Sequences

• A172431 → Veronese 2 → θ+1
  1 · 1 · 1, 6 · 1, 20 … Σ 1, 1, 7, 21, 58, 178, 517, 1483, …
  (−∞, 0]nonnegative
• A105070: T(n,k) = 2^k*binomial(n,2k+1), where 0 <= k <= floor((n-1)/2), n >= 1.
  1 · 2 · 3, 2 · 4, 8 … Σ 1, 2, 5, 12, 29, 70, 169, 408, …
  (−∞, 0)nonnegative
• A144438: Triangle T(n,k) by rows: T(n, k) = (n-k+1)*T(n-1, k-1) + k*T(n-1, k) + T(n-2, k-1) with T(n, 1) = T(n, n) = 1.
  1 · 1, 1 · 1, 5, 1 · 1, 14, 14, 1 … Σ 1, 2, 7, 30, 157, 972, 6961, 56660, …
  (−∞, 0)nonnegative
• A086645 → basis A013610 → x ↦ x+1
  1 · 5, 3 · 41, 42, 9 · 365, 549, 243, 27 … Σ 1, 8, 92, 1184, 15632, 207488, 2757056, …
  (−∞, −1]nonnegative
• A038259 → basis A007318 → (θ+1)²
  1 · 11, 20 · 121, 440, 225 · 1331, 7260, 7425, 2000 … Σ 1, 31, 786, 18016, 388096, 8011776, …
  (−∞, 0]nonnegative
• A120910 → D → x ↦ x+1
  3 · 18, 6 · 81, 54, 9 · 324, 324, 108, 12 … Σ 0, 3, 24, 144, 768, 3840, 18432, 86016, …
  (−∞, −1]nonnegativerational roots
• A091042 → basis A007318
  1 · 4, 3 · 16, 20, 5 · 64, 112, 56, 7 … Σ 1, 7, 41, 239, 1393, 8119, 47321, …
  (−∞, −1]nonnegative
• A204420 → basis A013609 → x ↦ x+1
  1 · 3, 2 · 45, 48, 12 · 1575, 2130, 900, 120 … Σ 1, 5, 105, 4725, 363825, 42567525, …
  (−∞, −1]nonnegativerational roots
• A111577 → Pₙ + Pₙ₊₁
  2, 1 · 2, 6, 1 · 2, 26, 13, 1 · 2, 106, 117, 23, 1 … Σ 3, 9, 42, 249, 1737, 13872, 124401, …
  (−∞, ∞)nonnegative
• A249139 → basis A013609 → basis A008277
  1 · 6, 2 · 11, 4 · 41, 30, 4 … Σ 1, 8, 15, 75, 188, 789, 2313, 9060, …
  (−∞, 0]nonnegative
• A038226 → basis A013609 → basis A008288
  729, 1120, 256 · 19683, 51632, 28928, 4096 … Σ 2105, 104339, 5177521, 256944571, …
  [−3−2√2, −3+2√2]nonnegative
• A008955 → basis A013610 → D+1
  1 · 5, 3 · 49, 111, 36 · 760, 3486, 4329, 972 … Σ 1, 8, 196, 9547, 771515, 93254890, …
  (−∞, 0]nonnegative
• Veronese parent of A109447 → θ+1
  0, 2, 3 · 1, 4, 3 · 0, 2, 9, 12, 5 · 1, 8, 18, 16, 5 … Σ 5, 8, 28, 48, 144, 256, 704, 1280, …
  (−∞, 0]nonnegativerational roots
• A026729 → basis A013611 → D+1
  1 · 5, 4 · 14, 44, 16 · 31, 188, 272, 64 … Σ 1, 9, 74, 555, 3965, 27400, 184925, …
  (−∞, 0]nonnegative
• A081581 → D
  1 · 8, 2 · 15, 30, 3 · 22, 156, 66, 4 … Σ 0, 1, 10, 48, 248, 1100, 4872, 20608, …
  (−∞, 0]nonnegative
• A159854 → basis A013609 → basis A007318
  9, 12, 4 · 36, 66, 40, 8 · 144, 336, 292, 112, 16 … Σ 25, 150, 900, 5400, 32400, 194400, …
  (−∞, −1]nonnegativerational roots
