preserver_image / derivative_polynomial, shift 0

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410 sequences

• A003506: Triangle of denominators in Leibniz's Harmonic Triangle a(n,k), n >= 1, 1 <= k <= n.
  A007318 → D
  1 · 2, 2 · 3, 6, 3 · 4, 12, 12, 4 … row sums 1, 4, 12, 32, 80, 192, 448, 1024, …
  A003506 (−∞, 0] nonnegative rational roots
• basis-map coefficients of A132812 → D
  2 · 3, 6 · -12, 24, 12 · -20, -40, 90, 20 … row sums 0, 2, 9, 24, 50, 90, 147, 224, …
  (−∞, ∞)
• A145596 → D
  2 · 8, 6 · 20, 40, 12 · 40, 150, 120, 20 … row sums 0, 2, 14, 72, 330, 1430, 6006, 24752, …
  (−∞, 0] nonnegative
• A038207 → D
  1 · 4, 2 · 12, 12, 3 · 32, 48, 24, 4 … row sums 0, 1, 6, 27, 108, 405, 1458, 5103, …
  (−∞, −1] nonnegative rational roots
• A007318 → ×(−(1/2)n+(1/2)n²) → D
  2, 2 · 9, 18, 9 · 24, 72, 72, 24 … row sums 0, 0, 4, 36, 192, 800, 2880, 9408, …
  (−∞, 0] nonnegative rational roots
• A114655 → D+1
  2 · 6, 2 · 20, 16, 2 · 64, 96, 30, 2 … row sums 2, 8, 38, 192, 1002, 5336, 28814, …
  (−∞, 0] nonnegative
• A152842 → D+1
  1 · 4, 3 · 5, 10, 3 · 8, 37, 42, 9 … row sums 1, 7, 18, 96, 224, 1088, 2432, 11264, …
  (−∞, 0] nonnegative
• A059344 → D
  2 · 6 · 12, 24 · 20, 120 … row sums 0, 0, 2, 6, 36, 140, 750, 3402, …
  (−∞, 0] nonnegative
• A121574 → D
  1 · 5, 2 · 16, 16, 3 · 44, 74, 33, 4 … row sums 0, 1, 7, 35, 155, 642, 2550, 9841, …
  (−∞, 0] nonnegative
• A104684 → D+1
  1 · 3, 1 · 12, 8, 1 · 50, 54, 15, 1 … row sums 1, 4, 21, 120, 705, 4188, 24997, …
  (−∞, 0] nonnegative
• A023531 → 2D+1+2n → D+1
  1 · 5, 3 · 4, 14, 5 · 0, 12, 27, 7 … row sums 1, 8, 23, 46, 77, 116, 163, 218, …
  (−∞, 0] nonnegative
• A023531 → D+1
  1 · 1, 1 · 0, 2, 1 · 0, 0, 3, 1 … row sums 1, 2, 3, 4, 5, 6, 7, 8, …
  (−∞, 0] nonnegative rational roots
• A062196 → D
  3 · 8, 12 · 15, 60, 30 · 24, 180, 240, 60 … row sums 0, 3, 20, 105, 504, 2310, 10296, 45045, …
  (−∞, 0] nonnegative
• A108838 → ⊙ C(n+1,k+1) (shift +1) → D+1
  1 · 2, 1 · 5, 6, 1 · 11, 30, 13, 1 … row sums 1, 3, 12, 55, 276, 1477, 8296, 48393, …
  (−∞, 0] nonnegative
• A066325 → D+1
  1 · 1, 1 · -1, 2, 1 · -3, -3, 3, 1 … row sums 1, 2, 2, -2, -10, -4, 52, 92, …
  (−∞, ∞)
• A007318 → (θ+1)² → D+1
  1 · 5, 4 · 9, 26, 9 · 13, 66, 75, 16 … row sums 1, 9, 44, 170, 576, 1792, 5248, 14688, …
