Sequences

• A038331 → D+1
  264, 170, 25 · 3888, 3960, 1275, 125 … Σ 459, 9248, 181781, 3507882, 66733279, …
  (−∞, 0]nonnegativerational roots
• delannoy → basis A013611 → basis A013611
  1 · 6, 16 · 41, 208, 256 · 276, 2080, 5120, 4096 … Σ 1, 22, 505, 11572, 265189, 6077170, …
  (−∞, 0]nonnegative
• A103633 → basis A013609 → basis A013609
  1 · 3, 4 · 12, 28, 16 · 36, 132, 160, 64 … Σ 1, 7, 56, 392, 3136, 21952, 175616, …
  (−∞, 0]nonnegativerational roots
• A038231 → Veronese 2 (j=1) → D+1
  1 · 8 · 49, 1 · 272, 16 … Σ 0, 1, 8, 50, 288, 1603, 8776, 47604, …
  (−∞, 0]nonnegative
• A120909 → basis A008277
  3 · 9, 6 · 27, 48, 12 · 81, 294, 180, 24 … Σ 3, 15, 87, 579, 4347, 36231, 330927, …
  (−∞, 0]nonnegative
• basis-map coefficients of A112227 → D → D+1
  2, 2 · 0, 6, 3 · 0, 0, 12, 4 · 0, 0, 0, 20, 5 … Σ 4, 9, 16, 25, 36, 49, 64, 81, …
  (−∞, 0]nonnegativerational roots
• A011973 → basis A008277 → D
  1 · 2 · 6, 2 · 13, 6 … Σ 0, 0, 1, 2, 8, 19, 57, 144, …
  (−∞, 0]nonnegative
• A110441 → basis A013611 → (θ+1)²
  1 · 4, 16 · 14, 128, 144 · 48, 704, 1728, 1024 … Σ 1, 20, 286, 3504, 39236, 413936, …
  (−∞, 0]nonnegative
• A038325 → x ↦ x/(x+1)
  1 · 11, 22 · 121, 484, 484 · 1331, 7986, 15972, 10648 … Σ 1, 33, 1089, 35937, 1185921, 39135393, …
  [−1, 0]nonnegativerational roots
• A028262 → basis A013609
  1 · 2, 2 · 5, 10, 4 · 10, 30, 28, 8 … Σ 1, 4, 19, 76, 304, 1216, 4864, 19456, …
  (−∞, 0]nonnegative
• A143683 → γ → D
  8 · 16 · 24, 128 · 32, 384 … Σ 0, 0, 8, 16, 152, 416, 2344, 7472, …
  (−∞, 0]nonnegative
• A249251 → Veronese 2
  1 · 1 · 1, 6 · 1, 21 … Σ 1, 1, 7, 22, 70, 235, 775, 2557, …
  (−∞, 0]nonnegative
• A081581 → γ → θ+1
  1 · 1 · 1, 12 · 1, 24 … Σ 1, 1, 13, 25, 145, 373, 1573, 4609, …
  (−∞, 0]nonnegative
• A038220 → basis A013611
  1 · 5, 8 · 25, 80, 64 · 125, 600, 960, 512 … Σ 1, 13, 169, 2197, 28561, 371293, …
  [−1, 0]nonnegativerational roots
• A038337 → basis A013611
  529, 2024, 1936 · 12167, 69828, 133584, 85184 … Σ 4489, 300763, 20151121, 1350125107, …
  (−∞, 0]nonnegativerational roots
• A139548 → basis A013610 → x ↦ x+1
  1 · 50, 60, 18 · 2500, 6000, 5400, 2160, 324 … Σ 1, 128, 16384, 2097152, 268435456, …
  (−∞, −1]nonnegativerational roots
• A188440 → basis A013609
  1 · 1 · 3, 4 · 3, 4 … Σ 1, 1, 7, 7, 49, 49, 343, 343, …
  (−∞, 0]nonnegativerational roots
