Sequences

• A062196 → (θ+1)²
  1 · 1, 12 · 1, 32, 54 · 1, 60, 270, 160 … Σ 1, 13, 87, 491, 2562, 12762, 61611, …
  (−∞, 0]nonnegative
• A257618 → x ↦ x/(x+1)
  1 · 2, 4 · 4, 48, 48 · 8, 496, 1440, 960 … Σ 1, 6, 100, 2904, 117520, 6105696, …
  [−1, 0]nonnegative
• A225470 → basis A013611 → D
  4 · 36, 32 · 396, 576, 192 · 5400, 10080, 5760, 1024 … Σ 0, 4, 68, 1164, 22264, 481256, …
  (−∞, 0]nonnegative
• A075499 → x ↦ x/(x+1)
  16, 44, 29 · 64, 304, 440, 201 … Σ 89, 1009, 13457, 210105, 3747753, …
  [−1, 0]nonnegative
• A124932 → basis A013611
  1 · 5, 12 · 18, 84, 96 · 56, 384, 864, 640 … Σ 1, 17, 198, 1944, 17280, 143856, …
  (−∞, 0]nonnegativerational roots
• A081579 → basis A013609 → basis A013609
  1 · 4, 4 · 28, 48, 16 · 160, 416, 320, 64 … Σ 1, 8, 92, 960, 10256, 108928, 1158592, …
  (−∞, 0]nonnegative
• A062264 → reverse → D
  1 · 12, 2 · 63, 42, 3 · 224, 336, 96, 4 … Σ 0, 1, 14, 108, 660, 3575, 18018, 86632, …
  (−∞, 0]nonnegative
• A081578 → Veronese 2
  1 · 1 · 1, 1 · 1, 9 … Σ 1, 1, 2, 10, 35, 91, 260, 820, …
  (−∞, 0]nonnegative
• A134309 → basis A007318
  1 · 1, 1 · 2, 4, 2 · 4, 12, 12, 4 … Σ 1, 2, 8, 32, 128, 512, 2048, 8192, …
  (−∞, 0]nonnegativerational roots
• A099040 → basis A013609 → basis A013609
  1 · 6, 8 · 42, 104, 64 · 288, 1056, 1280, 512 … Σ 1, 14, 210, 3136, 46844, 699720, …
  (−∞, 0]nonnegative
• A136394 → basis A013611
  1 · 1 · 2, 4 · 6, 20 … Σ 1, 1, 6, 26, 176, 1296, 11296, 110176, …
  (−∞, 0]nonnegative
• A078812 → x ↦ x+1 → θ+1
  1 · 3, 2 · 8, 12, 3 · 21, 50, 27, 4 … Σ 1, 5, 23, 102, 441, 1871, 7823, 32332, …
  (−∞, 0]nonnegative
• A027466 → basis A013609 → (θ+1)²
  1 · 8, 8 · 64, 128, 36 · 512, 1536, 864, 128 … Σ 1, 16, 228, 3040, 38800, 480000, …
  (−∞, 0]nonnegative
• A286724 → D+1
  1 · 3, 1 · 16, 10, 1 · 120, 108, 21, 1 … Σ 1, 4, 27, 250, 2917, 40896, 667999, …
  (−∞, 0]nonnegative
• A137597 → reverse
  1 · 1, 2 · 1, 5, 5 · 1, 9, 22, 15 … Σ 1, 3, 11, 47, 227, 1215, 7107, 44959, …
  (−∞, 0]nonnegative
• A193728 → basis A007318
  1 · 3, 1 · 21, 16, 3 · 147, 175, 69, 9 … Σ 1, 4, 40, 400, 4000, 40000, 400000, …
  (−∞, 0]nonnegativerational roots
• A007318 → Veronese 2 (j=1)
  1 · 2 · 3, 1 · 4, 4 … Σ 0, 1, 2, 4, 8, 16, 32, 64, …
  (−∞, 0]nonnegative
• A116412 → basis A007318 → reverse
  1 · 1, 4 · 1, 8, 13 · 1, 12, 42, 43 … Σ 1, 5, 22, 98, 436, 1940, 8632, 38408, …
