preserver_image / derivative_polynomial, shift 0

Image under a real-rootedness preserver. All operations

410 sequences

• A075497 → D+1
  1 · 3, 1 · 10, 8, 1 · 36, 52, 15, 1 … row sums 1, 4, 19, 104, 641, 4380, 32803, …
  (−∞, 0] nonnegative
• A116414 → D
  1 · 8, 2 · 42, 24, 3 · 184, 174, 48, 4 … row sums 0, 1, 10, 69, 410, 2252, 11790, 59767, …
  (−∞, 0] nonnegative
• A008278 → D
  1 · 3, 2 · 6, 14, 3 · 10, 50, 45, 4 … row sums 0, 1, 5, 23, 109, 544, 2876, 16113, …
  (−∞, 0] nonnegative
• basis-map coefficients of A112227 → D
  0, 2 · 0, 0, 3 · 0, 0, 0, 4 · 0, 0, 0, 0, 5 … row sums 2, 3, 4, 5, 6, 7, 8, 9, …
  (−∞, 0] nonnegative rational roots
• A103327 → D+1
  1 · 4, 1 · 15, 12, 1 · 42, 77, 24, 1 … row sums 1, 5, 28, 144, 704, 3328, 15360, 69632, …
  (−∞, 0] nonnegative
• A011973 → ⊙ C(n,k) → D+1
  1 · 1 · 3, 2 · 7, 6 … row sums 1, 1, 5, 13, 43, 131, 411, 1275, …
  (−∞, 0] nonnegative
• A008277 → θ+1
  1 · 1, 2 · 1, 6, 3 · 1, 14, 18, 4 … row sums 0, 1, 3, 10, 37, 151, 674, 3263, …
  (−∞, 0] nonnegative
• A165253 → D+1
  1 · 1 · 2, 1 · 4, 5, 1 … row sums 1, 1, 3, 10, 32, 99, 299, 887, …
  (−∞, 0] nonnegative
• A085880 → D
  1 · 4, 4 · 15, 30, 15 · 56, 168, 168, 56 … row sums 0, 1, 8, 60, 448, 3360, 25344, 192192, …
  (−∞, 0] nonnegative rational roots
• A391533 → D+1
  8, 6, 1 · 12, 18, 8, 1 · 16, 38, 31, 10, 1 … row sums 15, 39, 96, 228, 528, 1200, 2688, 5952, …
  (−∞, 0] nonnegative
• A008278 → D+1
  1 · 2, 1 · 4, 5, 1 · 7, 20, 10, 1 … row sums 1, 3, 10, 38, 161, 747, 3753, 20253, …
  (−∞, 0] nonnegative
• A110441 → D+1
  1 · 4, 1 · 13, 8, 1 · 38, 41, 12, 1 … row sums 1, 5, 22, 92, 372, 1468, 5688, 21728, …
  (−∞, 0] nonnegative
• A007318 → ×(1+2n+n²) → D
  4 · 18, 18 · 48, 96, 48 · 100, 300, 300, 100 … row sums 0, 4, 36, 192, 800, 2880, 9408, 28672, …
  (−∞, 0] nonnegative rational roots
• A143683 → D+1
  1 · 2, 1 · 11, 12, 1 · 20, 57, 22, 1 … row sums 1, 3, 24, 100, 528, 2352, 11008, 48960, …
  (−∞, 0] nonnegative
• basis-map coefficients of A297191, shifted → D
  0, 2 · 0, 0, 0, 4 · 0, 0, 0, 0, 0, 6 … row sums 0, 2, 4, 6, 8, 10, 12, 14, …