• A038330 → basis A013611 → basis A013609
  1024, 2048, 1024 · 32768, 98304, 98304, 32768 … Σ 4096, 262144, 16777216, 1073741824, …
  (−∞, 0]nonnegativerational roots
• A163936 → reverse → (θ+1)²
  1 · 0, 4 · 0, 4, 18 · 0, 4, 72, 96 … Σ 1, 4, 22, 172, 1730, 21140, 303030, …
  (−∞, 0]nonnegative
• A038303 → basis A013609 → x ↦ x/(x+1)
  1 · 11, 13 · 121, 286, 169 · 1331, 4719, 5577, 2197 … Σ 1, 24, 576, 13824, 331776, 7962624, …
  [−1, 0]nonnegativerational roots
• A038320 → basis A013611
  289, 816, 576 · 4913, 20808, 29376, 13824 … Σ 1681, 68921, 2825761, 115856201, …
  (−∞, 0]nonnegativerational roots
• A053124 → D+1
  1 · 2, 4 · -13, 16, 16 · 36, -152, 96, 64 … Σ 1, 6, 19, 44, 85, 146, 231, 344, …
  (−∞, ∞)
• basis-map coefficients of A297191, shifted → basis A008288 → (θ+1)²
  1 · 1, 12, 9 · 1, 28, 117, 112, 25 … Σ 1, 22, 283, 2892, 26069, 217122, …
  (−∞, 0]nonnegative
• A125092 → reverse → θ+1
  1 · 4, 2 · 9, 16, 3 · 16, 54, 36, 4 … Σ 1, 6, 28, 110, 384, 1232, 3712, 10656, …
  (−∞, 0]nonnegative
• A094638 → basis A013610 → (θ+1)²
  1 · 2, 12 · 6, 84, 162 · 24, 552, 2349, 2592 … Σ 1, 14, 252, 5517, 142353, 4231998, …
  (−∞, 0]nonnegative
• A108838 → x ↦ x+1 → reverse
  2 · 2, 5 · 2, 12, 14 · 2, 21, 56, 42 … Σ 2, 7, 28, 121, 550, 2591, 12536, 61921, …
  (−∞, 0]nonnegative
• A081581: Pascal-(1,6,1) array.
  1 · 1, 1 · 1, 8, 1 · 1, 15, 15, 1 … Σ 1, 2, 10, 32, 124, 440, 1624, 5888, …
  (−∞, 0)nonnegative
• A371259 → D
  1 · 100, 2 · 9864, 400, 3 · 1099296, 68128, 1032, 4 … Σ 0, 1, 102, 10267, 1168460, 154447181, …
  (−∞, 0]nonnegative
• A124932 → (θ+1)²
  1 · 2, 12 · 3, 36, 54 · 4, 72, 216, 160 … Σ 1, 14, 93, 452, 1840, 6672, 22288, …
  (−∞, 0]nonnegative
• A034870 → basis A013611 → basis A008277
  1 · 36, 64, 16 · 1296, 8704, 9856, 3072, 256 … Σ 1, 116, 23184, 7059776, 2983399680, …
  (−∞, 0]nonnegative
• A130534 → basis A013610 → basis A008277
  1 · 5, 3 · 30, 42, 9 · 210, 510, 243, 27 … Σ 1, 8, 81, 990, 14121, 229428, 4170969, …
  (−∞, 0]nonnegative
• A257623 → θ+1
  1 · 3, 6 · 9, 96, 27 · 27, 1002, 1503, 108 … Σ 1, 9, 132, 2640, 66528, 2018016, …
  (−∞, 0]nonnegative
• A228955 → basis A008277
  1 · 2, 1 · 8, 6 · 48, 54, 6 … Σ 1, 3, 14, 108, 1104, 14520, 232560, …
  (−∞, 0]nonnegative
• A121574 → basis A013611 → basis A007318
  1 · 7, 4 · 54, 60, 16 · 413, 684, 368, 64 … Σ 1, 11, 130, 1529, 17989, 211640, …