  (−∞, 0]nonnegative
• A081581 → basis A013610
  1 · 2, 3 · 10, 30, 9 · 32, 144, 162, 27 … Σ 1, 5, 49, 365, 3001, 23765, 190849, …
  (−∞, 0]nonnegative
• A030528 → basis A013611 → basis A013610
  1 · 6, 12 · 35, 144, 144 · 205, 1272, 2592, 1728 … Σ 1, 18, 323, 5797, 104040, 1867229, …
  (−∞, 0]nonnegative
• A371259 → (θ+1)²
  1 · 36, 4 · 1764, 400, 9 · 112896, 39456, 1800, 16 … Σ 1, 40, 2173, 154168, 13853865, …
  (−∞, 0]nonnegative
• A038336 → x ↦ x+1 → basis A013610
  1024, 1920, 900 · 32768, 92160, 86400, 27000 … Σ 3844, 238328, 14776336, 916132832, …
  (−∞, 0]nonnegativerational roots
• A089503 → reverse
  1 · 4, 1 · 30, 12, 1 · 336, 168, 24, 1 … Σ 1, 5, 43, 529, 8501, 169021, 4010455, …
  (−∞, 0]nonnegative
• A063967 → basis A013611 → (θ+1)²
  1 · 2, 16 · 6, 80, 144 · 16, 320, 1152, 1024 … Σ 1, 18, 230, 2512, 25052, 235224, …
  (−∞, 0]nonnegative
• A128099 → D → D+1
  2 · 4 · 14, 8 · 32, 24 … Σ 0, 0, 2, 4, 22, 56, 178, 460, …
  (−∞, 0]nonnegative
• A131689 → D+1
  1 · 1, 1 · 1, 5, 2 · 1, 13, 24, 6 … Σ 1, 2, 8, 44, 308, 2612, 25988, 296564, …
  (−∞, 0]nonnegative
• A013620 → D+1
  1 · 5, 3 · 16, 30, 9 · 44, 144, 135, 27 … Σ 1, 8, 55, 350, 2125, 12500, 71875, …
  (−∞, 0]nonnegativerational roots
• A059364 → basis A013611 → D+1
  1 · 7, 4 · 59, 108, 32 · 593, 1992, 1904, 384 … Σ 1, 11, 199, 4873, 149489, 5498659, …
  (−∞, 0]nonnegative
• A147716 → basis A013609 → x ↦ x+1
  1 · 17, 2 · 289, 68, 4 · 4913, 1734, 204, 8 … Σ 1, 19, 361, 6859, 130321, 2476099, …
  (−∞, −1]nonnegativerational roots
• A143491 → basis A013610 → x ↦ x/(x+1)
  12, 45, 42 · 60, 321, 570, 336 … Σ 99, 1287, 19305, 328185, 6235515, …
  [−1, 0]nonnegativerational roots
• A127773 → D+1
  1 · 3, 3 · 0, 12, 6 · 0, 0, 30, 10 … Σ 1, 6, 18, 40, 75, 126, 196, 288, …
  (−∞, 0]nonnegativerational roots
• A008459 → basis A013609 → (θ+1)²
  1 · 2, 8 · 6, 48, 36 · 20, 240, 432, 128 … Σ 1, 10, 90, 820, 7390, 65484, 571060, …
  (−∞, 0]nonnegative
• A193727: Mirror of the triangle A193726.
  1 · 2, 1 · 10, 9, 2 · 50, 65, 28, 4 … Σ 1, 3, 21, 147, 1029, 7203, 50421, …
  (−∞, 0)nonnegativerational roots
• A099093 → x ↦ x−12
  1 · -36, 3 · 1260, -213, 9 · -44064, 11232, -954, 27 … Σ 1, -33, 1056, -33759, 1079199, …
  (32/3, 12]
• A340556: E2(n, k), the second-order Eulerian numbers with E2(0, k) = δ_{0, k}. Triangle read by rows, E2(n, k) for 0 <= k <= n.
