Sequences

• A104684 → x ↦ x/(x+1)
  1 · 2, 3 · 6, 18, 13 · 20, 90, 132, 63 … Σ 1, 5, 37, 305, 2641, 23525, 213445, …
  [−1, 0]nonnegative
• A131689 → x ↦ x/(x+1)
  1 · 0, 1 · 0, 1, 3 · 0, 1, 8, 13 … Σ 1, 1, 4, 22, 160, 1456, 15904, 202672, …
  [−1, 0]nonnegative
• A152830: Triangle read by rows, A007318 rows repeated four times .
  1 · 1 · 1 · 1 … Σ 1, 1, 1, 1, 2, 2, 2, 2, …
  (−∞, 0]nonnegativerational roots
• A207606 → basis A013609 → basis A013610
  43, 114, 72 · 206, 816, 1044, 432 … Σ 229, 2498, 27249, 297241, 3242402, …
  (−∞, 0]nonnegative
• A249252 → basis A013610
  1 · 5, 12 · 17, 72, 72 · 61, 372, 720, 432 … Σ 1, 17, 161, 1585, 15553, 152657, …
  (−∞, 0]nonnegative
• A113214 → x ↦ x−5
  1 · -3, 1 · 10, -7, 1 · -35, 37, -11, 1 … Σ 1, -2, 4, -8, 16, -32, 64, -128, …
  (1, 5]
• A039755 → x ↦ x+1 → x ↦ x/(x+1)
  1 · 2, 3 · 6, 18, 13 · 24, 106, 152, 71 … Σ 1, 5, 37, 353, 4009, 52253, 764557, …
  [−1, 0]nonnegative
• A028421: theta_plus_one of Triangle T(n,k), 0 <= k <= n, read by rows, giving coefficients of the polynomial (x+1)(x+2)...(x+n), expanded in increasing powers …
  1 · 1, 2 · 2, 6, 3 · 6, 22, 18, 4 … Σ 1, 3, 11, 50, 274, 1764, 13068, 109584, …
  (−∞, 0)nonnegative
• A078812 → D+1
  1 · 3, 1 · 7, 6, 1 · 14, 22, 9, 1 … Σ 1, 4, 14, 46, 145, 444, 1331, 3926, …
  (−∞, 0]nonnegative
• A146988: Triangle, read by rows, T(n, k) = binomial(n, k) for n < 2 and binomial(n, k) + 4^(n-1) * binomial(n-2, k-1) otherwise.
  1 · 1, 1 · 1, 6, 1 · 1, 19, 19, 1 … Σ 1, 2, 8, 40, 272, 2080, 16448, 131200, …
  (−∞, 0)nonnegative
• A029653 → basis A013611
  1 · 3, 4 · 6, 20, 16 · 12, 64, 112, 64 … Σ 1, 7, 42, 252, 1512, 9072, 54432, …
  (−∞, 0]nonnegativerational roots
• A135838 → x ↦ x+1
  1 · 4, 2 · 8, 8, 2 · 32, 48, 24, 4 … Σ 1, 6, 18, 108, 324, 1944, 5832, 34992, …
  (−∞, −1]nonnegativerational roots
• A099097 → basis A007318 → D+1
  1 · 6, 3 · 29, 37, 9 · 126, 267, 168, 27 … Σ 1, 9, 75, 588, 4436, 32580, 234596, …
  (−∞, 0]nonnegative
• A062196 → reverse
  1 · 3, 1 · 6, 8, 1 · 10, 30, 15, 1 … Σ 1, 4, 15, 56, 210, 792, 3003, 11440, …
  (−∞, 0]nonnegative
• A127648 → D → D
  6 · 0, 24 · 0, 0, 60 · 0, 0, 0, 120 … Σ 0, 0, 0, 6, 24, 60, 120, 210, …
  (−∞, 0]nonnegativerational roots
• basis-map coefficients of A030528, shifted → basis A013610 → reverse
  1 · -3, -1 · 9, 6, 1 · -27, -27, -9, -1 … Σ 1, -4, 16, -64, 256, -1024, 4096, …
  (−∞, −1]rational roots
• basis-map coefficients of A113214, shifted → x ↦ x+1 → basis A008277
  1 · -3, -1 · 9, 7, 1 · -27, -37, -12, -1 … Σ 1, -4, 17, -77, 372, -1915, 10481, …
  (−∞, 0]
• A193726 → basis A008277
  1 · 3, 2 · 21, 39, 10 · 147, 573, 365, 50 … Σ 1, 5, 70, 1135, 20885, 428250, 9648085, …
