Sequences

• A172431: Even row Pascal-square read by antidiagonals.
  1 · 1, 2 · 1, 4, 3 · 1, 6, 10, 4 … Σ 1, 3, 8, 21, 55, 144, 377, 987, …
  (−∞, 0)nonnegative
• A034870 → Veronese 2 (j=1)
  2 · 4, 4 · 6, 20, 6 · 8, 56, 56, 8 … Σ 0, 2, 8, 32, 128, 512, 2048, 8192, …
  (−∞, 0]nonnegative
• basis-map coefficients of A026729, shifted → basis A013611
  1 · -1, -4 · 1, 8, 16 · -1, -12, -48, -64 … Σ 1, -5, 25, -125, 625, -3125, 15625, …
  (−∞, 0]rational roots
• A094305 → D+1
  1 · 6, 3 · 18, 24, 6 · 40, 90, 60, 10 … Σ 1, 9, 48, 200, 720, 2352, 7168, 20736, …
  (−∞, 0]nonnegativerational roots
• A035607 → x ↦ x/(x+1)
  1 · 1, 3 · 1, 6, 7 · 1, 9, 23, 17 … Σ 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 … Σ 1, 4, 20, 120, 840, 6720, 60480, …
  (−∞, −1]nonnegativerational roots
• A352880: Triangle read by rows: T(n,k) = number of vertices of degree k in an origami flip graph OFG(A2n).
  8 · 12, 18 · 16, 64, 32 · 20, 150, 200, 50 … Σ 8, 30, 112, 420, 1584, 6006, 22880, …
  (−∞, 0)nonnegative
• A038279 → basis A013610
  1 · 9, 3 · 81, 54, 9 · 729, 729, 243, 27 … Σ 1, 12, 144, 1728, 20736, 248832, …
  (−∞, 0]nonnegativerational roots
• A131431 → D
  4 · 0, 14 · 0, 0, 30 · 0, 0, 0, 52 … Σ 0, 4, 14, 30, 52, 80, 114, 154, …
  (−∞, 0]nonnegativerational roots
• A322944 → Pₙ + Pₙ₊₁
  2, 1 · 3, 7, 1 · 8, 44, 16, 1 · 30, 310, 203, 29, 1 … Σ 3, 11, 69, 573, 5799, 68703, 929241, …
  (−∞, ∞)nonnegative
• A038325 → Pₙ + Pₙ₊₁
  12, 11 · 132, 253, 121 · 1452, 4235, 4114, 1331 … Σ 23, 506, 11132, 244904, 5387888, …
  (−∞, ∞)nonnegativerational roots
• A038327 → basis A007318
  1 · 13, 1 · 169, 26, 1 · 2197, 507, 39, 1 … Σ 1, 14, 196, 2744, 38416, 537824, …
  (−∞, 0]nonnegativerational roots
• A062264 → D+1
  1 · 6, 5 · 13, 42, 15 · 22, 147, 168, 35 … Σ 1, 11, 70, 372, 1815, 8437, 38038, …
  (−∞, 0]nonnegative
• A099040 → x ↦ x−6
  1 · -12, 2 · 132, -46, 4 · -1440, 768, -136, 8 … Σ 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 … Σ 1, 2, 13, 44, 205, 806, 3457, 14168, …
  (−∞, 0)nonnegative
• A304236 → basis A008277
  1 · 1 · 4, 3 · 7, 6 … Σ 1, 1, 7, 13, 64, 160, 706, 2107, …
  (−∞, 0]nonnegative
• A013620 → basis A013611
  1 · 5, 12 · 25, 120, 144 · 125, 900, 2160, 1728 … Σ 1, 17, 289, 4913, 83521, 1419857, …
  (−∞, 0]nonnegativerational roots
• A103633 → basis A008277
  1 · 1, 1 · 2, 4, 1 · 2, 10, 7, 1 … Σ 1, 2, 7, 20, 87, 322, 1657, 7432, …
  (−∞, 0]nonnegative
• A126216 → θ+1
  1 · 2, 2 · 5, 10, 3 · 14, 42, 27, 4 … Σ 1, 4, 18, 87, 439, 2278, 12052, 64669, …
  (−∞, 0]nonnegative
• A062190 → x ↦ x+1
  1 · 7, 6 · 36, 56, 21 · 165, 360, 252, 56 … Σ 1, 13, 113, 833, 5641, 36365, 227305, …
  (−∞, −1]nonnegative
• A152828 → basis A013610
  1 · 1 · 1 · 2, 3 … Σ 1, 1, 1, 5, 5, 5, 25, 25, …
  (−∞, 0]nonnegativerational roots
• theta_plus_one of a(n) = 1 if n is of the form m(m+3)/2, otherwise 0.
