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1381 sequences

• A334218 → (θ+1)²
  1 · 1 · 0, 8 · 0, 12, 27 … row sums 1, 1, 8, 39, 224, 1520, 11880, 105000, …
  (−∞, 0] nonnegative
• A064861 → x ↦ x+1
  6, 7, 2 · 18, 33, 20, 4 · 36, 84, 73, 28, 4 … row sums 15, 75, 225, 1125, 3375, 16875, 50625, …
  (−∞, −1] nonnegative rational roots
• A100862 → D+1
  1 · 2, 1 · 4, 5, 1 · 7, 18, 9, 1 … row sums 1, 3, 10, 35, 129, 497, 1996, 8325, …
  (−∞, 0] nonnegative
• basis-map coefficients of A113214, shifted → x ↦ x/(x+1)
  1 · -1, -2 · 1, 4, 4 · -1, -6, -12, -8 … row sums 1, -3, 9, -27, 81, -243, 729, -2187, …
  [−1, 0] rational roots
• A007318 → (1/3+(1/2)n+(1/6)n²)θ+1+(3/2)n+(1/2)n² → D+1
  1 · 7, 4 · 22, 36, 10 · 50, 140, 110, 20 … row sums 1, 11, 68, 320, 1280, 4592, 15232, …
  (−∞, 0] nonnegative
• A007318 → (1/3+(1/2)n+(1/6)n²)θ+1+(3/2)n+(1/2)n² → x ↦ x+1
  1 · 7, 4 · 32, 36, 10 · 120, 200, 110, 20 … row sums 1, 11, 78, 450, 2295, 10773, 47628, …
  (−∞, −1] nonnegative rational roots
• A132014: T(n,j) for double application of an iterated mixed order Laguerre transform: Coefficients of Laguerre polynomial (-1)^n*n!*L(n,2-n,x).
  A023531 → D²−2D+1 (shift -1)
  1 · -2, 1 · 2, -4, 1 · 0, 6, -6, 1 … row sums 1, -1, -1, 1, 5, 11, 19, 29, …
  A132014 (−∞, ∞)
• A008292 → γ (scale 1/4) (shift +1) → (θ+1)²
  1 · 2 · 4, 8 · 8, 64 … row sums 1, 2, 12, 72, 512, 4144, 37632, 379008, …
  (−∞, 0] nonnegative
• A172431 → basis A007318
  1 · 3, 2 · 8, 10, 3 · 21, 38, 22, 4 … row sums 1, 5, 21, 85, 341, 1365, 5461, 21845, …
  (−∞, −1] nonnegative
• basis-map coefficients of Riordan array (1+2x,x(1+x)). shifted by x -> -x + 0
  1 · -1, -1 · 1, 2, 1 · -1, -3, -3, -1 … row sums 1, -2, 4, -8, 16, -32, 64, -128, …
  (−∞, −1] rational roots
• A013620 → D
  3 · 12, 18 · 36, 108, 81 · 96, 432, 648, 324 … row sums 0, 3, 30, 225, 1500, 9375, 56250, …
  (−∞, 0] nonnegative rational roots
• A007318 → ×(1+(3/2)n+(1/2)n²) → θ+1
  1 · 3, 6 · 6, 24, 18 · 10, 60, 90, 40 … row sums 1, 9, 48, 200, 720, 2352, 7168, 20736, …
  (−∞, 0] nonnegative rational roots
• A007318 → θ+1+n → x ↦ x+1
  1 · 5, 3 · 16, 18, 5 · 44, 72, 39, 7 … row sums 1, 8, 39, 162, 621, 2268, 8019, 27702, …
  (−∞, −1] nonnegative rational roots
• A207607 → θ+1
  1 · 1, 4 · 1, 10, 6 · 1, 18, 27, 8 … row sums 1, 5, 17, 54, 166, 499, 1475, 4303, …
  (−∞, 0] nonnegative
• A249251 → (θ+1)²
  1 · 1, 12 · 1, 24, 54 · 1, 36, 189, 192 … row sums 1, 13, 79, 418, 2014, 9127, 39583, …
  (−∞, 0] nonnegative
• A120909: Triangle read by rows: T(n,k) is the number of ternary words of length n having k runs (i.e., subwords of maximal length) of identical letters (1 <= k <= n).
