veronese_section / r=2, j=0, shift 0

Veronese coefficient section. All operations

112 sequences

• A038231 → Veronese 2
  1 · 4 · 16, 1 · 64, 12 … row sums 1, 4, 17, 76, 353, 1684, 8177, 40156, …
  (−∞, 0] nonnegative
• A010054 → reverse → Veronese 2
  1 · 0, 7 · 0, 0, 13 · 0, 0, 0, 19 … row sums 1, 0, 7, 0, 13, 0, 19, 0, …
  (−∞, 0] nonnegative rational roots
• A122431 → Veronese 2
  1, 3 · 0, 3, 1 · 0, 1, 3 · 0, 0, 3, 1 … row sums 4, 4, 4, 4, 4, 4, 4, 4, …
  (−∞, 0] nonnegative rational roots
• A027465 → Veronese 2
  1 · 3 · 9, 1 · 27, 9 … row sums 1, 3, 10, 36, 136, 528, 2080, 8256, …
  (−∞, 0] nonnegative
• A178822 → Veronese 2
  1 · 6 · 21, 21 · 56, 168 … row sums 1, 6, 42, 224, 1008, 4032, 14784, …
  (−∞, 0] nonnegative
• A081580 → Veronese 2
  1 · 1 · 1, 1 · 1, 13 … row sums 1, 1, 2, 14, 63, 171, 532, 2044, …
  (−∞, 0] nonnegative
• delannoy → Veronese 2
  1 · 1 · 1, 1 · 1, 5 … row sums 1, 1, 2, 6, 15, 35, 84, 204, …
  (−∞, 0] nonnegative
• A099093 → Veronese 2
  1 · 0, 9 · 0, 18 · 0, 9, 81 … row sums 1, 0, 9, 18, 90, 324, 1215, 4698, …
  (−∞, 0] nonnegative
• A133080 → Veronese 2
  1 · 1 · 0, 1 · 0, 1 … row sums 1, 1, 1, 1, 1, 1, 1, 1, …
  (−∞, 0] nonnegative rational roots
• A028326 → Veronese 2
  2 · 2 · 2, 2 · 2, 6 … row sums 2, 2, 4, 8, 16, 32, 64, 128, …
  (−∞, 0] nonnegative
• A007318 → D → Veronese 2
  1 · 2 · 3, 3 · 4, 12 … row sums 0, 1, 2, 6, 16, 40, 96, 224, …
  (−∞, 0] nonnegative
• A125662 → Veronese 2
  1 · 3 · 8, 1 · 21, 9 … row sums 1, 3, 9, 30, 107, 393, 1459, 5436, …
  (−∞, 0] nonnegative
• A091044 → Veronese 2
  1 · 2 · 3, 3 · 4, 28 … row sums 1, 2, 6, 32, 136, 512, 2016, 8192, …
  (−∞, 0] nonnegative
• A038208 → Veronese 2
  1 · 2 · 4, 4 · 8, 24 … row sums 1, 2, 8, 32, 128, 512, 2048, 8192, …
  (−∞, 0] nonnegative
• A122542 → Veronese 2
  1 · 0, 1 · 0, 4 · 0, 8, 1 … row sums 1, 0, 1, 4, 9, 20, 49, 120, …
  (−∞, 0] nonnegative
• A026374 → Veronese 2
  1 · 1 · 1, 1 · 1, 4 … row sums 1, 1, 2, 5, 13, 25, 62, 125, …
  (−∞, 0] nonnegative
• A178821 → Veronese 2
  1 · 5 · 15, 15 · 35, 105 … row sums 1, 5, 30, 140, 560, 2016, 6720, 21120, …
  (−∞, 0] nonnegative
• A249251 → Veronese 2
  1 · 1 · 1, 6 · 1, 21 … row sums 1, 1, 7, 22, 70, 235, 775, 2557, …
  (−∞, 0] nonnegative
• A304236 → Veronese 2
  1 · 1 · 1 · 1 … row sums 1, 1, 1, 1, 10, 28, 55, 91, …
  (−∞, 0] nonnegative
• A132393 → Veronese 2
  1 · 0, 1 · 0, 3 · 0, 11, 1 … row sums 1, 0, 1, 3, 12, 60, 360, 2520, …
  (−∞, 0] nonnegative
• A116414 → Veronese 2
  1 · 4 · 13, 1 · 40, 12 … row sums 1, 4, 14, 52, 209, 880, 3773, 16252, …
  (−∞, 0] nonnegative
• A081578 → Veronese 2
  1 · 1 · 1, 1 · 1, 9 … row sums 1, 1, 2, 10, 35, 91, 260, 820, …
  (−∞, 0] nonnegative
• basis-map coefficients of A021012 → Veronese 2
  1 · 0, 2 · 0, 0, 24 · 0, 0, 0, 720 … row sums 1, 0, 2, 0, 24, 0, 720, 0, …
  (−∞, 0] nonnegative rational roots
• A099040 → Veronese 2
  1 · 0, 4 · 0, 8 · 0, 4, 16 … row sums 1, 0, 4, 8, 20, 64, 160, 448, …
  (−∞, 0] nonnegative
• A159854 → Veronese 2
  0, 1 · 0, 1 · 0, 1, 1 · 0, 1, 3 … row sums 1, 1, 2, 4, 8, 16, 32, 64, …
  (−∞, 0] nonnegative
