preserver_image

Image under a real-rootedness preserver. All operations

1381 sequences

• A113413 → basis A007318
  1 · 3, 1 · 7, 6, 1 · 17, 23, 9, 1 … row sums 1, 4, 14, 50, 178, 634, 2258, 8042, …
  (−∞, −1] nonnegative
• A034870 → θ+1
  1 · 1, 4, 3 · 1, 8, 18, 16, 5 … row sums 1, 8, 48, 256, 1280, 6144, 28672, …
  (−∞, 0] nonnegative rational roots
• A081581 → basis A007318
  1 · 2, 1 · 10, 10, 1 · 32, 48, 18, 1 … row sums 1, 3, 21, 99, 549, 2835, 15093, 79299, …
  (−∞, −1] 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
• A026374 → x ↦ x+1
  1 · 2, 1 · 5, 5, 1 · 10, 15, 7, 1 … row sums 1, 3, 11, 33, 121, 363, 1331, 3993, …
  (−∞, −1] nonnegative
• A033282 → D+1
  1 · 3, 2 · 6, 15, 5 · 10, 51, 63, 14 … row sums 1, 5, 26, 138, 743, 4043, 22180, …
  (−∞, 0] nonnegative
• A145596 → x ↦ x+1
  1 · 4, 2 · 14, 14, 3 · 48, 72, 32, 4 … row sums 1, 6, 31, 156, 785, 3978, 20335, …
  (−∞, −1] nonnegative
• A154986 → basis A007318
  1 · 2, 1 · 6, 6, 1 · 24, 36, 14, 1 … row sums 1, 3, 13, 75, 537, 4611, 46053, 525483, …
  (−∞, −1] nonnegative
• A008277: Triangle of Stirling numbers of the second kind, S2(n,k), n >= 1, 1 <= k <= n.
  1 · 1, 1 · 1, 3, 1 · 1, 7, 6, 1 … row sums 1, 2, 5, 15, 52, 203, 877, 4140, …
  A008277 (−∞, 0) nonnegative
• A249250 → reverse
  1 · 3, 1 · 3, 6, 1 · 3, 15, 9, 1 … row sums 1, 4, 10, 28, 76, 208, 568, 1552, …
  (−∞, 0] nonnegative
• basis-map coefficients of Square array of binomial coefficients T(n,k) = binomial(n,k), n >= 0, k >= 0, read by downward antidiagonals. shifted by x -> -x + 0
  1 · 0, -1 · 0, 0, 1 · 0, 0, 0, -1 … row sums 1, -1, 1, -1, 1, -1, 1, -1, …
  [−1, 0] rational roots
• A304236 → D+1
  1 · 1 · 4, 3 · 7, 6 … row sums 1, 1, 7, 13, 46, 106, 301, 739, …
  (−∞, 0] nonnegative
• A007318 → D+1 → D+1
  1 · 3, 1 · 7, 6, 1 · 13, 21, 9, 1 … row sums 1, 4, 14, 44, 128, 352, 928, 2368, …
  (−∞, 0] nonnegative
• A099093 → D
  3 · 3, 18 · 0, 36, 81 · 0, 18, 243, 324 … row sums 0, 3, 21, 117, 585, 2754, 12474, 54999, …
  (−∞, 0] nonnegative
• A091044 → basis A007318
  1 · 4, 2 · 16, 16, 3 · 64, 96, 40, 4 … row sums 1, 6, 35, 204, 1189, 6930, 40391, …
  (−∞, −1] nonnegative
• A060920 → D+1
  1 · 3, 1 · 10, 7, 1 · 33, 38, 12, 1 … row sums 1, 4, 18, 84, 390, 1784, 8042, 35804, …
  (−∞, ∞) nonnegative
• A038231: Triangle whose (i,j)-th entry is binomial(i,j)*4^(i-j).