  3 · 3, 6 · 3, 12, 12 · 3, 18, 36, 24 … row sums 3, 9, 27, 81, 243, 729, 2187, 6561, …
  A120909 (−∞, 0) nonnegative rational roots
• A099093 → x ↦ x−9
  1 · -27, 3 · 702, -159, 9 · -18225, 6237, -711, 27 … row sums 1, -24, 552, -12672, 290880, -6676992, …
  (23/3, 9]
• A026729 → θ+1
  1 · 0, 2 · 0, 2, 3 · 0, 0, 6, 4 … row sums 1, 2, 5, 10, 20, 38, 71, 130, …
  (−∞, 0] nonnegative
• A081582 → θ+1
  1 · 1, 2 · 1, 18, 3 · 1, 34, 51, 4 … row sums 1, 3, 22, 90, 447, 1925, 8572, 36612, …
  (−∞, 0] nonnegative
• A008292 → x ↦ x+1
  1 · 2, 1 · 6, 6, 1 · 24, 36, 14, 1 … row sums 1, 3, 13, 75, 541, 4683, 47293, 545835, …
  (−∞, −1] nonnegative
• A007318 → (θ+1)² → (θ+1)²
  1 · 1, 16 · 1, 32, 81 · 1, 48, 243, 256 … row sums 1, 17, 114, 548, 2200, 7872, 25984, …
  (−∞, 0] nonnegative
• A063007 → D+1
  1 · 3, 2 · 7, 18, 6 · 13, 72, 90, 20 … row sums 1, 5, 31, 195, 1221, 7593, 46915, …
  (−∞, 0] nonnegative
• A053117 → D
  2 · 0, 8 · -4, 0, 24 · 0, -24, 0, 64 … row sums 0, 2, 8, 20, 40, 70, 112, 168, …
  (−∞, ∞)
• A038208 → θ+1
  1 · 2, 4 · 4, 16, 12 · 8, 48, 72, 32 … row sums 1, 6, 32, 160, 768, 3584, 16384, 73728, …
  (−∞, 0] nonnegative rational roots
• basis-map coefficients of A021012 → reverse
  1 · -1 · 2 · -6 … row sums 1, -1, 2, -6, 24, -120, 720, -5040, …
  (−∞, 0] rational roots
• A123519 → D
  6, 8 · 12, 40, 24 · 20, 120, 168, 64 … row sums 14, 76, 372, 1718, 7642, 33112, 140712, …
  (−∞, 0] nonnegative
• A124932: Triangle read by rows: T(n,k) = k*(k+1)*binomial(n,k)/2 (1 <= k <= n).
  A007318 → (1/2+(1/2)n)θ+1+n
  1 · 2, 3 · 3, 9, 6 · 4, 18, 24, 10 … row sums 1, 5, 18, 56, 160, 432, 1120, 2816, …
  A124932 (−∞, 0] nonnegative rational roots
• A111125 → reverse
  1 · 1, 3 · 1, 5, 5 · 1, 7, 14, 7 … row sums 1, 4, 11, 29, 76, 199, 521, 1364, …
  (−∞, 0] nonnegative
• A104684: Triangle read by rows: T(n,k) is the number of lattice paths from (0,0) to (n,n) using steps E=(1,0), N=(0,1) and D=(1,1) (i.e., bilateral Schroeder paths), having k D=(1,1) steps.
  1 · 2, 1 · 6, 6, 1 · 20, 30, 12, 1 … row sums 1, 3, 13, 63, 321, 1683, 8989, 48639, …
  A104684 (−∞, 0) nonnegative
• A152198 → D+1
  1 · 1 · 2, 1 · 2, 1 … row sums 1, 1, 3, 3, 8, 8, 20, 20, …
  (−∞, 0] nonnegative rational roots
• A008292 → γ (scale 1/4) (shift +1) → D+1
  1 · 2 · 6, 2 · 24, 16 … row sums 1, 2, 8, 40, 240, 1680, 13440, 120960, …
  (−∞, 0] nonnegative
• A126351 → x ↦ x/(x+1)
  1 · 1, 3 · 1, 7, 10 · 1, 12, 40, 37 … row sums 1, 4, 18, 90, 494, 2946, 18926, 130066, …
  [−1, 0] nonnegative
• A113953 → x ↦ x−2
  1 · -2, 1 · 0, -2, 1 · 8, -4, -2, 1 … row sums 1, -1, -1, 3, -1, -5, 7, 3, …
  (−6, 2]
• A008278 → x ↦ x+1
  1 · 2, 1 · 5, 5, 1 · 15, 23, 10, 1 … row sums 1, 3, 11, 49, 257, 1539, 10299, 75905, …
  (−∞, −1] nonnegative
• A011973 → D+1
  1 · 1 · 2, 1 · 3, 2 … row sums 1, 1, 3, 5, 10, 18, 33, 59, …
  (−∞, 0] nonnegative
• A178821: Triangle read by rows: T(n,k) = binomial(n+4,4) * binomial(n,k), 0 <= k <= n.
