Sequences

• 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
• basis-map coefficients of A113214, shifted → Veronese 2 → basis A013609
  1 · -1 · 2, 2 · -4, -6 … Σ 1, -1, 4, -10, 28, -76, 208, -568, …
  (−∞, 0]
• A131431 → θ+1 → basis A013611
  1 · 8, 32 · 21, 168, 336 · 40, 480, 1920, 2560 … Σ 1, 40, 525, 5000, 40625, 300000, …
  (−∞, 0]nonnegativerational roots
• A207607 → basis A013611 → basis A013609
  1 · 11, 16 · 76, 200, 128 · 521, 1992, 2496, 1024 … Σ 1, 27, 404, 6033, 90091, 1345332, …
  (−∞, 0]nonnegative
• A094638 → basis A013609 → basis A008277
  1 · 4, 2 · 28, 38, 8 · 280, 776, 404, 48 … Σ 1, 6, 74, 1508, 45492, 1892232, …
  (−∞, 0]nonnegative
• A038284 → (θ+1)²
  64, 384, 324 · 512, 4608, 7776, 3456 … Σ 772, 16352, 320656, 5970944, 107103808, …
  (−∞, 0]nonnegative
• A126351 → D
  2 · 5, 8 · 9, 38, 24 · 14, 110, 195, 64 … Σ 0, 2, 13, 71, 383, 2129, 12360, 75242, …
  (−∞, 0]nonnegative
• A081580 → basis A007318 → D
  1 · 9, 2 · 42, 32, 3 · 202, 248, 69, 4 … Σ 0, 1, 11, 77, 523, 3225, 19383, 112693, …
  (−∞, 0]nonnegative
• A038319 → basis A013611 → (θ+1)²
  256, 2560, 3600 · 4096, 61440, 172800, 128000 … Σ 6416, 366336, 19097856, 937598976, …
  (−∞, 0]nonnegative
• A038279 → D
  1 · 16, 2 · 192, 48, 3 · 2048, 768, 96, 4 … Σ 0, 1, 18, 243, 2916, 32805, 354294, …
  (−∞, 0]nonnegativerational roots
• A130123 → D → basis A008277
  2 · 8, 8 · 24, 72, 24 · 64, 448, 384, 64 … Σ 0, 2, 16, 120, 960, 8320, 77952, …
  (−∞, 0]nonnegative
• A207824 → basis A013611 → (θ+1)²
  1 · 6, 16 · 35, 192, 144 · 204, 1696, 2592, 1024 … Σ 1, 22, 371, 5516, 76085, 997826, …
  (−∞, 0]nonnegative
• A038226 → basis A013611 → basis A007318
  1849, 2752, 1024 · 79507, 177504, 132096, 32768 … Σ 5625, 421875, 31640625, 2373046875, …
  (−∞, −1]nonnegativerational roots
• 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
• A054142 → reverse → D+1
  1 · 2, 1 · 4, 5, 1 · 7, 16, 8, 1 … Σ 1, 3, 10, 32, 99, 299, 887, 2595, …
  (−∞, 0]nonnegative
• A102662 → D
  3 · 5, 6 · 7, 22, 9 · 9, 46, 51, 12 … Σ 0, 3, 11, 38, 118, 349, 997, 2780, …
  (−∞, 0]nonnegative
• A146988 → basis A013609
  1 · 2, 2 · 8, 16, 4 · 40, 120, 88, 8 … Σ 1, 4, 28, 256, 3328, 50176, 790528, …
  (−∞, 0]nonnegative
• A261711 → θ+1
  1 · 4 · 15, 2 · 56, 16 … Σ 1, 4, 17, 72, 304, 1280, 5376, 22528, …
  (−∞, 0]nonnegative
• basis-map coefficients of A113214, shifted → basis A013609 → D
  -2 · 8, 8 · -24, -48, -24 · 64, 192, 192, 64 … Σ 0, -2, 16, -96, 512, -2560, 12288, …
  (−∞, 0]rational roots
• A209414 → basis A013610
  1 · 2, 3 · 6, 18, 9 · 18, 84, 108, 27 … Σ 1, 5, 33, 237, 1737, 12789, 94257, …
  (−∞, 0]nonnegative
• A137338 → D+1
  1 · 0, 1 · -3, -1, 1 · 9, -6, -3, 1 … Σ 1, 1, -3, 1, 13, -61, 223, -867, …
  (−∞, ∞)
• A059364 → θ+1
  1 · 2, 2 · 6, 14, 6 · 24, 92, 87, 24 … Σ 1, 4, 26, 227, 2463, 31818, 476004, …
  (−∞, 0]nonnegative
• A125662 → reverse → D
  3 · 6, 16 · 9, 50, 63 · 12, 102, 270, 220 … Σ 0, 3, 22, 122, 604, 2809, 12554, 54580, …
  (−∞, 0]nonnegative
• A059364 → D+1
  1 · 3, 1 · 13, 11, 2 · 70, 104, 47, 6 … Σ 1, 4, 26, 227, 2463, 31818, 476004, …