  (−∞, 0] nonnegative rational roots
• basis-map coefficients of A026729 → D
  1 · 0, 2 · 0, 0, 3 · 0, 0, 0, 4 … row sums 0, 1, 2, 3, 4, 5, 6, 7, …
  (−∞, 0] nonnegative rational roots
• A249251 → D+1
  1 · 4, 3 · 7, 18, 6 · 10, 51, 57, 12 … row sums 1, 7, 31, 130, 520, 2017, 7651, 28537, …
  (−∞, 0] nonnegative
• A053122 → D
  1 · -4, 2 · 10, -12, 3 · -20, 42, -24, 4 … row sums 0, 1, -2, 1, 2, -4, 2, 3, …
  (−∞, ∞)
• A013609 → D
  2 · 4, 8 · 6, 24, 24 · 8, 48, 96, 64 … row sums 0, 2, 12, 54, 216, 810, 2916, 10206, …
  (−∞, 0] nonnegative rational roots
• A081582 → D+1
  1 · 2, 1 · 10, 11, 1 · 18, 51, 20, 1 … row sums 1, 3, 22, 90, 447, 1925, 8572, 36612, …
  (−∞, 0] nonnegative
• delannoy → D
  1 · 3, 2 · 5, 10, 3 · 7, 26, 21, 4 … row sums 0, 1, 5, 18, 58, 175, 507, 1428, …
  (−∞, 0] nonnegative
• A110441 → D
  1 · 6, 2 · 23, 18, 3 · 72, 96, 36, 4 … row sums 0, 1, 8, 44, 208, 908, 3776, 15200, …
  (−∞, 0] nonnegative
• chebyshev_u → D+1
  1 · 2, 2 · -1, 8, 4 · -4, -4, 24, 8 … row sums 1, 4, 11, 24, 45, 76, 119, 176, …
  (−∞, ∞)
• A125662 → D
  1 · 6, 2 · 25, 18, 3 · 90, 102, 36, 4 … row sums 0, 1, 8, 46, 232, 1091, 4912, 21468, …
  (−∞, 0] nonnegative
• A038231 → D
  1 · 8, 2 · 48, 24, 3 · 256, 192, 48, 4 … row sums 0, 1, 10, 75, 500, 3125, 18750, 109375, …
  (−∞, 0] nonnegative rational roots
• A145597 → D+1
  1 · 6, 3 · 21, 27, 6 · 55, 135, 75, 10 … row sums 1, 9, 54, 275, 1287, 5733, 24752, …
  (−∞, 0] nonnegative
• A062145 → D+1
  1 · 5, 4 · 11, 30, 10 · 19, 108, 105, 20 … row sums 1, 9, 51, 252, 1170, 5247, 23023, …
  (−∞, 0] nonnegative
• A103327 → D
  1 · 10, 2 · 35, 42, 3 · 84, 252, 108, 4 … row sums 0, 1, 12, 80, 448, 2304, 11264, 53248, …
  (−∞, 0] nonnegative
• A034870 → D
  2, 2 · 4, 12, 12, 4 · 6, 30, 60, 60, 30, 6 … row sums 0, 4, 32, 192, 1024, 5120, 24576, …
  (−∞, 0] nonnegative rational roots
• A059473 → D
  2 · 10, 8 · 32, 64, 24 · 88, 296, 264, 64 … row sums 0, 2, 18, 120, 712, 3960, 21144, …
  (−∞, 0] nonnegative
• A093375: Array T(m,n) read by ascending antidiagonals: T(m,n) = m*binomial(n+m-2, n-1) for m, n >= 1.
