preserver_image / derivative_polynomial, shift 0

Image under a real-rootedness preserver. All operations

410 sequences

• A008292 → γ (shift +1) → D
  2 · 8 · 22, 32 · 52, 272 … row sums 0, 0, 2, 8, 54, 324, 2370, 18288, …
  (−∞, 0] nonnegative
• A334218 → D
  2 · 3, 6 · 4, 32, 12 · 5, 110, 165, 20 … row sums 0, 0, 2, 9, 48, 300, 2160, 17640, …
  (−∞, 0] nonnegative
• A008292 → D+1
  1 · 2, 1 · 5, 6, 1 · 12, 33, 14, 1 … row sums 1, 3, 12, 60, 360, 2520, 20160, 181440, …
  (−∞, 0] nonnegative
• A113953 → D
  1 · 2, 2 · 0, 8, 3 · 0, 8, 18, 4 … row sums 0, 1, 4, 11, 30, 73, 176, 407, …
  (−∞, 0] nonnegative
• A172431 → D+1
  1 · 3, 2 · 5, 10, 3 · 7, 26, 22, 4 … row sums 1, 5, 18, 59, 185, 564, 1685, 4957, …
  (−∞, 0] nonnegative
• A143495 → D+1
  1 · 4, 1 · 16, 9, 1 · 64, 61, 15, 1 … row sums 1, 5, 26, 141, 799, 4736, 29371, …
  (−∞, 0] nonnegative
• A104684 → D
  1 · 6, 2 · 30, 24, 3 · 140, 180, 60, 4 … row sums 0, 1, 8, 57, 384, 2505, 16008, 100849, …
  (−∞, 0] nonnegative
• A034870 → D+1
  1 · 3, 4, 1 · 5, 16, 18, 8, 1 … row sums 1, 8, 48, 256, 1280, 6144, 28672, …
  (−∞, 0] nonnegative rational roots
• basis-map coefficients of A026729, shifted → D
  -1 · 0, 2 · 0, 0, -3 · 0, 0, 0, 4 … row sums 0, -1, 2, -3, 4, -5, 6, -7, …
  (−∞, 0] rational roots
• A038208 → D
  2 · 8, 8 · 24, 48, 24 · 64, 192, 192, 64 … row sums 0, 2, 16, 96, 512, 2560, 12288, 57344, …
  (−∞, 0] nonnegative rational roots
• A114687 → D
  2 · 6, 8 · 12, 48, 24 · 20, 160, 240, 64 … row sums 0, 2, 14, 84, 484, 2750, 15546, 87752, …
  (−∞, 0] nonnegative
• A008292 → γ (scale 1/4) → D
  2 · 16 · 88, 32 · 416, 544 … row sums 0, 0, 2, 16, 120, 960, 8400, 80640, …
  (−∞, 0] nonnegative
• A052553 → D+1
  1 · 1 · 2, 1 · 3, 2 … row sums 1, 1, 3, 5, 10, 18, 33, 59, …
  (−∞, 0] nonnegative
• basis-map coefficients of A026729 → basis A056242 → D+1
  1 · 3, 2 · 6, 13, 4 · 10, 41, 40, 8 … row sums 1, 5, 23, 99, 408, 1632, 6388, 24596, …
  (−∞, 0] nonnegative
• A007318 → (1/3+(1/2)n+(1/6)n²)θ+1+(3/2)n+(1/2)n² → D
  4 · 16, 20 · 40, 100, 60 · 80, 300, 360, 140 … row sums 0, 4, 36, 200, 880, 3360, 11648, 37632, …
  (−∞, 0] nonnegative rational roots
• A081581 → D
  1 · 8, 2 · 15, 30, 3 · 22, 156, 66, 4 … row sums 0, 1, 10, 48, 248, 1100, 4872, 20608, …
  (−∞, 0] nonnegative
• A102547 → reverse → D
  1 · 0, 2 · 0, 0, 3 · 0, 0, 3, 4 … row sums 1, 2, 3, 7, 13, 21, 36, 61, …
  (−∞, 0] nonnegative
• narayana → D
  1 · 3, 2 · 6, 12, 3 · 10, 40, 30, 4 … row sums 0, 1, 5, 21, 84, 330, 1287, 5005, …
  (−∞, 0] nonnegative
• A075497 → D
  1 · 6, 2 · 28, 24, 3 · 120, 200, 60, 4 … row sums 0, 1, 8, 55, 384, 2841, 22504, 190863, …
  (−∞, 0] nonnegative
• A232535 → D
  2 · 8, 6 · 18, 50, 12 · 32, 196, 168, 20 … row sums 0, 2, 14, 80, 416, 2048, 9728, 45056, …
  (−∞, 0] nonnegative
• A207606 → D
  7, 4 · 16, 22, 6 · 30, 72, 45, 8 … row sums 11, 44, 155, 510, 1608, 4924, 14761, …
  (−∞, 0] nonnegative
• A116414 → D+1
  1 · 5, 1 · 21, 10, 1 · 82, 66, 15, 1 … row sums 1, 6, 32, 164, 819, 4012, 19363, 92352, …
  (−∞, 0] nonnegative
• A131689 → D
  1 · 1, 4 · 1, 12, 18 · 1, 28, 108, 96 … row sums 0, 1, 5, 31, 233, 2071, 21305, 249271, …
  (−∞, 0] nonnegative
• A116412 → D
  1 · 6, 2 · 21, 18, 3 · 60, 90, 36, 4 … row sums 0, 1, 8, 42, 190, 797, 3192, 12391, …
  (−∞, 0] nonnegative
