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1381 sequences

• A013620 → (θ+1)²
  1 · 2, 12 · 4, 48, 81 · 8, 144, 486, 432 … row sums 1, 14, 133, 1070, 7825, 53750, 353125, …
  (−∞, 0] nonnegative
• A011973 → ⊙ C(n,k) → D
  2 · 6 · 12, 12 · 20, 60 … row sums 0, 0, 2, 6, 24, 80, 270, 882, …
  (−∞, 0] nonnegative
• A023531 → 2D+1 → reverse
  1 · 1, 2 · 1, 4 · 1, 6 … row sums 1, 3, 5, 7, 9, 11, 13, 15, …
  (−∞, 0] nonnegative rational roots
• A116666: Triangle, row sums = number of edges in n-dimensional hypercubes.
  A007318 → 2θ+1
  1 · 1, 3 · 1, 6, 5 · 1, 9, 15, 7 … row sums 1, 4, 12, 32, 80, 192, 448, 1024, …
  A116666 (−∞, 0] nonnegative rational roots
• A122542 → (θ+1)²
  1 · 0, 4 · 0, 8, 9 · 0, 8, 36, 16 … row sums 1, 4, 17, 60, 201, 640, 1969, 5896, …
  (−∞, 0] nonnegative
• A052553 → x ↦ x+1
  1 · 1 · 2, 1 · 3, 2 … row sums 1, 1, 3, 5, 11, 21, 43, 85, …
  (−∞, −1] nonnegative
• A165253 → (θ+1)²
  1 · 1 · 1, 4 · 1, 12, 9 … row sums 1, 1, 5, 22, 86, 313, 1085, 3629, …
  (−∞, 0] nonnegative
• A007318 → θ+1+n → D
  3 · 8, 10 · 15, 36, 21 · 24, 84, 96, 36 … row sums 0, 3, 18, 72, 240, 720, 2016, 5376, …
  (−∞, 0] nonnegative rational roots
• A198954: Expansion of the rotational partition function for a heteronuclear diatomic molecule.
  A010054 → D∘x
  1 · 3 · 5 · 7 … row sums 1, 3, 5, 7, 9, 11, 13, 15, …
  A198954 (−∞, −1] [−1, 0] nonnegative rational roots
• A143494 → θ+1
  1 · 2, 2 · 4, 10, 3 · 8, 38, 27, 4 … row sums 1, 4, 17, 77, 372, 1915, 10481, 60814, …
  (−∞, 0] nonnegative
• A116412 → θ+1
  1 · 3, 2 · 6, 12, 3 · 12, 42, 27, 4 … row sums 1, 5, 21, 85, 332, 1266, 4741, 17507, …
  (−∞, 0] nonnegative
• A172431 → ⊙ C(n,k+1) (shift -1) → (θ+1)²
  1 · 1, 4 · 1, 16, 9 · 1, 36, 90, 16 … row sums 1, 5, 26, 143, 788, 4332, 23735, …
  (−∞, 0] nonnegative
• A102547 → reverse → x ↦ x+1
  1, 1 · 1, 2, 1 · 1, 3, 3, 1 · 2, 7, 9, 5, 1 … row sums 2, 4, 8, 24, 64, 160, 416, 1088, …
  (−∞, −1] nonnegative
• A007318 → θ+1+n → D+1
  1 · 5, 3 · 11, 18, 5 · 19, 51, 39, 7 … row sums 1, 8, 34, 116, 352, 992, 2656, 6848, …
  (−∞, 0] nonnegative
• A060920 → x ↦ x+1
