Sequences

• A391403 → x ↦ x+1 → D+1
  1 · 1 · 5, 2 · 13, 6 … Σ 1, 1, 7, 19, 85, 301, 1211, 4607, …
  (−∞, 0]nonnegative
• A207823 → basis A013609 → basis A013611
  1 · 7, 8 · 48, 112, 64 · 329, 1160, 1344, 512 … Σ 1, 15, 224, 3345, 49951, 745920, …
  (−∞, 0]nonnegative
• A038220 → basis A013610 → basis A013610
  1 · 11, 18 · 121, 396, 324 · 1331, 6534, 10692, 5832 … Σ 1, 29, 841, 24389, 707281, 20511149, …
  (−∞, 0]nonnegativerational roots
• A200139 → basis A008277
  1 · 2, 1 · 6, 6, 1 · 18, 30, 11, 1 … Σ 1, 3, 13, 60, 295, 1543, 8566, 50333, …
  (−∞, 0]nonnegative
• A136124 → x ↦ x+1 → D
  1 · 7, 2 · 47, 24, 3 · 342, 238, 54, 4 … Σ 0, 1, 9, 74, 638, 5944, 60216, 662640, …
  (−∞, 0]nonnegative
• A038330 → basis A013609 → basis A008277
  576, 448, 64 · 13824, 18944, 6144, 512 … Σ 1088, 39424, 1523712, 62750720, …
  (−∞, 0]nonnegative
• A093561 → basis A013611
  1 · 5, 4 · 10, 28, 16 · 20, 96, 144, 64 … Σ 1, 9, 54, 324, 1944, 11664, 69984, …
  (−∞, 0]nonnegativerational roots
• A097806: Riordan array (1+x, 1) read by rows.
  1 · 1, 1 · 0, 1, 1 · 0, 0, 1, 1 … Σ 1, 2, 2, 2, 2, 2, 2, 2, …
  (−∞, 0]nonnegativerational roots
• A075497 → D+1 → D+1
  1 · 4, 1 · 18, 10, 1 · 88, 82, 18, 1 … Σ 1, 5, 29, 189, 1357, 10601, 89329, …
  (−∞, 0]nonnegative
• A152830 → basis A013609 → basis A008277
  1 · 1 · 1 · 1 … Σ 1, 1, 1, 1, 6, 6, 6, 6, …
  (−∞, 0]nonnegative
• A038221 → basis A013609 → θ+1
  1 · 6, 12 · 36, 144, 108 · 216, 1296, 1944, 864 … Σ 1, 18, 288, 4320, 62208, 870912, …
  (−∞, 0]nonnegativerational roots
• A136572 → (θ+1)² → D
  4 · 0, 36 · 0, 0, 288 · 0, 0, 0, 2400 … Σ 0, 4, 36, 288, 2400, 21600, 211680, …
  (−∞, 0]nonnegativerational roots
• A367270 → basis A013611 → basis A013610
  1 · 1 · 11, 24 · 106, 432, 432 … Σ 1, 1, 35, 970, 25059, 631806, 15809678, …
  (−∞, 0]nonnegative
• A178822 → basis A013609 → basis A008277
  1 · 24, 12 · 336, 420, 84 · 3584, 8512, 4032, 448 … Σ 1, 36, 840, 16576, 304416, 5435136, …
  (−∞, 0]nonnegative
• A038279 → basis A013611 → x ↦ x/(x+1)
  1 · 9, 13 · 81, 234, 169 · 729, 3159, 4563, 2197 … Σ 1, 22, 484, 10648, 234256, 5153632, …
  [−1, 0]nonnegativerational roots
• basis-map coefficients of A026729, shifted → (θ+1)²
  1 · 0, -4 · 0, 0, 9 · 0, 0, 0, -16 … Σ 1, -4, 9, -16, 25, -36, 49, -64, …
  [−1, 0]rational roots
• A053117 → x ↦ x+1 → D
  2 · 8, 8 · 20, 48, 24 · 40, 168, 192, 64 … Σ 0, 2, 16, 92, 464, 2182, 9824, 42936, …