  (−∞, 0] nonnegative
• A133087 → D
  1 · 2, 2 · 5, 8, 3 · 4, 12, 12, 4 … row sums 0, 1, 4, 16, 32, 112, 192, 640, …
  (−∞, 0] nonnegative rational roots
• delannoy → D+1
  1 · 2, 1 · 4, 5, 1 · 6, 15, 8, 1 … row sums 1, 3, 10, 30, 87, 245, 676, 1836, …
  (−∞, 0] nonnegative
• A008292 → D
  1 · 4, 2 · 11, 22, 3 · 26, 132, 78, 4 … row sums 0, 1, 6, 36, 240, 1800, 15120, 141120, …
  (−∞, 0] nonnegative
• A099097 → D+1
  1 · 3, 3 · 1, 19, 9 · 0, 12, 87, 27 … row sums 1, 6, 29, 126, 516, 2034, 7807, 29382, …
  (−∞, 0] nonnegative
• A013610 → D+1
  1 · 4, 3 · 7, 24, 9 · 10, 63, 108, 27 … row sums 1, 7, 40, 208, 1024, 4864, 22528, …
  (−∞, 0] nonnegative rational roots
• A132812 → D
  2 · 9, 6 · 24, 48, 12 · 50, 200, 150, 20 … row sums 0, 2, 15, 84, 420, 1980, 9009, 40040, …
  (−∞, 0] nonnegative
• A030528 → D
  1 · 2, 2 · 1, 6, 3 · 0, 6, 12, 4 … row sums 0, 1, 4, 10, 22, 45, 88, 167, …
  (−∞, 0] nonnegative
• A108299 → D
  -1 · -1, -2 · -1, -4, 3 · -1, -6, 6, 4 … row sums 0, -1, -3, -2, 3, 7, 4, -5, …
  (−∞, ∞)
• A154986 → D+1
  1 · 2, 1 · 5, 6, 1 · 12, 33, 14, 1 … row sums 1, 3, 12, 60, 360, 2520, 20160, 181440, …
  (−∞, 0] nonnegative
• A038207 → D+1
  1 · 3, 1 · 8, 6, 1 · 20, 24, 9, 1 … row sums 1, 4, 15, 54, 189, 648, 2187, 7290, …
  (−∞, 0] nonnegative rational roots
• A102365 → D
  1 · 5, 2 · 18, 30, 3 · 58, 258, 111, 4 … row sums 0, 0, 1, 7, 51, 431, 4208, 46824, …
  (−∞, 0] nonnegative
• A108838 → D+1
  2 · 5, 2 · 12, 12, 2 · 25, 50, 21, 2 … row sums 2, 7, 26, 98, 372, 1419, 5434, 20878, …
  (−∞, 0] nonnegative
• A094638 → D
  1 · 3, 4 · 6, 22, 18 · 10, 70, 150, 96 … row sums 0, 1, 7, 46, 326, 2556, 22212, 212976, …
  (−∞, 0] nonnegative
• A143495 → D
  1 · 7, 2 · 37, 24, 3 · 175, 194, 54, 4 … row sums 0, 1, 9, 64, 427, 2821, 18890, 129683, …
  (−∞, 0] nonnegative
• A008277 → θ+1 → D+1
  1 · 3, 2 · 7, 12, 3 · 15, 50, 30, 4 … row sums 1, 5, 22, 99, 471, 2386, 12867, 73681, …
  (−∞, 0] nonnegative
• A135838 → D+1
  1 · 4, 2 · 6, 8, 2 · 16, 36, 24, 4 … row sums 1, 6, 16, 80, 192, 896, 2048, 9216, …
  (−∞, 0] nonnegative rational roots
• A120910 → D+1
  3 · 9, 3 · 24, 18, 3 · 60, 72, 27, 3 … row sums 3, 12, 45, 162, 567, 1944, 6561, 21870, …
  (−∞, 0] nonnegative rational roots