  A163936 → reverse
  1 · 0, 1 · 0, 1, 2 · 0, 1, 8, 6 … Σ 1, 1, 3, 15, 105, 945, 10395, 135135, …
  (−∞, 0]nonnegative
• A356546 → x ↦ x+1 → (θ+1)²
  1 · 4, 8 · 24, 96, 54 · 160, 960, 1080, 320 … Σ 1, 12, 174, 2520, 35910, 503496, …
  (−∞, 0]nonnegative
• A173018 → x ↦ x+1 → (θ+1)²
  1 · 1 · 2, 4 · 6, 24, 9 … Σ 1, 1, 6, 39, 310, 2935, 32186, 400855, …
  (−∞, 0]nonnegative
• A178820 → basis A013611 → θ+1
  1 · 8, 32 · 40, 320, 480 · 160, 1920, 5760, 5120 … Σ 1, 40, 840, 12960, 166320, 1886976, …
  (−∞, 0]nonnegativerational roots
• A286718 → basis A013609 → D+1
  1 · 4, 2 · 24, 22, 4 · 212, 252, 84, 8 … Σ 1, 6, 50, 556, 7788, 131888, 2622352, …
  (−∞, 0]nonnegative
• A143685 → basis A007318
  1 · 2, 1 · 13, 13, 1 · 44, 66, 24, 1 … Σ 1, 3, 27, 135, 891, 5103, 31347, …
  (−∞, −1]nonnegative
• Triangle read by rows: T(n, k) = 2^n * [x^k] hypergeom([-n, -n, 1], [1], x).
  4, 16, 8 · 8, 72, 144, 48 · 16, 256, 1152, 1536, 384 … Σ 28, 272, 3344, 49472, 852928, 16758016, …
  (−∞, 0)nonnegative
• A188440 → basis A007318 → x ↦ x+1
  1 · 1 · 5, 2 · 5, 2 … Σ 1, 1, 7, 7, 49, 49, 343, 343, …
  (−∞, −1]nonnegativerational roots
• A133080 → Veronese 2 (j=1)
  1 · 0, 1 · 0, 0, 1 · 0, 0, 0, 1 … Σ 0, 1, 0, 1, 0, 1, 0, 1, …
  (−∞, 0]nonnegativerational roots
• A094638 → θ+1 → basis A008277
  1 · 3, 2 · 13, 24, 6 · 70, 279, 177, 24 … Σ 1, 5, 43, 550, 9806, 232236, 7037682, …
  (−∞, 0]nonnegative
• A274496 → basis A013610 → θ+1
  1 · 2 · 4, 12 · 8, 24 … Σ 1, 2, 16, 32, 220, 440, 2800, 5600, …
  (−∞, 0]nonnegativerational roots
• A053122 → D+1
  1 · -1, 1 · -1, -2, 1 · 6, -2, -3, 1 … Σ 1, 0, -2, 2, 1, -4, 3, 2, …
  (−∞, ∞)
• A079638 → basis A013610
  1 · 4, 3 · 24, 33, 9 · 192, 366, 189, 27 … Σ 1, 7, 66, 774, 10800, 174240, 3185280, …
  (−∞, 0]nonnegative
• A153656 → basis A013610
  2 · 46, 69 · 1058, 3174, 18 … Σ 2, 115, 4250, 243430, 9428150, …
  (−∞, 0]nonnegative
• A038322: Triangle whose (i,j)-th entry is binomial(i,j)*11^(i-j)*8^j.
  1 · 11, 8 · 121, 176, 64 · 1331, 2904, 2112, 512 … Σ 1, 19, 361, 6859, 130321, 2476099, …
  (−∞, −1]nonnegativerational roots
• A093645 → basis A007318
  1 · 11, 1 · 22, 13, 1 · 44, 48, 15, 1 … Σ 1, 12, 36, 108, 324, 972, 2916, 8748, …
  (−∞, 0]nonnegativerational roots