  1 · 0, 2 · 0, 0, 3 · 0, 0, 0, 4 … Σ 1, 2, 3, 4, 5, 6, 7, 8, …
  (−∞, 0]nonnegativerational roots
• type_b_eulerian → γ
  1 · 1 · 1, 4 · 1, 20 … Σ 1, 1, 5, 21, 153, 1209, 12285, 140589, …
  (−∞, 0]nonnegative
• A033282 → θ+1
  1 · 1, 4 · 1, 10, 15 · 1, 18, 63, 56 … Σ 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.
  1 · 2, 2 · 3, 6, 3 · 4, 12, 12, 4 … Σ 1, 4, 12, 32, 80, 192, 448, 1024, …
  (−∞, 0)nonnegativerational roots
• A102365: Triangle T(n,k), 0 <= k <= n, read by rows: given by [ 1, 0, 3, 0, 5, 0, 7, 0, 9, 0, ...] DELTA [ 0, 1, 0, 2, 0, 3, 0, 4, 0, 5, 0, ...] where DELTA is…
  1 · 1 · 1, 1 · 1, 5, 1 … Σ 1, 1, 2, 7, 35, 226, 1787, 16717, …
  (−∞, 0)nonnegative
• basis-map coefficients of A132812 → D
  2 · 3, 6 · -12, 24, 12 · -20, -40, 90, 20 … Σ 0, 2, 9, 24, 50, 90, 147, 224, …
  (−∞, ∞)
• A038243: Triangle whose (i,j)-th entry is 5^(i-j)*binomial(i,j).
  1 · 5, 1 · 25, 10, 1 · 125, 75, 15, 1 … Σ 1, 6, 36, 216, 1296, 7776, 46656, …
  (−∞, −1]nonnegativerational roots
• A091044 → θ+1
  1 · 2, 4 · 3, 20, 9 · 4, 56, 84, 16 … Σ 1, 6, 32, 160, 768, 3584, 16384, 73728, …
  (−∞, 0]nonnegative
• A166973 → Pₙ + Pₙ₊₁
  2, 1 · 2, 8, 1 · 2, 50, 19, 1 · 2, 302, 259, 35, 1 … Σ 3, 11, 72, 599, 5843, 65696, 836377, …
  (−∞, ∞)nonnegative
• A225470 → basis A013611
  1 · 3, 4 · 18, 36, 16 · 162, 396, 288, 64 … Σ 1, 7, 70, 910, 14560, 276640, 6086080, …
  (−∞, 0]nonnegativerational roots
• A145596 → D
  2 · 8, 6 · 20, 40, 12 · 40, 150, 120, 20 … Σ 0, 2, 14, 72, 330, 1430, 6006, 24752, …
  (−∞, 0]nonnegative
• A055356 → θ+1
  1 · 1 · 1, 2 · 1, 8, 6 … Σ 1, 1, 3, 15, 101, 851, 8603, 101423, …
  (−∞, 0]nonnegative
• A118884: Triangle read by rows: T(n,k) is the number of binary sequences of length n containing k subsequences 0011 (n,k>=0).