  (−∞, 0]nonnegative
• A109983 → θ+1
  1 · 0, 2, 6 · 0, 0, 3, 24, 30 … Σ 1, 8, 57, 384, 2505, 16008, 100849, …
  (−∞, 0]nonnegative
• A011973 → basis A013611 → basis A013609
  1 · 1 · 6, 8 · 11, 16 … Σ 1, 1, 14, 27, 209, 560, 3277, 10557, …
  (−∞, 0]nonnegative
• basis-map coefficients of A021012 → Veronese 2 (j=1)
  -1 · 0, -6 · 0, 0, -120 · 0, 0, 0, -5040 … Σ 0, -1, 0, -6, 0, -120, 0, -5040, …
  (−∞, 0]rational roots
• A104684 → basis A013611 → (θ+1)²
  1 · 3, 16 · 13, 128, 144 · 63, 912, 2160, 1024 … Σ 1, 19, 285, 4159, 59905, 849507, …
  (−∞, 0]nonnegative
• A121574 → basis A013609 → x ↦ x/(x+1)
  1 · 3, 5 · 10, 34, 28 · 33, 169, 283, 155 … Σ 1, 8, 72, 640, 5696, 50688, 451072, …
  [−1, 0]nonnegative
• A038319 → basis A013610 → D+1
  736, 930, 225 · 15616, 33120, 20925, 3375 … Σ 1891, 73036, 2710981, 97893226, …
  (−∞, 0]nonnegativerational roots
• A225471 → basis A007318 → D+1
  1 · 5, 1 · 44, 14, 1 · 560, 224, 27, 1 … Σ 1, 6, 59, 812, 14389, 312114, 8011695, …
  (−∞, 0]nonnegative
• A253284 → x ↦ x/(x+1)
  1 · 2, 4 · 6, 30, 36 · 24, 216, 600, 528 … Σ 1, 6, 72, 1368, 36000, 1213920, …
  [−1, 0]nonnegative
• A257616 → D
  2 · 32, 8 · 312, 624, 24 · 2656, 17472, 7968, 64 … Σ 0, 2, 40, 960, 28160, 985600, 40212480, …
  (−∞, 0]nonnegative
• A113214 → θ+1
  1 · 2, 2 · 0, 6, 3 · 0, 4, 12, 4 … Σ 1, 4, 9, 20, 40, 78, 147, 272, …
  (−∞, 0]nonnegative
• A304236 → basis A007318 → basis A013609
  1 · 1 · 7, 6 · 13, 12 … Σ 1, 1, 13, 25, 181, 481, 2653, 8425, …
  (−∞, −1]nonnegative
• A028246 → x ↦ x/(x+1)
  1 · 1, 2 · 1, 5, 6 · 1, 10, 29, 26 … Σ 1, 3, 12, 66, 480, 4368, 47712, 608016, …
  [−1, 0)nonnegative
• A152842 → reverse → x ↦ x/(x+1)
  1 · 3, 4 · 3, 10, 8 · 9, 42, 64, 32 … Σ 1, 7, 21, 147, 441, 3087, 9261, 64827, …
  [−1, 0]nonnegativerational roots
• A200536 → basis A013609 → D
  14, 16 · 168, 584, 672, 256 … Σ 0, 30, 1680, 70560, 2634240, 92198400, …
  (−∞, 0]nonnegativerational roots
• A257614 → Pₙ + Pₙ₊₁
  3, 2 · 6, 30, 4 · 12, 272, 248, 8 … Σ 5, 40, 540, 10080, 239400, 6894720, …
  (−∞, ∞)nonnegative
• A122542 → reverse → θ+1
  1 · 1 · 1, 4 · 1, 8, 6 … Σ 1, 1, 5, 15, 45, 129, 361, 991, …
  (−∞, 0]nonnegative
• A038220 → basis A007318
  1 · 5, 2 · 25, 20, 4 · 125, 150, 60, 8 … Σ 1, 7, 49, 343, 2401, 16807, 117649, …
  (−∞, −1]nonnegativerational roots
• A038255 → basis A013610 → D
  3 · 42, 18 · 441, 378, 81 · 4116, 5292, 2268, 324 … Σ 0, 3, 60, 900, 12000, 150000, 1800000, …
  (−∞, 0]nonnegativerational roots
• A136572 → D → basis A013610
  1 · 4, 12 · 18, 108, 162 · 96, 864, 2592, 2592 … Σ 0, 1, 16, 288, 6144, 153600, 4423680, …
  (−∞, 0]nonnegativerational roots
• A134991: Triangle of Ward numbers T(n,k) read by rows.