• A013610 → basis A013611 → basis A008288
  1 · 16, 12 · 256, 528, 144 · 4096, 14400, 10368, 1728 … Σ 1, 28, 928, 30592, 1008640, 33255424, …
  [−3−2√2, −3+2√2]nonnegative
• A102547 → reverse → D
  1 · 0, 2 · 0, 0, 3 · 0, 0, 3, 4 … Σ 1, 2, 3, 7, 13, 21, 36, 61, …
  (−∞, 0]nonnegative
• A122542 → reverse → basis A013611
  1 · 1 · 3, 8 · 7, 32, 32 … Σ 1, 1, 11, 71, 481, 3241, 21851, 147311, …
  (−∞, 0]nonnegative
• A081577 → x ↦ x+1 → D+1
  1 · 3, 1 · 12, 8, 1 · 40, 44, 13, 1 … Σ 1, 4, 21, 98, 455, 2064, 9241, 40894, …
  (−∞, 0]nonnegative
• A053117 → x ↦ x+1 → D+1
  1 · 4, 2 · 11, 16, 4 · 24, 68, 48, 8 … Σ 1, 6, 31, 148, 673, 2962, 12735, 53800, …
  (−∞, 0]nonnegative
• A013611 → basis A007318 → basis A008277
  1 · 9, 4 · 81, 88, 16 · 729, 1468, 624, 64 … Σ 1, 13, 185, 2885, 49137, 908797, …
  (−∞, 0]nonnegative
• A059364 → basis A013610 → x ↦ x/(x+1)
  1 · 3, 6 · 15, 63, 66 · 105, 681, 1470, 1056 … Σ 1, 9, 144, 3312, 99360, 3676320, …
  [−1, 0]nonnegativerational roots
• A178822 → Veronese 2 → D
  21 · 168 · 756, 252 · 2520, 2520 … Σ 0, 0, 21, 168, 1008, 5040, 22176, …
  (−∞, 0]nonnegative
• A008277 → θ+2 (shift +1) → x ↦ x/(x+1)
  2 · 2, 5 · 2, 13, 15 · 2, 27, 72, 52 … Σ 2, 7, 30, 153, 898, 5919, 43102, …
  [−1, 0]nonnegative
• A038208 → D → basis A008277
  2 · 16, 8 · 96, 120, 24 · 512, 1216, 576, 64 … Σ 0, 2, 24, 240, 2368, 24160, 258816, …
  (−∞, 0]nonnegative
• A046716 → x ↦ x+1 → x ↦ x+1
  1 · 3, 1 · 11, 7, 1 · 53, 50, 14, 1 … Σ 1, 4, 19, 118, 1021, 12088, 183727, …
  (−∞, −1]nonnegative
• A028326 → basis A013609 → basis A013609
  2 · 8, 8 · 32, 64, 32 · 128, 384, 384, 128 … Σ 2, 16, 128, 1024, 8192, 65536, 524288, …
  (−∞, 0]nonnegativerational roots
• A274498 → basis A013611
  1 · 3 · 9, 24 · 27, 72 … Σ 1, 3, 33, 99, 1089, 3267, 35937, …
  (−∞, 0]nonnegativerational roots
• A137320 → basis A013610 → reverse
  1 · 6, 2 · 36, 30, 6 · 216, 324, 156, 24 … Σ 1, 8, 72, 720, 7920, 95040, 1235520, …
  (−∞, 0]nonnegativerational roots
• A059364 → basis A013611 → (θ+1)²
  1 · 3, 16 · 15, 176, 288 · 105, 1952, 6768, 6144 … Σ 1, 19, 479, 14969, 557825, 24136635, …
  (−∞, 0]nonnegative
• A034870 → Veronese 2 (j=1) → basis A013611
  2 · 8, 16 · 32, 128, 96 · 128, 768, 1280, 512 … Σ 0, 2, 24, 256, 2688, 28160, 294912, …
  (−∞, 0]nonnegative
• narayana → D
  1 · 3, 2 · 6, 12, 3 · 10, 40, 30, 4 … Σ 0, 1, 5, 21, 84, 330, 1287, 5005, …
  (−∞, 0]nonnegative
• A075497 → D