  1 · 3, 1 · 11, 7, 1 · 43, 41, 12, 1 … row sums 1, 4, 19, 97, 508, 2683, 14209, 75316, …
  (−∞, ∞) nonnegative
• A035607 → reverse
  1 · 2, 1 · 2, 4, 1 · 2, 8, 6, 1 … row sums 1, 3, 7, 17, 41, 99, 239, 577, …
  (−∞, 0] nonnegative
• A007318 → ×(1+2n+n²) → x ↦ x+1
  1 · 8, 4 · 36, 36, 9 · 128, 192, 96, 16 … row sums 1, 12, 81, 432, 2025, 8748, 35721, …
  (−∞, −1] nonnegative rational roots
• A007318 → D+1 → x ↦ x/(x+1)
  1 · 2, 3 · 3, 10, 8 · 4, 21, 36, 20 … row sums 1, 5, 21, 81, 297, 1053, 3645, 12393, …
  [−1, 0] nonnegative rational roots
• A008459 → D+1
  1 · 2, 1 · 5, 6, 1 · 10, 27, 12, 1 … row sums 1, 3, 12, 50, 210, 882, 3696, 15444, …
  (−∞, 0] nonnegative
• A007318 → θ+1 → D
  2 · 4, 6 · 6, 18, 12 · 8, 36, 48, 20 … row sums 0, 2, 10, 36, 112, 320, 864, 2240, …
  (−∞, 0] nonnegative rational roots
• A125662 → x ↦ x/(x+1)
  1 · 3, 4 · 8, 22, 15 · 21, 88, 122, 56 … row sums 1, 7, 45, 287, 1829, 11655, 74269, …
  [−1, −1/2) nonnegative
• A143494 → D
  1 · 5, 2 · 19, 18, 3 · 65, 110, 42, 4 … row sums 0, 1, 7, 40, 221, 1241, 7218, 43807, …
  (−∞, 0] nonnegative
• basis-map coefficients of A145596 → D
  2 · 2, 6 · -8, 16, 12 · -10, -30, 60, 20 … row sums 0, 2, 8, 20, 40, 70, 112, 168, …
  (−∞, ∞)
• A133080 → D
  1 · 0, 2 · 0, 2, 3 · 0, 0, 0, 4 … row sums 0, 1, 2, 5, 4, 9, 6, 13, …
  (−∞, 0] nonnegative rational roots
• A344565 → θ+1
  3 · 15, 30 · 45, 180, 135 · 105, 630, 945, 420 … row sums 3, 45, 360, 2100, 10080, 42336, 161280, …
  (−∞, 0] nonnegative rational roots
• A196347 → γ
  1 · 1 · 2 · 6 … row sums 1, 1, 2, 6, 24, 120, 720, 5040, …
  (−∞, 0] nonnegative rational roots
• A007318 → ×(−(1/2)n+(1/2)n²) → x ↦ x+1
  4, 4, 1 · 24, 36, 18, 3 · 96, 192, 144, 48, 6 … row sums 0, 0, 9, 81, 486, 2430, 10935, 45927, …
  (−∞, −1] nonnegative rational roots
• A134082: Triangle read by rows, (n-1) zeros followed by (2n, 1).
  A023531 → 2D+1
  1 · 2, 1 · 0, 4, 1 · 0, 0, 6, 1 … row sums 1, 3, 5, 7, 9, 11, 13, 15, …
  A134082 (−∞, 0] nonnegative rational roots
• A033282: Triangle read by rows: T(n, k) is the number of diagonal dissections of a convex n-gon into k+1 regions.
