Sequences

• A121574 → D+1
  1 · 3, 1 · 9, 7, 1 · 24, 32, 11, 1 … Σ 1, 4, 17, 68, 264, 1002, 3739, 13768, …
  (−∞, 0]nonnegative
• A062145 → θ+1
  1 · 1, 8 · 1, 20, 30 · 1, 36, 135, 80 … Σ 1, 9, 51, 252, 1170, 5247, 23023, …
  (−∞, 0]nonnegative
• A063967 → reverse
  1 · 1, 1 · 1, 3, 2 · 1, 5, 7, 3 … Σ 1, 2, 6, 16, 44, 120, 328, 896, …
  (−∞, 0]nonnegative
• A113214 → basis A013609
  1 · 3, 2 · 4, 10, 4 · 7, 26, 28, 8 … Σ 1, 5, 18, 69, 261, 990, 3753, 14229, …
  (−∞, 0]nonnegative
• A008292 → γ (scale 1/4) (shift +1) → x ↦ x+1
  1 · 2 · 6, 2 · 24, 16 … Σ 1, 2, 8, 40, 256, 1952, 17408, 177280, …
  (−∞, −1]nonnegative
• A132393 → basis A013609
  1 · 1, 2 · 2, 6, 4 · 6, 22, 24, 8 … Σ 1, 3, 12, 60, 360, 2520, 20160, 181440, …
  (−∞, 0]nonnegativerational roots
• A039755 → D+1
  1 · 2, 1 · 5, 6, 1 · 14, 31, 12, 1 … Σ 1, 3, 12, 58, 324, 2044, 14320, 109960, …
  (−∞, 0]nonnegative
• basis-map coefficients of A021012 → Veronese 2
  1 · 0, 2 · 0, 0, 24 · 0, 0, 0, 720 … Σ 1, 0, 2, 0, 24, 0, 720, 0, …
  (−∞, 0]nonnegativerational roots
• A216973: Exponential Riordan array [x*exp(x),x].
  1 · 2, 2 · 3, 6, 3 · 4, 12, 12, 4 … Σ 0, 1, 4, 12, 32, 80, 192, 448, …
  (−∞, −1]nonnegativerational roots
• A172431 → Veronese 2 (j=1)
  2 · 4 · 6, 4 · 8, 20 … Σ 0, 2, 4, 10, 28, 72, 188, 494, …
  (−∞, 0]nonnegative
• A128813 → basis A008277
  1 · 2, 1 · 8, 13, 3 · 56, 217, 135, 18 … Σ 1, 3, 24, 426, 14356, 817201, 72259579, …
  (−∞, 0]nonnegative
• A093565: (8,1) Pascal triangle.
  1 · 8, 1 · 8, 9, 1 · 8, 17, 10, 1 … Σ 1, 9, 18, 36, 72, 144, 288, 576, …
  (−∞, 0)nonnegativerational roots
• A207823: Triangle of coefficients of Chebyshev's S(n,x+4) polynomials (exponents of x in increasing order).
  1 · 4, 1 · 15, 8, 1 · 56, 46, 12, 1 … Σ 1, 5, 24, 115, 551, 2640, 12649, 60605, …
  (−6, −2)nonnegative
• A126351 → D
  2 · 5, 8 · 9, 38, 24 · 14, 110, 195, 64 … Σ 0, 2, 13, 71, 383, 2129, 12360, 75242, …
  (−∞, 0]nonnegative
• A007318 → ×(−(1/2)n+(1/2)n²) → D+1
  3, 4, 1 · 12, 27, 18, 3 · 30, 96, 108, 48, 6 … Σ 0, 0, 8, 60, 288, 1120, 3840, 12096, …
  (−∞, 0]nonnegativerational roots
• A102662 → D
  3 · 5, 6 · 7, 22, 9 · 9, 46, 51, 12 … Σ 0, 3, 11, 38, 118, 349, 997, 2780, …
  (−∞, 0]nonnegative
• A137338 → D+1
  1 · 0, 1 · -3, -1, 1 · 9, -6, -3, 1 … Σ 1, 1, -3, 1, 13, -61, 223, -867, …
  (−∞, ∞)
• A390433: Triangle read by rows, Lah numbers with level 2.