• A103633 → D
  1 · 1, 2 · 0, 2, 3 · 0, 2, 6, 4 … row sums 0, 1, 3, 5, 12, 16, 36, 44, …
  (−∞, 0] nonnegative rational roots
• A013611 → D
  4 · 8, 32 · 12, 96, 192 · 16, 192, 768, 1024 … row sums 0, 4, 40, 300, 2000, 12500, 75000, …
  (−∞, 0] nonnegative rational roots
• A143685 → D
  1 · 11, 2 · 21, 42, 3 · 31, 282, 93, 4 … row sums 0, 1, 13, 66, 410, 2015, 10371, 49588, …
  (−∞, 0] nonnegative
• A135838 → D
  2 · 4, 4 · 12, 24, 12 · 16, 48, 48, 16 … row sums 0, 2, 8, 48, 128, 640, 1536, 7168, …
  (−∞, 0] nonnegative rational roots
• A081577 → D+1
  1 · 2, 1 · 5, 6, 1 · 8, 21, 10, 1 … row sums 1, 3, 12, 40, 132, 420, 1312, 4032, …
  (−∞, 0] nonnegative
• A008277 → θ+1 → x ↦ x+1
  1 · 3, 2 · 10, 12, 3 · 37, 62, 30, 4 … row sums 0, 1, 5, 25, 133, 761, 4677, 30745, …
  (−∞, −1] nonnegative
• A136572 → D
  1 · 0, 4 · 0, 0, 18 · 0, 0, 0, 96 … row sums 0, 1, 4, 18, 96, 600, 4320, 35280, …
  (−∞, 0] nonnegative rational roots
• A133080 → D+1
  1 · 2, 1 · 0, 2, 1 · 0, 2, 4, 1 … row sums 1, 3, 3, 7, 5, 11, 7, 15, …
  (−∞, 0] nonnegative
• A030528 → D+1
  1 · 2, 1 · 2, 4, 1 · 1, 7, 6, 1 … row sums 1, 3, 7, 15, 30, 58, 109, 201, …
  (−∞, 0] nonnegative
• A007318 → D → D+1
  1 · 4, 2 · 9, 12, 3 · 16, 36, 24, 4 … row sums 0, 1, 6, 24, 80, 240, 672, 1792, …
  (−∞, 0] nonnegative rational roots
• A011973 → x ↦ x−1/4 → D+1
  1 · 2 · 7, 4 · 20, 16 … row sums 1, 2, 11, 36, 133, 454, 1551, 5192, …
  (−∞, 0] nonnegative
• A054142 → D
  1 · 3, 2 · 5, 12, 3 · 7, 30, 30, 4 … row sums 0, 1, 5, 20, 71, 235, 744, 2285, …
  (−∞, 0] nonnegative
• A114655 → D
  2 · 12, 4 · 48, 48, 6 · 160, 320, 120, 8 … row sums 0, 2, 16, 102, 608, 3530, 20256, …
  (−∞, 0] nonnegative
• A136572 → D+1
  1 · 1, 1 · 0, 4, 2 · 0, 0, 18, 6 … row sums 1, 2, 6, 24, 120, 720, 5040, 40320, …
  (−∞, 0] nonnegative rational roots
• A122431 → D+1
  4, 9, 6, 1 · 1, 7, 12, 7, 1 · 0, 2, 10, 15, 8, 1 … row sums 20, 28, 36, 44, 52, 60, 68, 76, …
  (−∞, 0] nonnegative
• basis-map coefficients of A112227 → D+1
  0, 2, 1 · 0, 0, 3, 1 · 0, 0, 0, 4, 1 … row sums 3, 4, 5, 6, 7, 8, 9, 10, …
  (−∞, 0] nonnegative rational roots
• A227450 → D+1
  2 · 6, 4 · 14, 28, 8 · 30, 124, 96, 16 … row sums 2, 10, 50, 266, 1522, 9354, 61490, …
  (−∞, 0] nonnegative