, 0] nonnegative
• A143495 → D+1
  1 · 4, 1 · 16, 9, 1 · 64, 61, 15, 1 … row sums 1, 5, 26, 141, 799, 4736, 29371, …
  (−∞, 0] nonnegative
• A078812 → θ+1
  1 · 2, 2 · 3, 8, 3 · 4, 20, 18, 4 … row sums 1, 4, 14, 46, 145, 444, 1331, 3926, …
  (−∞, 0] nonnegative
• A227450 → (θ+1)²
  2 · 2, 16 · 2, 48, 72 · 2, 112, 432, 256 … row sums 2, 18, 122, 802, 5402, 37922, 278938, …
  (−∞, 0] nonnegative
• A181371: Triangle read by rows: T(n,k) is the number of ternary words (i.e., finite sequences of 0's, 1's and 2's) of length n having k occurrences of 01's (0 <= k <= floor(n/2)).
  A011973 → x ↦ (1/9)x−1/9
  1 · 3 · 8, 1 · 21, 6 … row sums 1, 3, 9, 27, 81, 243, 729, 2187, …
  A181371 (−∞, 1] nonnegative
• A102662 → x ↦ x/(x+1)
  1 · 1, 4 · 1, 7, 9 · 1, 10, 28, 22 … row sums 1, 5, 17, 61, 217, 773, 2753, 9805, …
  [−1, 0] nonnegative
• A104684 → D
  1 · 6, 2 · 30, 24, 3 · 140, 180, 60, 4 … row sums 0, 1, 8, 57, 384, 2505, 16008, 100849, …
  (−∞, 0] nonnegative
• A249252 → basis A007318
  1 · 5, 4 · 17, 24, 8 · 61, 124, 80, 16 … row sums 1, 9, 49, 281, 1601, 9129, 52049, …
  (−∞, −1] nonnegative
• A081581: Pascal-(1,6,1) array.
  1 · 1, 1 · 1, 8, 1 · 1, 15, 15, 1 … row sums 1, 2, 10, 32, 124, 440, 1624, 5888, …
  A081581 (−∞, 0) nonnegative
• A007318 → (1/2+(1/2)n)θ+1+n → (θ+1)²
  1 · 2, 12 · 3, 36, 54 · 4, 72, 216, 160 … row sums 1, 14, 93, 452, 1840, 6672, 22288, …
  (−∞, 0] nonnegative
• A249250 → x ↦ x+1
  1 · 4, 3 · 10, 12, 3 · 28, 48, 24, 3 … row sums 1, 7, 25, 103, 409, 1639, 6553, 26215, …
  (−∞, −1] nonnegative
• A030528: Triangle read by rows: T(n,k) = binomial(k,n-k).
  1 · 1, 1 · 0, 2, 1 · 0, 1, 3, 1 … row sums 1, 2, 3, 5, 8, 13, 21, 34, …
  A030528 (−4, 0] nonnegative
• A034870 → D+1
  1 · 3, 4, 1 · 5, 16, 18, 8, 1 … row sums 1, 8, 48, 256, 1280, 6144, 28672, …
  (−∞, 0] nonnegative rational roots
• A159854 → x ↦ x+1
  1, 2, 1 · 2, 5, 4, 1 · 4, 12, 13, 6, 1 … row sums 4, 12, 36, 108, 324, 972, 2916, 8748, …
  (−∞, −1] nonnegative rational roots
• A091044: One half of odd-numbered entries of even-numbered rows of Pascal's triangle A007318.
  1 · 2, 2 · 3, 10, 3 · 4, 28, 28, 4 … row sums 1, 4, 16, 64, 256, 1024, 4096, 16384, …
  A091044 (−∞, 0) nonnegative