  1 · 0, 1 · 0, 4, 1 · 0, 36, 20, 1 … Σ 1, 1, 5, 57, 1169, 37673, 1749541, …
  (−∞, 0]nonnegative
• A013618 → basis A013611
  144, 1056, 1936 · 1728, 19008, 69696, 85184 … Σ 3136, 175616, 9834496, 550731776, …
  (−∞, 0]nonnegativerational roots
• A282629: Sheffer triangle (exp(x), exp(3*x) - 1). Named S2[3,1].
  1 · 1, 3 · 1, 15, 9 · 1, 63, 108, 27 … Σ 1, 4, 25, 199, 1876, 20257, 245017, …
  (−∞, 0)nonnegative
• A128099 → Veronese 2 (j=1)
  2 · 4 · 6 · 8 … Σ 0, 0, 2, 4, 6, 8, 18, 44, …
  (−∞, 0]nonnegative
• A225470 → Pₙ + Pₙ₊₁
  3, 1 · 12, 8, 1 · 90, 73, 16, 1 … Σ 4, 21, 180, 2106, 31104, 554040, …
  (−∞, ∞)nonnegativerational roots
• A116414 → basis A007318
  1 · 5, 1 · 22, 10, 1 · 95, 69, 15, 1 … Σ 1, 6, 33, 180, 981, 5346, 29133, …
  (−9, −1)nonnegative
• A113214 → x ↦ x−2
  1 · 0, 1 · -2, -1, 1 · 4, -2, -2, 1 … Σ 1, 1, -2, 1, 1, -2, 1, 1, …
  (−2, 2]
• A111125: Triangle read by rows: T(k,s) = ((2*k+1)/(2*s+1))*binomial(k+s,2*s), 0 <= s <= k.
  1 · 3, 1 · 5, 5, 1 · 7, 14, 7, 1 … Σ 1, 4, 11, 29, 76, 199, 521, 1364, …
  (−4, 0)nonnegative
• A249250 → D
  3 · 6, 6 · 9, 30, 9 · 12, 72, 72, 12 … Σ 0, 3, 12, 48, 168, 564, 1824, 5760, …
  (−∞, 0]nonnegative
• A013612 → basis A013610
  36, 180, 225 · 216, 1620, 4050, 3375 … Σ 441, 9261, 194481, 4084101, 85766121, …
  (−∞, 0]nonnegativerational roots
• A038303 → basis A007318
  1 · 11, 1 · 121, 22, 1 · 1331, 363, 33, 1 … Σ 1, 12, 144, 1728, 20736, 248832, …
  (−∞, 0]nonnegativerational roots
• A038328 → basis A013609
  196, 112, 16 · 2744, 2352, 672, 64 … Σ 324, 5832, 104976, 1889568, 34012224, …
  (−∞, 0]nonnegativerational roots
• A139548 → basis A013609
  1 · 8, 16, 8 · 64, 256, 384, 256, 64 … Σ 1, 32, 1024, 32768, 1048576, 33554432, …
  (−∞, 0]nonnegativerational roots
• A008288 → D
  1 · 3, 2 · 5, 10, 3 · 7, 26, 21, 4 … Σ 0, 1, 5, 18, 58, 175, 507, 1428, …
  (−∞, 0]nonnegative
• A269944 → basis A013609
  1 · 1, 2 · 2, 6, 4 · 10, 34, 32, 8 … Σ 1, 3, 12, 84, 1008, 19152, 536256, …
  (−∞, 0]nonnegativerational roots
• A027467 → basis A013609
  1 · 16, 2 · 256, 64, 4 · 4096, 1536, 192, 8 … Σ 1, 18, 324, 5832, 104976, 1889568, …
  (−∞, 0]nonnegativerational roots
• A094816: Triangle read by rows: T(n,k) are the coefficients of Charlier polynomials: A046716 transposed, for 0 <= k <= n.
  1 · 1, 1 · 1, 3, 1 · 1, 8, 6, 1 … Σ 1, 2, 5, 16, 65, 326, 1957, 13700, …
  (−∞, 0)nonnegative
• A347056: Triangle read by rows: T(n,k) = (n+1)*(n+2)*(k+3)*binomial(n,k)/6, 0 <= k <= n.