  A007318 → D+1
  1 · 2, 1 · 3, 4, 1 · 4, 9, 6, 1 … row sums 1, 3, 8, 20, 48, 112, 256, 576, …
  A093375 (−∞, 0] nonnegative rational roots
• A011973 → x ↦ x+2 (shift +1) → D+1
  1 · 4, 1 · 7, 2 · 18, 9, 1 … row sums 1, 5, 9, 28, 62, 165, 391, 983, …
  (−∞, 0] nonnegative
• A063967 → D+1
  1 · 2, 1 · 5, 5, 1 · 10, 17, 8, 1 … row sums 1, 3, 11, 36, 116, 364, 1124, 3424, …
  (−∞, 0] nonnegative
• A008288 → D+1
  1 · 2, 1 · 4, 5, 1 · 6, 15, 8, 1 … row sums 1, 3, 10, 30, 87, 245, 676, 1836, …
  (−∞, 0] nonnegative
• A094816 → D
  1 · 3, 2 · 8, 12, 3 · 24, 58, 30, 4 … row sums 0, 1, 5, 23, 116, 669, 4429, 33375, …
  (−∞, 0] nonnegative
• A023531 → basis A008277
  1 · 1, 1 · 1, 3, 1 · 1, 7, 6, 1 … row sums 1, 2, 5, 15, 52, 203, 877, 4140, …
  (−∞, 0] nonnegative
• A274498 → D
  6 · 18 · 36, 72 · 108, 216 … row sums 0, 0, 6, 18, 108, 324, 1458, 4374, …
  (−∞, 0] nonnegative rational roots
• A132774: A natural number operator.
  A023531 → 2D+1+2n
  1 · 2, 3 · 0, 4, 5 · 0, 0, 6, 7 … row sums 1, 5, 9, 13, 17, 21, 25, 29, …
  A132774 [−1, 0] nonnegative rational roots
• A027465 → D
  1 · 6, 2 · 27, 18, 3 · 108, 108, 36, 4 … row sums 0, 1, 8, 48, 256, 1280, 6144, 28672, …
  (−∞, 0] nonnegative rational roots
• A081577 → D
  1 · 4, 2 · 7, 14, 3 · 10, 44, 30, 4 … row sums 0, 1, 6, 24, 88, 300, 984, 3136, …
  (−∞, 0] nonnegative
• basis-map coefficients of A113214, shifted → D
  -1 · 2, 2 · -3, -6, -3 · 4, 12, 12, 4 … row sums 0, -1, 4, -12, 32, -80, 192, -448, …
  (−∞, 0] rational roots
• A091044 → D+1
  1 · 4, 2 · 13, 16, 3 · 32, 84, 40, 4 … row sums 1, 6, 32, 160, 768, 3584, 16384, 73728, …
  (−∞, 0] nonnegative
• A059344 → ⊙ 1/k! (shift -1) → D
  2 · 6 · 12, 12 · 20, 60 … row sums 0, 0, 2, 6, 24, 80, 270, 882, …
  (−∞, 0] nonnegative
• A145597 → D
  3 · 15, 12 · 45, 90, 30 · 105, 378, 315, 60 … row sums 0, 3, 27, 165, 858, 4095, 18564, 81396, …
  (−∞, 0] nonnegative
• A159854 → D
  0, 2 · 0, 2, 3 · 0, 2, 6, 4 · 0, 2, 9, 12, 5 … row sums 2, 5, 12, 28, 64, 144, 320, 704, …
  (−∞, 0] nonnegative rational roots
• A059344 → ⊙ 1/k! (shift -1) → D+1
  1 · 1 · 3, 2 · 7, 6 … row sums 1, 1, 5, 13, 43, 131, 411, 1275, …
  (−∞, 0] nonnegative
• A178821 → D
  5 · 30, 30 · 105, 210, 105 · 280, 840, 840, 280 … row sums 0, 5, 60, 420, 2240, 10080, 40320, …
  (−∞, 0] nonnegative rational roots
• A159854 → D+1
  0, 2, 1 · 0, 2, 4, 1 · 0, 2, 7, 6, 1 … row sums 3, 7, 16, 36, 80, 176, 384, 832, …
  (−∞, 0] nonnegative
• A128099 → D
  2 · 4 · 6, 8 · 8, 24 … row sums 0, 0, 2, 4, 14, 32, 82, 188, …
  (−∞, 0] nonnegative
• A102365 → D+1
  1 · 1 · 2, 1 · 6, 7, 1 … row sums 1, 1, 3, 14, 86, 657, 5995, 63541, …
  (−∞, 0] nonnegative