  (−∞, 0]nonnegative
• A038305 → basis A013610 → (θ+1)²
  169, 936, 729 · 2197, 18252, 28431, 11664 … Σ 1834, 60544, 1854688, 54027952, …
  (−∞, 0]nonnegative
• A091042 → basis A013609 → basis A013611
  1 · 10, 24 · 76, 320, 320 · 568, 3360, 6272, 3584 … Σ 1, 34, 716, 13784, 259216, 4842784, …
  (−∞, 0]nonnegative
• A154986 → D+1 → x ↦ x+1
  1 · 3, 1 · 12, 8, 1 · 60, 64, 17, 1 … Σ 1, 4, 21, 142, 1161, 11200, 123981, …
  (−∞, −1]nonnegative
• A013620 → basis A013610 → reverse
  1 · 9, 5 · 81, 90, 25 · 729, 1215, 675, 125 … Σ 1, 14, 196, 2744, 38416, 537824, …
  (−∞, 0]nonnegativerational roots
• A280580 → x ↦ x+1
  1 · 2, 1 · 9, 8, 1 · 51, 63, 18, 1 … Σ 1, 3, 18, 133, 1094, 9614, 88372, …
  (−∞, −1]nonnegative
• A019538 → D
  2 · 6, 12 · 14, 72, 72 · 30, 300, 720, 480 … Σ 0, 2, 18, 158, 1530, 16622, 201978, …
  (−∞, 0]nonnegative
• A274496 → θ+1
  1 · 2 · 2, 4 · 4, 8 … Σ 1, 2, 6, 12, 32, 64, 160, 320, …
  (−∞, 0]nonnegativerational roots
• A013609 → basis A013610 → x ↦ x/(x+1)
  1 · 3, 9 · 9, 54, 81 · 27, 243, 729, 729 … Σ 1, 12, 144, 1728, 20736, 248832, …
  [−1, 0]nonnegativerational roots
• A372873 → basis A013611
  1 · 2, 8 · 5, 36, 64 · 14, 144, 480, 512 … Σ 1, 10, 105, 1150, 13025, 151250, …
  (−∞, 0]nonnegative
• A027467 → basis A013611 → x ↦ x+1
  1 · 20, 4 · 400, 160, 16 · 8000, 4800, 960, 64 … Σ 1, 24, 576, 13824, 331776, 7962624, …
  (−∞, −1]nonnegativerational roots
• A010054: a(n) = 1 if n is a triangular number, otherwise 0.
  1 · 1 · 1 · 1 … Σ 1, 1, 1, 1, 1, 1, 1, 1, …
  (−∞, −1][−1, 0][−3−2√2, −3+2√2]+2
• A008556 → D+1
  1 · 2 · 8, 2 · 32, 12 … Σ 1, 2, 10, 44, 208, 992, 4784, 23200, …
  (−∞, 0]nonnegative
• A178821 → basis A007318 → basis A013610
  1 · 15, 15 · 135, 270, 135 · 945, 2835, 2835, 945 … Σ 1, 30, 540, 7560, 90720, 979776, …
  (−∞, 0]nonnegativerational roots
• A122542 → basis A008277
  1 · 1, 1 · 3, 5, 1 · 7, 21, 10, 1 … Σ 1, 2, 9, 39, 186, 953, 5225, 30484, …
  (−∞, 0]nonnegative
• A159854 → Veronese 2 (j=1) → (θ+1)²
  0, 4 · 0, 8 · 0, 12, 9 · 0, 16, 36 … Σ 0, 4, 8, 21, 52, 126, 300, 704, …
  (−∞, 0]nonnegative
• A085881 → basis A013611 → basis A008277
  1 · 6, 4 · 108, 192, 48 · 3240, 11760, 7200, 960 … Σ 1, 10, 348, 23160, 2434320, 365208480, …
  (−∞, 0]nonnegative
• A026729: Square array of binomial coefficients T(n,k) = binomial(n,k), n >= 0, k >= 0, read by downward antidiagonals.