  1 · 5, 5 · 15, 30, 15 · 35, 105, 105, 35 … row sums 1, 10, 60, 280, 1120, 4032, 13440, …
  A178821 (−∞, 0) nonnegative rational roots
• A007318 → ×(1+(3/2)n+(1/2)n²) → D+1
  1 · 6, 3 · 18, 24, 6 · 40, 90, 60, 10 … row sums 1, 9, 48, 200, 720, 2352, 7168, 20736, …
  (−∞, 0] nonnegative rational roots
• A035607 → x ↦ x/(x+1)
  1 · 1, 3 · 1, 6, 7 · 1, 9, 23, 17 … row sums 1, 4, 14, 50, 178, 634, 2258, 8042, …
  [−1, 0] nonnegative
• A137320 → x ↦ x+1
  1 · 2, 2 · 6, 10, 4 · 24, 52, 36, 8 … row sums 1, 4, 20, 120, 840, 6720, 60480, …
  (−∞, −1] nonnegative rational roots
• A352880: Triangle read by rows: T(n,k) = number of vertices of degree k in an origami flip graph OFG(A2n).
  A007318 → ⊙ C(n+1,k+1) (shift +2)
  8 · 12, 18 · 16, 64, 32 · 20, 150, 200, 50 … row sums 8, 30, 112, 420, 1584, 6006, 22880, …
  A352880 (−∞, 0] nonnegative
• A010054 → reverse → D
  4 · 0, 14 · 0, 0, 30 · 0, 0, 0, 52 … row sums 0, 4, 14, 30, 52, 80, 114, 154, …
  (−∞, 0] nonnegative rational roots
• A062264 → D+1
  1 · 6, 5 · 13, 42, 15 · 22, 147, 168, 35 … row sums 1, 11, 70, 372, 1815, 8437, 38038, …
  (−∞, 0] nonnegative
• A099040 → x ↦ x−6
  1 · -12, 2 · 132, -46, 4 · -1440, 768, -136, 8 … row sums 1, -10, 90, -800, 7100, -63000, 559000, …
  (4, 6]
• A143685: Pascal-(1,9,1) array.
  1 · 1, 1 · 1, 11, 1 · 1, 21, 21, 1 … row sums 1, 2, 13, 44, 205, 806, 3457, 14168, …
  A143685 (−∞, 0) nonnegative
• A126216 → θ+1
  1 · 2, 2 · 5, 10, 3 · 14, 42, 27, 4 … row sums 1, 4, 18, 87, 439, 2278, 12052, 64669, …
  (−∞, 0] nonnegative
• A062190 → x ↦ x+1
  1 · 7, 6 · 36, 56, 21 · 165, 360, 252, 56 … row sums 1, 13, 113, 833, 5641, 36365, 227305, …
  (−∞, −1] nonnegative
• A023531 → θ+1
  1 · 0, 2 · 0, 0, 3 · 0, 0, 0, 4 … row sums 1, 2, 3, 4, 5, 6, 7, 8, …
  (−∞, 0] nonnegative rational roots
• A033282 → θ+1
  1 · 1, 4 · 1, 10, 15 · 1, 18, 63, 56 … row sums 1, 5, 26, 138, 743, 4043, 22180, …
  (−∞, 0] nonnegative
• A003506: Triangle of denominators in Leibniz's Harmonic Triangle a(n,k), n >= 1, 1 <= k <= n.
  A007318 → D
  1 · 2, 2 · 3, 6, 3 · 4, 12, 12, 4 … row sums 1, 4, 12, 32, 80, 192, 448, 1024, …
  A003506 (−∞, 0] nonnegative rational roots
• basis-map coefficients of A132812 → D
  2 · 3, 6 · -12, 24, 12 · -20, -40, 90, 20 … row sums 0, 2, 9, 24, 50, 90, 147, 224, …
  (−∞, ∞)