preserver_image / mobius, shift 0
Image under a real-rootedness preserver. All operations
Parameters (20)
- all
- derivative_polynomial, shift 0 422 proof steps, 410 sequences
- euler_polynomial, shift 0 367 proof steps, 352 sequences
- affine, shift 0 333 proof steps, 318 sequences
- reversal, shift 0 169 proof steps, 164 sequences
- mobius, shift 0 160 proof steps, 160 sequences
- affine, shift -1 5 proof steps, 5 sequences
- hadamard_multiplier, shift 0 5 proof steps, 5 sequences
- affine, shift 1 4 proof steps, 4 sequences
- reversal, shift 1 4 proof steps, 4 sequences
- hadamard_multiplier, shift 2 3 proof steps, 3 sequences
- affine, shift 2 2 proof steps, 2 sequences
- euler_polynomial, shift 1 2 proof steps, 2 sequences
- hadamard_multiplier, shift -1 2 proof steps, 2 sequences
- reversal, shift -1 1 proof steps, 1 sequences
- derivative_of_power_multiple, shift 0 1 proof steps, 1 sequences
- derivative_of_power_multiple, shift 1 1 proof steps, 1 sequences
- derivative_polynomial, shift -1 1 proof steps, 1 sequences
- derivative_polynomial, shift 2 1 proof steps, 1 sequences
- euler_polynomial, shift 2 1 proof steps, 1 sequences
- hadamard_multiplier, shift 1 1 proof steps, 1 sequences
160 sequences
-
A007318 → θ+1 → x ↦ x/(x+1)
1 · 1, 3 · 1, 6, 8 · 1, 9, 24, 20 … row sums 1, 4, 15, 54, 189, 648, 2187, 7290, …
-
A081580 → x ↦ x/(x+1)
1 · 1, 2 · 1, 9, 9 · 1, 16, 42, 28 … row sums 1, 3, 19, 87, 451, 2223, 11179, 55767, …
-
A108838 → x ↦ x/(x+1)
2 · 3, 5 · 4, 16, 14 · 5, 35, 70, 42 … row sums 2, 8, 34, 152, 706, 3376, 16514, 82256, …
-
A249252 → x ↦ x/(x+1)
1 · 1, 5 · 1, 10, 17 · 1, 15, 59, 61 … row sums 1, 6, 28, 136, 656, 3168, 15296, 73856, …
-
A136572: Triangle read by rows: row n consists of n zeros followed by n!.
1 · 0, 1 · 0, 0, 2 · 0, 0, 0, 6 … row sums 1, 1, 2, 6, 24, 120, 720, 5040, …
-
A178821 → x ↦ x/(x+1)
1 · 5, 10 · 15, 60, 60 · 35, 210, 420, 280 … row sums 1, 15, 135, 945, 5670, 30618, 153090, …
-
A062196 → x ↦ x/(x+1)
1 · 1, 4 · 1, 10, 15 · 1, 18, 63, 56 … row sums 1, 5, 26, 138, 743, 4043, 22180, …
-
A021009: Triangle of coefficients of Laguerre polynomials n!*L_n(x) (rising powers of x).
A123202 → x ↦ x/(x+1)1 · 1, -1 · 2, -4, 1 · 6, -18, 9, -1 … row sums 1, 0, -1, -4, -15, -56, -185, -204, …
-
A099093 → x ↦ x/(x+1)
1 · 0, 3 · 0, 3, 12 · 0, 0, 18, 45 … row sums 1, 3, 15, 63, 279, 1215, 5319, 23247, …
-
A126216 → x ↦ x/(x+1)
1 · 2, 3 · 5, 15, 11 · 14, 63, 93, 45 … row sums 1, 5, 31, 215, 1597, 12425, 99955, …