• A207607 → D
  2 · 5, 4 · 9, 18, 6 · 14, 50, 39, 8 … row sums 0, 2, 9, 33, 111, 355, 1098, 3316, …
  (−∞, 0] nonnegative
• A131689 → D+1
  1 · 1, 1 · 1, 5, 2 · 1, 13, 24, 6 … row sums 1, 2, 8, 44, 308, 2612, 25988, 296564, …
  (−∞, 0] nonnegative
• A013620 → D+1
  1 · 5, 3 · 16, 30, 9 · 44, 144, 135, 27 … row sums 1, 8, 55, 350, 2125, 12500, 71875, …
  (−∞, 0] nonnegative rational roots
• A010054 → reverse → D+1
  1 · 3, 3 · 0, 12, 6 · 0, 0, 30, 10 … row sums 1, 6, 18, 40, 75, 126, 196, 288, …
  (−∞, 0] nonnegative rational roots
• A053122 → D+1
  1 · -1, 1 · -1, -2, 1 · 6, -2, -3, 1 … row sums 1, 0, -2, 2, 1, -4, 3, 2, …
  (−∞, ∞)
• A081580 → D
  1 · 7, 2 · 13, 26, 3 · 19, 122, 57, 4 … row sums 0, 1, 9, 42, 202, 855, 3567, 14308, …
  (−∞, 0] nonnegative
• A064861 → D
  3, 4 · 5, 16, 12 · 6, 26, 36, 16 … row sums 7, 33, 84, 324, 756, 2700, 6048, 20736, …
  (−∞, 0] nonnegative rational roots
• A121574 → D+1
  1 · 3, 1 · 9, 7, 1 · 24, 32, 11, 1 … row sums 1, 4, 17, 68, 264, 1002, 3739, 13768, …
  (−∞, 0] nonnegative
• A039755 → D+1
  1 · 2, 1 · 5, 6, 1 · 14, 31, 12, 1 … row sums 1, 3, 12, 58, 324, 2044, 14320, 109960, …
  (−∞, 0] nonnegative
• A216973: Exponential Riordan array [x*exp(x),x].
  A007318 → D
  1 · 2, 2 · 3, 6, 3 · 4, 12, 12, 4 … row sums 0, 1, 4, 12, 32, 80, 192, 448, …
  A216973 (−∞, −1] nonnegative rational roots
• A126351 → D
  2 · 5, 8 · 9, 38, 24 · 14, 110, 195, 64 … row sums 0, 2, 13, 71, 383, 2129, 12360, 75242, …
  (−∞, 0] nonnegative
• A007318 → ×(−(1/2)n+(1/2)n²) → D+1
  3, 4, 1 · 12, 27, 18, 3 · 30, 96, 108, 48, 6 … row sums 0, 0, 8, 60, 288, 1120, 3840, 12096, …
  (−∞, 0] nonnegative rational roots
• A102662 → D
  3 · 5, 6 · 7, 22, 9 · 9, 46, 51, 12 … row sums 0, 3, 11, 38, 118, 349, 997, 2780, …
  (−∞, 0] nonnegative
• A137338 → D+1
  1 · 0, 1 · -3, -1, 1 · 9, -6, -3, 1 … row sums 1, 1, -3, 1, 13, -61, 223, -867, …
  (−∞, ∞)
• A249250 → D
  3 · 6, 6 · 9, 30, 9 · 12, 72, 72, 12 … row sums 0, 3, 12, 48, 168, 564, 1824, 5760, …
  (−∞, 0] nonnegative
• A008288 → D
  1 · 3, 2 · 5, 10, 3 · 7, 26, 21, 4 … row sums 0, 1, 5, 18, 58, 175, 507, 1428, …
  (−∞, 0] nonnegative
• 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
• A091044 → ⊙ C(n+2,k+1) → D+1
  1 · 2, 1 · 6, 7, 1 · 15, 42, 17, 1 … row sums 1, 3, 14, 75, 438, 2702, 17324, 114291, …
  (−∞, 0] nonnegative
• A007318 → basis A049020 → D+1
  1 · 3, 1 · 10, 7, 1 · 37, 40, 12, 1 … row sums 1, 4, 18, 90, 494, 2946, 18926, 130066, …
  (−∞, 0] nonnegative
• A152828 → D+1
  1 · 1 · 1 · 2, 1 … row sums 1, 1, 1, 3, 3, 3, 8, 8, …
  (−∞, 0] nonnegative rational roots
• A039756 → D
  1 · 4, 2 · 9, 26, 3 · 16, 116, 120, 4 … row sums 0, 1, 6, 38, 256, 1844, 14296, 119160, …
  (−∞, 0] nonnegative
• A124038 → D+1
  1 · -1, 1 · -3, 0, 1 · 0, -6, 1, 1 … row sums 1, 0, -2, -4, -3, 2, 7, 6, …
  (−∞, ∞)
• A169803 → D
  1 · 2 · 3, 2 · 4, 6 … row sums 0, 1, 2, 5, 10, 20, 38, 71, …
  (−∞, 0] nonnegative
• A085880 → D+1
  1 · 2, 1 · 6, 8, 2 · 20, 45, 30, 5 … row sums 1, 3, 16, 100, 672, 4704, 33792, …
  (−∞, 0] nonnegative rational roots
• A033282 → D+1
  1 · 3, 2 · 6, 15, 5 · 10, 51, 63, 14 … row sums 1, 5, 26, 138, 743, 4043, 22180, …
  (−∞, 0] nonnegative
• A304236 → D+1
  1 · 1 · 4, 3 · 7, 6 … row sums 1, 1, 7, 13, 46, 106, 301, 739, …
  (−∞, 0] nonnegative