  (−∞, −1]nonnegative
• 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
• Veronese parent of A109447 → Veronese 2 (j=1) → D+1
  1 · 2 · 4, 3 · 8, 4 … Σ 1, 2, 7, 12, 36, 64, 176, 320, …
  (−∞, 0]nonnegative
• A330798 → θ+1
  1 · 2, 4 · 6, 30, 27 · 20, 168, 336, 192 … Σ 1, 6, 63, 716, 8285, 96210, 1116395, …
  (−∞, 0]nonnegative
• A130534 → basis A013610 → reverse
  1 · 3, 2 · 9, 15, 6 · 27, 81, 78, 24 … Σ 1, 5, 30, 210, 1680, 15120, 151200, …
  (−∞, 0]nonnegativerational roots
• A114687 → basis A007318 → basis A013609
  1 · 5, 4 · 29, 44, 16 · 185, 408, 288, 64 … Σ 1, 9, 89, 945, 10577, 123129, 1476841, …
  (−∞, 0]nonnegative
• A059110 → reverse
  1 · 1, 1 · 1, 4, 3 · 1, 9, 21, 13 … Σ 1, 2, 8, 44, 304, 2512, 24064, 261536, …
  (−∞, 0]nonnegative
• A013618 → basis A013611
  144, 1056, 1936 · 1728, 19008, 69696, 85184 … Σ 3136, 175616, 9834496, 550731776, …
  (−∞, 0]nonnegativerational roots
• A013618 → (θ+1)²
  1, 88, 1089 · 1, 132, 3267, 21296 … Σ 1178, 24696, 457920, 7852032, …
  (−∞, 0]nonnegative
• A122542 → x ↦ x+1 → basis A013609
  1 · 2, 2 · 8, 12, 4 · 28, 60, 40, 8 … Σ 1, 4, 24, 136, 776, 4424, 25224, …
  (−∞, 0]nonnegative
• 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
• A144698 → θ+1
  1 · 1, 8 · 1, 26, 48 · 1, 64, 339, 256 … Σ 1, 9, 75, 660, 6300, 65520, 740880, …
  (−∞, 0]nonnegative
• A225470 → Pₙ + Pₙ₊₁
  3, 1 · 12, 8, 1 · 90, 73, 16, 1 … Σ 4, 21, 180, 2106, 31104, 554040, …
  (−∞, ∞)nonnegativerational roots
• A178821 → basis A013610 → basis A013609
  1 · 25, 30 · 375, 900, 540 · 4375, 15750, 18900, 7560 … Σ 1, 55, 1815, 46585, 1024870, 20292426, …
  (−∞, 0]nonnegativerational roots
• A102413 → basis A013609
  1 · 2, 2 · 6, 12, 4 · 14, 42, 36, 8 … Σ 1, 4, 22, 100, 466, 2164, 10054, 46708, …
  (−∞, 0]nonnegative
• basis-map coefficients of A371080, shifted → (θ+1)²
  1 · 0, 4 · 0, 12, 9 · 0, 72, 81, 16 … Σ 1, 4, 21, 169, 1852, 25752, 434380, …
  (−∞, 0]nonnegative
• A093645 → basis A013611
  1 · 11, 4 · 22, 52, 16 · 44, 192, 240, 64 … Σ 1, 15, 90, 540, 3240, 19440, 116640, …
  (−∞, 0]nonnegativerational roots
• A120910 → Veronese 2 (j=1) → D+1
  3 · 12 · 39, 3 · 120, 24 … Σ 0, 3, 12, 42, 144, 489, 1644, 5472, …
  (−∞, 0]nonnegative
• A116414 → basis A007318
  1 · 5, 1 · 22, 10, 1 · 95, 69, 15, 1 … Σ 1, 6, 33, 180, 981, 5346, 29133, …
  (−9, −1)nonnegative
• A038207 → Veronese 2 (j=1) → basis A013610
  1 · 4 · 13, 3 · 40, 24 … Σ 0, 1, 4, 16, 64, 256, 1024, 4096, …
  (−∞, 0]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]
• A013620 → basis A008288 → θ+1
  1 · 5, 6 · 25, 78, 27 · 125, 666, 567, 108 … Σ 1, 11, 130, 1466, 15991, 170357, …
  (−∞, 0]nonnegative
• A114687 → basis A013609 → x ↦ x+1
  1 · 7, 4 · 55, 60, 16 · 469, 744, 384, 64 … Σ 1, 11, 131, 1661, 22101, 305151, …
  (−∞, −1]nonnegative
• A008288 → basis A013611 → θ+1
  1 · 2, 8 · 5, 40, 48 · 12, 144, 384, 256 … Σ 1, 10, 93, 796, 6509, 51582, 399665, …
  (−∞, 0]nonnegative
• type_b_eulerian → γ → (θ+1)²
  1 · 1 · 1, 16 · 1, 80 … Σ 1, 1, 17, 81, 1009, 9713, 134305, …
  (−∞, 0]nonnegative