  1 · 4, 1 · 16, 8, 1 · 64, 48, 12, 1 … row sums 1, 5, 25, 125, 625, 3125, 15625, 78125, …
  A038231 (−∞, −1] nonnegative rational roots
• A021010: Triangle of coefficients of Laguerre polynomials L_n(x) (powers of x in decreasing order).
  A144084 → x ↦ −x (shift -1)
  1 · -1, 1 · 1, -4, 2 · -1, 9, -18, 6 … row sums 1, 0, -1, -4, -15, -56, -185, -204, …
  A021010 [0, ∞)
• A007318 → (θ+1)² → D
  4 · 8, 18 · 12, 54, 48 · 16, 108, 192, 100 … row sums 0, 4, 26, 114, 416, 1360, 4128, 11872, …
  (−∞, 0] nonnegative
• A137320 → reverse
  1 · 2 · 4, 2 · 8, 12, 4 … row sums 1, 2, 6, 24, 120, 720, 5040, 40320, …
  (−∞, 0] nonnegative rational roots
• A100861 → (θ+1)²
  1 · 1 · 1, 4 · 1, 12 … row sums 1, 1, 5, 13, 52, 176, 706, 2710, …
  (−∞, 0] nonnegative
• A126216 → D
  1 · 5, 2 · 21, 18, 3 · 84, 112, 42, 4 … row sums 0, 1, 7, 42, 242, 1375, 7773, 43876, …
  (−∞, 0] nonnegative
• A007318 → θ+1 → D+1
  1 · 3, 2 · 5, 10, 3 · 7, 24, 21, 4 … row sums 1, 5, 18, 56, 160, 432, 1120, 2816, …
  (−∞, 0] nonnegative
• narayana → γ (shift +1) → x ↦ x+1
  1 · 1 · 2, 1 · 4, 3 … row sums 1, 1, 3, 7, 21, 61, 191, 603, …
  (−∞, −1] nonnegative
• A104684 → x ↦ x/(x+1)
  1 · 2, 3 · 6, 18, 13 · 20, 90, 132, 63 … row sums 1, 5, 37, 305, 2641, 23525, 213445, …
  [−1, 0] nonnegative
• A131689 → x ↦ x/(x+1)
  1 · 0, 1 · 0, 1, 3 · 0, 1, 8, 13 … row sums 1, 1, 4, 22, 160, 1456, 15904, 202672, …
  [−1, 0] nonnegative
• A113214 → x ↦ x−5
  1 · -3, 1 · 10, -7, 1 · -35, 37, -11, 1 … row sums 1, -2, 4, -8, 16, -32, 64, -128, …
  (1, 5]
• A130534 → θ+1
  1 · 1, 2 · 2, 6, 3 · 6, 22, 18, 4 … row sums 1, 3, 11, 50, 274, 1764, 13068, 109584, …
  (−∞, 0] nonnegative
• A078812 → D+1
  1 · 3, 1 · 7, 6, 1 · 14, 22, 9, 1 … row sums 1, 4, 14, 46, 145, 444, 1331, 3926, …
  (−∞, 0] nonnegative
• A135838 → x ↦ x+1
  1 · 4, 2 · 8, 8, 2 · 32, 48, 24, 4 … row sums 1, 6, 18, 108, 324, 1944, 5832, 34992, …
  (−∞, −1] nonnegative rational roots
• A062196 → reverse
  1 · 3, 1 · 6, 8, 1 · 10, 30, 15, 1 … row sums 1, 4, 15, 56, 210, 792, 3003, 11440, …
  (−∞, 0] nonnegative
• A113214 → θ+1
  1 · 2, 2 · 0, 6, 3 · 0, 4, 12, 4 … row sums 1, 4, 9, 20, 40, 78, 147, 272, …
  (−∞, 0] nonnegative
• A038220 → basis A007318
  1 · 5, 2 · 25, 20, 4 · 125, 150, 60, 8 … row sums 1, 7, 49, 343, 2401, 16807, 117649, …
  (−∞, −1] nonnegative rational roots
• basis-map coefficients of A026729, shifted → D+1
  1 · -1, -1 · 0, 2, 1 · 0, 0, -3, -1 … row sums 1, -2, 3, -4, 5, -6, 7, -8, …
  (−∞, 0] rational roots
• A035607 → x ↦ x+1
  1 · 1 · 3, 2 · 7, 8, 2 … row sums 1, 1, 5, 17, 61, 217, 773, 2753, …
  (−∞, −1] nonnegative
• A099040 → x ↦ x−2
  1 · -4, 2 · 12, -14, 4 · -32, 64, -40, 8 … row sums 1, -2, 2, 0, -4, 8, -8, 0, …
  (0, 2]
• A114656 → x ↦ x/(x+1)
  1 · 2, 3 · 4, 14, 11 · 8, 48, 84, 45 … row sums 1, 5, 29, 185, 1257, 8925, 65445, …
  [−1, 0] nonnegative
• A152198: Triangle read by rows, A007318 rows repeated.