  1 · 0, 1 · 0, 1, 1 · 0, 0, 2, 1 … Σ 1, 1, 2, 3, 5, 8, 13, 21, …
  (−4, 0]nonnegative
• A088617 → basis A013611
  1 · 2, 4 · 6, 28, 32 · 22, 164, 400, 320 … Σ 1, 6, 66, 906, 13926, 229326, 3956106, …
  (−∞, 0]nonnegative
• A269947 → basis A008277
  1 · 1, 1 · 2, 4, 1 · 18, 42, 15, 1 … Σ 1, 2, 7, 76, 2279, 152776, 19564357, …
  (−∞, 0]nonnegative
• A103327 → basis A013610 → x ↦ x+1
  1 · 7, 3 · 61, 54, 9 · 547, 753, 297, 27 … Σ 1, 10, 124, 1624, 21520, 285856, …
  (−∞, −1]nonnegative
• A132393 → basis A013609 → θ+1
  1 · 1, 4 · 2, 12, 12 · 6, 44, 72, 32 … Σ 1, 5, 26, 154, 1044, 8028, 69264, …
  (−∞, 0]nonnegative
• A085841 → basis A013609
  1 · 7, 8 · 61, 144, 64 · 547, 2008, 2112, 512 … Σ 1, 15, 269, 5179, 102105, 2028071, …
  (−∞, 0]nonnegative
• A094638 → basis A013611 → basis A013610
  1 · 6, 12 · 66, 276, 288 · 1056, 6792, 14544, 10368 … Σ 1, 18, 630, 32760, 2260440, 194397840, …
  (−∞, 0]nonnegativerational roots
• A269945 → D+1
  1 · 1, 1 · 1, 3, 1 · 1, 11, 8, 1 … Σ 1, 2, 5, 21, 126, 1001, 10129, 126006, …
  (−∞, 0]nonnegative
• A306364: Triangular array of the number of binary, rooted, leaf-labeled tree topologies with n leaves and k cherries, n >= 2, 1 <= k <= floor(n/2).
  1 · 3 · 12, 3 · 60, 45 … Σ 1, 3, 15, 105, 945, 10395, 135135, …
  (−∞, 0)nonnegative
• A391533 → x ↦ x+1
  9, 6, 1 · 18, 21, 8, 1 · 36, 60, 37, 10, 1 … Σ 16, 48, 144, 432, 1296, 3888, 11664, …
  (−∞, −1]nonnegativerational roots
• A038319 → x ↦ x+1 → basis A008277
  441, 235, 25 · 9261, 8315, 1950, 125 … Σ 701, 19651, 573876, 17479751, …
  (−∞, 0]nonnegative
• A027467 → D+1
  1 · 16, 1 · 255, 32, 1 · 4050, 765, 48, 1 … Σ 1, 17, 288, 4864, 81920, 1376256, …
  (−∞, 0]nonnegativerational roots
• A085880 → basis A013609 → θ+1
  1 · 2, 4 · 8, 32, 24 · 40, 240, 360, 160 … Σ 1, 6, 64, 800, 10752, 150528, 2162688, …
  (−∞, 0]nonnegativerational roots
• A207824 → basis A013609
  1 · 6, 2 · 35, 24, 4 · 204, 212, 72, 8 … Σ 1, 8, 63, 496, 3905, 30744, 242047, …
  (−4, −2)nonnegative
• A178822 → x ↦ x+1 → reverse
  1 · 6, 12 · 21, 84, 84 · 56, 336, 672, 448 … Σ 1, 18, 189, 1512, 10206, 61236, 336798, …
  (−∞, 0]nonnegativerational roots
• A108838 → x ↦ x+1 → θ+1
  2 · 5, 4 · 14, 24, 6 · 42, 112, 63, 8 … Σ 2, 9, 44, 225, 1182, 6321, 34232, …
  (−∞, 0]nonnegative
• A156992 → basis A013610 → basis A013609
  1 · 10, 12 · 150, 360, 216 · 3000, 10800, 12960, 5184 … Σ 1, 22, 726, 31944, 1756920, 115956720, …
  (−∞, 0]nonnegativerational roots