  (−∞, 0]nonnegative
• A063967 → basis A013611
  1 · 2, 4 · 6, 20, 16 · 16, 80, 128, 64 … Σ 1, 6, 42, 288, 1980, 13608, 93528, …
  (−∞, 0]nonnegative
• basis-map coefficients of A112227 → basis A013609 → D+1
  5, 12, 4 · 7, 30, 36, 8 · 9, 56, 120, 96, 16 … Σ 21, 81, 297, 1053, 3645, 12393, 41553, …
  (−∞, 0]nonnegativerational roots
• A038338 → D
  288, 288 · 5184, 10368, 5184 … Σ 576, 20736, 663552, 19906560, …
  (−∞, 0]nonnegativerational roots
• A144440 → γ
  1 · 1 · 1, 9 · 1, 51 … Σ 1, 1, 10, 52, 559, 6112, 89494, …
  (−∞, 0]nonnegative
• A178821 → basis A013609 → basis A013611
  1 · 20, 40 · 240, 960, 960 … Σ 1, 60, 2160, 60480, 1451520, 31352832, …
  (−∞, 0]nonnegativerational roots
• A013611 → basis A008288
  1 · 5, 4 · 25, 56, 16 · 125, 476, 368, 64 … Σ 1, 9, 97, 1033, 11009, 117321, 1250273, …
  [−3−2√2, −3+2√2]nonnegative
• A207823 → basis A013611 → basis A008277
  1 · 9, 4 · 80, 88, 16 · 711, 1460, 624, 64 … Σ 1, 13, 184, 2859, 48583, 897296, …
  (−∞, 0]nonnegative
• A159854 → basis A013610 → basis A013609
  16, 48, 36 · 80, 336, 468, 216 … Σ 100, 1100, 12100, 133100, 1464100, …
  (−∞, 0]nonnegativerational roots
• A249250 → x ↦ x+1
  1 · 4, 3 · 10, 12, 3 · 28, 48, 24, 3 … Σ 1, 7, 25, 103, 409, 1639, 6553, 26215, …
  (−∞, −1]nonnegative
• A207606 → x ↦ x+1 → (θ+1)²
  13, 44, 18 · 34, 176, 153, 32 · 89, 620, 837, 368, 50 … Σ 75, 395, 1964, 9383, 43521, 197293, …
  (−∞, 0]nonnegative
• A137320 → Veronese 2 (j=1) → basis A007318
  2 · 2 · 12, 8 · 60, 48 … Σ 0, 2, 2, 20, 108, 736, 5760, 50848, …
  (−∞, −1]nonnegative
• A030528: Triangle read by rows: T(n,k) = binomial(k,n-k).
  1 · 1, 1 · 0, 2, 1 · 0, 1, 3, 1 … Σ 1, 2, 3, 5, 8, 13, 21, 34, …
  (−4, 0]nonnegative
• A225471 → basis A013610 → reverse
  1 · 3, 4 · 9, 36, 32 · 27, 216, 528, 384 … Σ 1, 7, 77, 1155, 21945, 504735, …
  (−∞, 0]nonnegativerational roots
• A130534 → basis A013610 → x ↦ x+1
  1 · 5, 3 · 30, 33, 9 · 210, 321, 162, 27 … Σ 1, 8, 72, 720, 7920, 95040, 1235520, …
  (−∞, −1]nonnegativerational roots
• A120909 → basis A013610
  3 · 9, 18 · 27, 108, 108 · 81, 486, 972, 648 … Σ 3, 27, 243, 2187, 19683, 177147, …
  [−1, 0]nonnegativerational roots
• A133214 → basis A013609 → basis A013609
  61, 128, 64 · 595, 1800, 1728, 512 … Σ 253, 4635, 89601, 1792575, 36677005, …
  (−∞, 0]nonnegative