  1 · 1 · 1, 1 · 1, 1 … row sums 1, 1, 2, 2, 4, 4, 8, 8, …
  A152198 A152815 (−∞, 0] nonnegative rational roots
• A028326 → basis A007318
  2 · 4, 2 · 8, 8, 2 · 16, 24, 12, 2 … row sums 2, 6, 18, 54, 162, 486, 1458, 4374, …
  (−∞, −1] nonnegative rational roots
• A023531 → (1/2)D²+2D+1 → θ+1
  1 · 2, 2 · 1, 8, 3 · 0, 6, 18, 4 … row sums 1, 4, 12, 28, 55, 96, 154, 232, …
  (−∞, 0] nonnegative
• A122542 → D
  1 · 2, 2 · 2, 8, 3 · 2, 16, 18, 4 … row sums 0, 1, 4, 13, 40, 117, 332, 921, …
  (−∞, 0] nonnegative
• A007318 → D → D
  2 · 6, 6 · 12, 24, 12 · 20, 60, 60, 20 … row sums 0, 0, 2, 12, 48, 160, 480, 1344, …
  (−∞, 0] nonnegative rational roots
• A034870 → (θ+1)²
  1 · 1, 8, 9 · 1, 16, 54, 64, 25 … row sums 1, 18, 160, 1120, 6912, 39424, 212992, …
  (−∞, 0] nonnegative
• A145597 → basis A007318
  1 · 6, 3 · 27, 27, 6 · 110, 165, 75, 10 … row sums 1, 9, 60, 360, 2061, 11529, 63728, …
  (−∞, −1] nonnegative
• A114655 → reverse
  2 · 2, 4 · 2, 12, 8 · 2, 24, 48, 16 … row sums 2, 6, 22, 90, 394, 1806, 8558, 41586, …
  (−∞, 0] nonnegative
• A103633 → D+1
  1 · 1, 1 · 1, 3, 1 · 0, 2, 4, 1 … row sums 1, 2, 5, 7, 16, 20, 44, 52, …
  (−∞, 0] nonnegative
• A059473 → x ↦ x+1
  1 · 4, 2 · 18, 18, 4 · 80, 120, 56, 8 … row sums 1, 6, 40, 264, 1744, 11520, 76096, …
  (−∞, −1] nonnegative
• A106800 → θ+1
  1 · 1 · 1, 2 · 1, 6, 3 … row sums 1, 1, 3, 10, 38, 161, 747, 3753, …
  (−∞, 0] nonnegative
• A001263 → (θ+1)²
  1 · 1, 4 · 1, 12, 9 · 1, 24, 54, 16 … row sums 1, 5, 22, 95, 406, 1722, 7260, 30459, …
  (−∞, 0] nonnegative
• chebyshev_t → D+1
  1 · 1, 1 · -1, 4, 2 · -3, -3, 12, 4 … row sums 1, 2, 5, 10, 17, 26, 37, 50, …
  (−∞, ∞)