  1 · 1, 3 · 1, 10, 15 · 1, 25, 105, 105 … Σ 1, 4, 26, 236, 2752, 39208, 660032, …
  (−1, 0)nonnegative
• A110441 → basis A013609 → D
  2 · 16, 8 · 88, 96, 24 · 416, 720, 384, 64 … Σ 0, 2, 24, 208, 1584, 11256, 76608, …
  (−∞, 0]nonnegative
• A094638 → Veronese 2 (j=1) → x ↦ x+1
  1 · 3 · 12, 6 · 60, 50 … Σ 0, 1, 3, 18, 110, 945, 8547, 96796, …
  (−∞, −1]nonnegative
• A038220 → basis A013611 → basis A008288
  1 · 13, 8 · 169, 272, 64 · 2197, 6040, 3520, 512 … Σ 1, 21, 505, 12269, 298289, 7252485, …
  [−3−2√2, −3+2√2]nonnegative
• A137320 → basis A013610 → x ↦ x/(x+1)
  1 · 2, 8 · 6, 42, 72 · 24, 228, 708, 720 … Σ 1, 10, 120, 1680, 26880, 483840, …
  [−1, 0]nonnegativerational roots
• A334218: Triangle read by rows: T(n,k) is the number of permutations of 1..n arranged in a circle with exactly k descents.
  1 · 1 · 0, 2 · 0, 3, 3 … Σ 1, 1, 2, 6, 24, 120, 720, 5040, …
  (−∞, 0]nonnegative
• A143685 → γ → basis A008277
  1 · 1 · 10, 9 · 19, 18 … Σ 1, 1, 19, 37, 460, 1288, 13456, 47899, …
  (−∞, 0]nonnegative
• A136521 → basis A013609
  1 · 2, 4 · 2, 8, 8 · 2, 12, 24, 16 … Σ 1, 6, 18, 54, 162, 486, 1458, 4374, …
  (−∞, 0]nonnegativerational roots
• A123519 → basis A013609 → basis A007318
  55, 60, 16 · 433, 696, 368, 64 … Σ 131, 1561, 18601, 221651, 2641211, …
  (−∞, 0]nonnegative
• A110441 → basis A013609 → basis A013610
  1 · 6, 6 · 34, 72, 36 · 192, 624, 648, 216 … Σ 1, 12, 142, 1680, 19876, 235152, …
  (−∞, 0]nonnegative
• A054142 → Veronese 2 (j=1) → x ↦ x+1
  1 · 3 · 6, 1 · 17, 10 … Σ 0, 1, 3, 7, 27, 83, 263, 855, …
  (−∞, −1]nonnegative
• A049374 → D+1
  1 · 7, 1 · 60, 20, 1 · 612, 348, 39, 1 … Σ 1, 8, 81, 1000, 14549, 242784, 4554613, …
  (−∞, 0]nonnegative
• A257616 → D+1
  1 · 4, 2 · 36, 40, 4 · 320, 936, 336, 8 … Σ 1, 6, 80, 1600, 42240, 1379840, …
  (−∞, 0]nonnegative