  1 · 6, 2 · 28, 24, 3 · 120, 200, 60, 4 … Σ 0, 1, 8, 55, 384, 2841, 22504, 190863, …
  (−∞, 0]nonnegative
• A099093 → x ↦ x+1 → D
  3 · 21, 18 · 117, 198, 81 · 585, 1476, 1215, 324 … Σ 0, 3, 39, 396, 3600, 30780, 253044, …
  (−∞, 0]nonnegative
• A013613 → x ↦ x+1 → x ↦ x/(x+1)
  1 · 7, 13 · 49, 182, 169 · 343, 1911, 3549, 2197 … Σ 1, 20, 400, 8000, 160000, 3200000, …
  [−1, 0]nonnegativerational roots
• A106246 → basis A007318 → reverse
  1 · 1, 3 · 1, 6, 6 · 1, 9, 18, 10 … Σ 1, 4, 13, 38, 104, 272, 688, 1696, …
  (−∞, 0]nonnegative
• A038221 → θ+1
  1 · 3, 6 · 9, 36, 27 · 27, 162, 243, 108 … Σ 1, 9, 72, 540, 3888, 27216, 186624, …
  (−∞, 0]nonnegativerational roots
• basis-map coefficients of A371080, shifted → basis A013610 → x ↦ x/(x+1)
  1 · 1, 4 · 4, 23, 28 · 28, 201, 426, 280 … Σ 1, 5, 55, 935, 21505, 623645, 21827575, …
  [−1, 0]nonnegativerational roots
• A161198 → basis A013610 → basis A013610
  1 · 9, 18 · 99, 360, 324 · 1287, 6462, 10692, 5832 … Σ 1, 27, 783, 24273, 801009, 28035315, …
  (−∞, 0]nonnegativerational roots
• A038322 → basis A013610 → x ↦ x/(x+1)
  1 · 19, 43 · 361, 1634, 1849 … Σ 1, 62, 3844, 238328, 14776336, …
  [−1, 0]nonnegativerational roots
• A114687 → θ+1 → (θ+1)²
  1 · 1, 16 · 1, 48, 108 · 1, 96, 648, 512 … Σ 1, 17, 157, 1257, 9441, 68153, 478381, …
  (−∞, 0]nonnegative
• A132393 → reverse → basis A013610
  1 · 1 · 2, 3 · 6, 21, 18 … Σ 1, 1, 5, 45, 585, 9945, 208845, …
  (−∞, 0]nonnegativerational roots
• delannoy → basis A013611 → basis A013610
  1 · 6, 12 · 41, 156, 144 · 276, 1560, 2880, 1728 … Σ 1, 18, 341, 6444, 121789, 2301750, …
  (−∞, 0]nonnegative
• A121574 → x ↦ x+1 → D
  1 · 7, 2 · 35, 22, 3 · 155, 152, 45, 4 … Σ 0, 1, 9, 60, 356, 1980, 10572, 54880, …
  (−∞, 0]nonnegative
• Hadamard-factor parent of A155495 → (θ+1)²
  1, 24, 9 · 1, 60, 135, 16 · 1, 112, 630, 448, 25 … Σ 34, 212, 1216, 6592, 34304, 173056, …
  (−∞, 0]nonnegative
• A360282 → basis A007318
  1 · 1, 1 · 5, 7, 2 · 25, 43, 21, 3 … Σ 1, 2, 14, 92, 614, 4172, 28748, 200216, …
  (−∞, −1]nonnegative
• A027465 → Veronese 2 (j=1) → basis A013609
  1 · 6 · 28, 2 · 120, 24 … Σ 0, 1, 6, 30, 144, 684, 3240, 15336, …
  (−∞, 0]nonnegative
• A132812 → basis A007318 → θ+1
  1 · 4, 4 · 15, 30, 9 · 56, 168, 108, 16 … Σ 1, 8, 54, 348, 2195, 13668, 84364, …
  (−∞, 0]nonnegative
• A008277 → θ+1 → x ↦ x/(x+1)
  1 · 1, 3 · 1, 8, 10 · 1, 17, 49, 37 … Σ 1, 4, 19, 104, 641, 4380, 32803, …
  [−1, 0]nonnegative