  1 · 3, 4 · 6, 16, 10 · 10, 40, 50, 20 … Σ 1, 7, 32, 120, 400, 1232, 3584, 9984, …
  (−∞, 0)nonnegativerational roots
• A344565 → x ↦ x/(x+1)
  3 · 15, 30 · 45, 180, 180 · 105, 630, 1260, 840 … Σ 3, 45, 405, 2835, 17010, 91854, 459270, …
  [−1, 0]nonnegativerational roots
• A113953 → basis A013611
  1 · 1, 4 · 3, 16, 16 · 5, 44, 112, 64 … Σ 1, 5, 35, 225, 1475, 9625, 62875, …
  (−∞, 0]nonnegative
• A038330 → basis A008277
  256, 144, 16 · 4096, 3904, 960, 64 … Σ 416, 9024, 204544, 4849664, 120303616, …
  (−∞, 0]nonnegative
• A142462 → Pₙ + Pₙ₊₁
  2, 1 · 2, 17, 1 · 2, 159, 144, 1 … Σ 3, 20, 306, 6912, 205344, 7551360, …
  (−∞, ∞)nonnegative
• A038321 → basis A007318
  324, 252, 49 · 5832, 6804, 2646, 343 … Σ 625, 15625, 390625, 9765625, 244140625, …
  (−∞, 0]nonnegativerational roots
• A103406 → x ↦ x+1
  1 · 3, 2 · 8, 10, 3 · 20, 36, 21, 4 … Σ 1, 5, 21, 81, 297, 1053, 3645, 12393, …
  (−∞, −1]nonnegativerational roots
• A151775: Triangle read by rows: T(n,k) = value of (d^2n/dx^2n) (tan^(2k)(x)/cos(x)) at the point x = 0.
  1 · 1, 2 · 5, 28, 24 · 61, 662, 1320, 720 … Σ 1, 3, 57, 2763, 250737, 36581523, …
  (−∞, 0]nonnegative
• A001263 → basis A013611
  1 · 2, 4 · 5, 20, 16 · 14, 84, 144, 64 … Σ 1, 6, 41, 306, 2426, 20076, 171481, …
  (−∞, 0]nonnegative
• A139548: Triangle T(n,k) with the coefficient of [x^k] of the polynomial (2*(x+1)^2)^n in row n, column k, 0<=k<=2n.
  1 · 2, 4, 2 · 4, 16, 24, 16, 4 … Σ 1, 8, 64, 512, 4096, 32768, 262144, …
  (−∞, 0)nonnegativerational roots
• A013609 → basis A008288
  1 · 3, 2 · 9, 16, 4 · 27, 82, 52, 8 … Σ 1, 5, 29, 169, 985, 5741, 33461, …
  [−3−2√2, −3+2√2]nonnegative
• A131431 → Veronese 2 (j=1)
  4 · 0, 10 · 0, 0, 16 · 0, 0, 0, 22 … Σ 0, 4, 0, 10, 0, 16, 0, 22, …
  (−∞, 0]nonnegativerational roots
• A056939 → x ↦ x/(x+1)
  1 · 1, 2 · 1, 6, 6 · 1, 13, 33, 22 … Σ 1, 3, 13, 69, 417, 2763, 19609, 146793, …
  [−1, 0]nonnegative
• A274498 → (θ+1)²
  1 · 3 · 3, 24 · 9, 72 … Σ 1, 3, 27, 81, 477, 1431, 7047, 21141, …
  (−∞, 0]nonnegative
• A290596: Triangle read by rows. A generalization of unsigned Lah numbers, called L[3,1].
  1 · 2, 1 · 10, 10, 1 · 80, 120, 24, 1 … Σ 1, 3, 21, 225, 3213, 57051, 1207953, …
  (−∞, 0)nonnegative
• A143683 → θ+1
  1 · 1, 2 · 1, 20, 3 · 1, 38, 57, 4 … Σ 1, 3, 24, 100, 528, 2352, 11008, 48960, …
  (−∞, 0]nonnegative