• A130123 → Veronese 2
  1 · 0, 4 · 0, 0, 16 · 0, 0, 0, 64 … row sums 1, 0, 4, 0, 16, 0, 64, 0, …
  (−∞, 0] nonnegative rational roots
• A010054: a(n) = 1 if n is a triangular number, otherwise 0.
  1 · 1 · 1 · 1 … row sums 1, 1, 1, 1, 1, 1, 1, 1, …
  A010054 (−∞, −1] [−1, 0] [−3−2√2, −3+2√2] nonnegative rational roots
• A120909 → Veronese 2
  3 · 3 · 3, 12 · 3, 36 … row sums 3, 3, 15, 39, 123, 363, 1095, 3279, …
  (−∞, 0] nonnegative
• A130534 → Veronese 2
  1 · 1 · 2, 1 · 6, 6 … row sums 1, 1, 3, 12, 60, 360, 2520, 20160, …
  (−∞, 0] nonnegative
• A099097 → Veronese 2
  1 · 0, 9 · 0, 6 · 0, 1, 81 … row sums 1, 0, 9, 6, 82, 108, 783, 1470, …
  (−∞, 0] nonnegative
• A113953 → Veronese 2
  1 · 0, 1 · 0, 4 · 0, 4, 1 … row sums 1, 0, 1, 4, 5, 8, 25, 44, …
  (−∞, 0] nonnegative
• A011973 → Veronese 2
  1 · 1 · 1 · 1 … row sums 1, 1, 1, 1, 2, 4, 7, 11, …
  (−∞, 0] nonnegative
• A232535 → Veronese 2
  1 · 1 · 1, 3 · 1, 25 … row sums 1, 1, 4, 26, 104, 376, 1504, 6176, …
  (−∞, 0] nonnegative
• A008288 → Veronese 2
  1 · 1 · 1, 1 · 1, 5 … row sums 1, 1, 2, 6, 15, 35, 84, 204, …
  (−∞, 0] nonnegative
• A121574 → Veronese 2
  1 · 2 · 4, 1 · 8, 8 … row sums 1, 2, 5, 16, 54, 180, 595, 1964, …
  (−∞, 0] nonnegative
• A082985 → Veronese 2
  1 · 1 · 1, 5 · 1, 14 … row sums 1, 1, 6, 15, 37, 100, 261, 681, …
  (−∞, 0] nonnegative
• A081577 → Veronese 2
  1 · 1 · 1, 1 · 1, 7 … row sums 1, 1, 2, 8, 24, 60, 160, 448, …
  (−∞, 0] nonnegative
• A113214 → Veronese 2
  1 · 2 · 0, 1 · 0, 4 … row sums 1, 2, 1, 4, 6, 8, 15, 24, …
  (−∞, 0] nonnegative
• A078812 → Veronese 2
  1 · 2 · 3, 1 · 4, 6 … row sums 1, 2, 4, 10, 27, 72, 189, 494, …
  (−∞, 0] nonnegative
• A030528 → Veronese 2
  1 · 1 · 0, 1 · 0, 3 … row sums 1, 1, 1, 3, 4, 6, 11, 17, …
  (−∞, 0] nonnegative
• A102662 → Veronese 2
  1 · 1 · 1, 3 · 1, 11 … row sums 1, 1, 4, 12, 27, 63, 154, 374, …
  (−∞, 0] nonnegative
• A188440 → Veronese 2
  1 · 1 · 1 · 1 … row sums 1, 1, 1, 1, 5, 5, 13, 13, …
  (−∞, 0] nonnegative
• A026729 → Veronese 2
  1 · 0, 1 · 0, 2 · 0, 1, 1 … row sums 1, 0, 1, 2, 2, 4, 7, 10, …
  (−∞, 0] nonnegative
• A038220 → Veronese 2
  1 · 3 · 9, 4 · 27, 36 … row sums 1, 3, 13, 63, 313, 1563, 7813, 39063, …
  (−∞, 0] nonnegative
• basis-map coefficients of A026729 → basis A056242 → Veronese 2
  1 · 1 · 1, 4 · 1, 16 … row sums 1, 1, 5, 17, 58, 198, 676, 2308, …
  (−∞, 0] nonnegative
• A011973 → basis A007318 → Veronese 2
  1 · 1 · 2 · 3 … row sums 1, 1, 2, 3, 6, 11, 22, 43, …
  (−∞, 0] nonnegative
• A198954: Expansion of the rotational partition function for a heteronuclear diatomic molecule.
  A010054 → D∘x
  1 · 3 · 5 · 7 … row sums 1, 3, 5, 7, 9, 11, 13, 15, …
  A198954 (−∞, −1] [−1, 0] nonnegative rational roots
• A013610 → Veronese 2
  1 · 1 · 1, 9 · 1, 27 … row sums 1, 1, 10, 28, 136, 496, 2080, 8128, …
  (−∞, 0] nonnegative
• A081582 → Veronese 2
  1 · 1 · 1, 1 · 1, 17 … row sums 1, 1, 2, 18, 99, 275, 900, 4068, …
  (−∞, 0] nonnegative
• A011973 → x ↦ x+2 (shift +1) → Veronese 2
  1 · 3 · 5 · 11, 1 … row sums 1, 3, 5, 12, 24, 55, 119, 271, …
  (−∞, 0] nonnegative