  A318772 → x ↦ (1/48)x−1/48
  1 · 2 · 4 · 8 … Σ 1, 2, 4, 8, 16, 32, 64, 128, …
  (−∞, 1]nonnegative
• A118800: Triangle read by rows: T satisfies the matrix products: C*T*C = T^-1 and T*C*T = C^-1, where C is Pascal's triangle.
  1 · 1, -1 · 2, -3, 1 · 4, -8, 5, -1 … Σ 1, 0, 0, 0, 0, 0, 0, 0, …
  [0, ∞)rational roots
• A003506 → x ↦ x+1
  1 · 4, 2 · 12, 12, 3 · 32, 48, 24, 4 … Σ 0, 1, 6, 27, 108, 405, 1458, 5103, …
  (−∞, −1]nonnegativerational roots
• A051339 → Pₙ + Pₙ₊₁
  -6, 1 · 49, -14, 1 · -448, 176, -23, 1 … Σ -5, 36, -294, 2688, -27216, 302400, …
  (−∞, ∞)rational roots
• A274498: Triangle read by rows: T(n,k) is the number of ternary words of length n having degree of asymmetry equal to k (n>=0; 0<=k<=n/2).
  1 · 3 · 3, 6 · 9, 18 … Σ 1, 3, 9, 27, 81, 243, 729, 2187, …
  (−∞, 0]nonnegativerational roots
• A028326 → γ
  2 · 2 · 2 · 2 … Σ 2, 2, 2, 2, 2, 2, 2, 2, …
  (−∞, 0]nonnegativerational roots
• A143683 → Veronese 2 (j=1)
  1 · 10 · 19, 1 · 28, 28 … Σ 0, 1, 10, 20, 56, 336, 1632, 5440, …
  (−∞, 0]nonnegative
• A172431 → basis A013609
  1 · 3, 4 · 8, 20, 12 · 21, 76, 88, 32 … Σ 1, 7, 40, 217, 1159, 6160, 32689, …
  (−∞, 0]nonnegative
• A286718 → basis A013611
  1 · 2, 4 · 10, 28, 16 · 80, 264, 240, 64 … Σ 1, 6, 54, 648, 9720, 174960, 3674160, …
  (−∞, 0]nonnegativerational roots
• A161198: Triangle of polynomial coefficients related to the series expansions of (1-x)^((-1-2*n)/2).
  1 · 1, 2 · 3, 8, 4 · 15, 46, 36, 8 … Σ 1, 3, 15, 105, 945, 10395, 135135, …
  (−∞, 0)nonnegativerational roots
• A099040 → x ↦ x−4
  1 · -8, 2 · 56, -30, 4 · -384, 320, -88, 8 … Σ 1, -6, 30, -144, 684, -3240, 15336, …
  (2, 4]
• A120910 → Veronese 2
  3 · 6 · 12, 3 · 24, 18 … Σ 3, 6, 15, 42, 123, 366, 1095, 3282, …
  (−∞, 0]nonnegative
• A145324 → basis A013609
  1 · 3, 4 · 12, 34, 24 · 60, 266, 392, 192 … Σ 1, 7, 70, 910, 14560, 276640, 6086080, …
  (−∞, 0]nonnegativerational roots
• A269947 → basis A013609
  1 · 1, 2 · 2, 6, 4 · 18, 58, 48, 8 … Σ 1, 3, 12, 132, 3960, 265320, 33960960, …
  (−∞, 0]nonnegativerational roots
• A038271 → basis A007318
  1 · 12, 5 · 144, 120, 25 · 1728, 2160, 900, 125 … Σ 1, 17, 289, 4913, 83521, 1419857, …
  (−∞, 0]nonnegativerational roots
• A038301 → basis A013609
  400, 880, 484 · 8000, 26400, 29040, 10648 … Σ 1764, 74088, 3111696, 130691232, …
  (−∞, 0]nonnegativerational roots
• A257620 → γ
  1 · 3 · 9, 18 · 27, 216 … Σ 1, 3, 27, 243, 3159, 45927, 807003, …
  (−∞, 0]nonnegative