  1 · 1, 2 · 1, 5, 5 · 1, 9, 21, 14 … row sums 1, 3, 11, 45, 197, 903, 4279, 20793, …
  A033282 (−1, 0) nonnegative
• A059344 → ⊙ 1/k! (shift -1) → θ+1
  1 · 1 · 1, 4 · 1, 12 … row sums 1, 1, 5, 13, 43, 131, 411, 1275, …
  (−∞, 0] nonnegative
• A023531 → (1/2)D²+2D+1 → D+1
  1 · 3, 1 · 5, 6, 1 · 3, 15, 9, 1 … row sums 1, 4, 12, 28, 55, 96, 154, 232, …
  (−∞, 0] nonnegative
• A102547 → reverse
  0, 1 · 0, 0, 1 · 0, 0, 0, 1 · 0, 0, 0, 1, 1 … row sums 1, 1, 1, 2, 3, 4, 6, 9, …
  (−∞, 0] nonnegative
• A026374 → x ↦ x/(x+1)
  1 · 1, 2 · 1, 5, 5 · 1, 7, 15, 10 … row sums 1, 3, 11, 33, 121, 363, 1331, 3993, …
  [−1, 0] nonnegative
• A081578 → x ↦ x/(x+1)
  1 · 1, 2 · 1, 7, 7 · 1, 12, 30, 20 … row sums 1, 3, 15, 63, 279, 1215, 5319, 23247, …
  [−1, 0] nonnegative
• A111125 → x ↦ x+1
  1 · 4, 1 · 11, 7, 1 · 29, 31, 10, 1 … row sums 1, 5, 19, 71, 265, 989, 3691, 13775, …
  (−5, −1) nonnegative
• A152842 → x ↦ x+1
  1 · 4, 3 · 8, 10, 3 · 32, 64, 42, 9 … row sums 1, 7, 21, 147, 441, 3087, 9261, 64827, …
  (−∞, −1] nonnegative rational roots
• A100862 → θ+1
  1 · 1, 2 · 1, 6, 3 · 1, 12, 18, 4 … row sums 1, 3, 10, 35, 129, 497, 1996, 8325, …
  (−∞, 0] nonnegative
• basis-map coefficients of A030528, shifted → reverse
  1 · -1 · 1 · -1 … row sums 1, -1, 1, -1, 1, -1, 1, -1, …
  (−∞, 0] rational roots
• delannoy → (θ+1)²
  1 · 1, 4 · 1, 12, 9 · 1, 20, 45, 16 … row sums 1, 5, 22, 82, 283, 923, 2892, 8788, …
  (−∞, 0] nonnegative
• A137338 → D
  1 · -3, 2 · 6, -12, 3 · -9, 52, -30, 4 … row sums 0, 1, -1, -3, 17, -57, 179, -631, …
  (−∞, ∞)
• A023531 → 2D+1 → (θ+1)²
  1 · 2, 4 · 0, 16, 9 · 0, 0, 54, 16 … row sums 1, 6, 25, 70, 153, 286, 481, 750, …
  (−∞, 0] nonnegative rational roots
• A152198 → D
  1 · 1 · 2, 2 · 2, 2 … row sums 0, 0, 1, 1, 4, 4, 12, 12, …
  (−∞, 0] nonnegative rational roots
• A133080 → (θ+1)²
  1 · 1, 4 · 0, 0, 9 · 0, 0, 9, 16 … row sums 1, 5, 9, 25, 25, 61, 49, 113, …
  (−∞, 0] nonnegative rational roots
• A100861 → θ+1
  1 · 1 · 1, 2 · 1, 6 … row sums 1, 1, 3, 7, 22, 66, 226, 778, …
  (−∞, 0] nonnegative
• A172431 → θ+1
  1 · 1, 4 · 1, 8, 9 · 1, 12, 30, 16 … row sums 1, 5, 18, 59, 185, 564, 1685, 4957, …
  (−∞, 0] nonnegative
• A063007 → D
  2 · 6, 12 · 12, 60, 60 · 20, 180, 420, 280 … row sums 0, 2, 18, 132, 900, 5910, 37926, …
  (−∞, 0] nonnegative
• A173018 → reverse (shift +1) → (θ+1)²
  1 · 0, 4 · 0, 4, 9 · 0, 4, 36, 16 … row sums 1, 4, 13, 56, 304, 1980, 15000, 129360, …
  (−∞, 0] nonnegative
• A078812 → reverse
  1 · 1, 2 · 1, 4, 3 · 1, 6, 10, 4 … row sums 1, 3, 8, 21, 55, 144, 377, 987, …
  (−∞, 0] nonnegative
• A081579 → D
  1 · 6, 2 · 11, 22, 3 · 16, 92, 48, 4 … row sums 0, 1, 8, 36, 160, 640, 2496, 9408, …
  (−∞, 0] nonnegative
• A023531 → 2D+1 → x ↦ x+1
  1 · 3, 1 · 5, 6, 1 · 7, 15, 9, 1 … row sums 1, 4, 12, 32, 80, 192, 448, 1024, …
  (−∞, −1] nonnegative rational roots