preserver_image / derivative_polynomial, 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
- hadamard_multiplier, shift 0 5 proof steps, 5 sequences
- affine, shift -1 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
- euler_polynomial, shift 1 2 proof steps, 2 sequences
- hadamard_multiplier, shift -1 2 proof steps, 2 sequences
- affine, shift 2 2 proof steps, 2 sequences
- euler_polynomial, shift 2 1 proof steps, 1 sequences
- hadamard_multiplier, shift 1 1 proof steps, 1 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
410 sequences
-
basis-map coefficients of A021012 → D
-1 · 0, 4 · 0, 0, -18 · 0, 0, 0, 96 … row sums 0, -1, 4, -18, 96, -600, 4320, -35280, …
-
A081582 → D
1 · 9, 2 · 17, 34, 3 · 25, 194, 75, 4 … row sums 0, 1, 11, 54, 298, 1375, 6429, 28476, …
-
A114656 → D+1
1 · 3, 1 · 10, 8, 1 · 32, 48, 15, 1 … row sums 1, 4, 19, 96, 501, 2668, 14407, 78592, …
-
A130534 → D+1
1 · 2, 1 · 5, 5, 1 · 17, 23, 9, 1 … row sums 1, 3, 11, 50, 274, 1764, 13068, 109584, …
-
A082985 → D
3 · 5, 10 · 7, 28, 21 · 9, 54, 90, 36 … row sums 0, 3, 15, 56, 189, 605, 1872, 5655, …
-
A028326 → D
2 · 4, 4 · 6, 12, 6 · 8, 24, 24, 8 … row sums 0, 2, 8, 24, 64, 160, 384, 896, …
-
A023531 → (θ+1)² → D+1
1 · 4, 4 · 0, 18, 9 · 0, 0, 48, 16 … row sums 1, 8, 27, 64, 125, 216, 343, 512, …
-
A038220 → D
2 · 12, 8 · 54, 72, 24 · 216, 432, 288, 64 … row sums 0, 2, 20, 150, 1000, 6250, 37500, …
-
A023531 → (1/2)D²+2D+1 → D
1 · 4, 2 · 3, 12, 3 · 0, 12, 24, 4 … row sums 0, 1, 6, 18, 40, 75, 126, 196, …
-
A013610 → D
3 · 6, 18 · 9, 54, 81 · 12, 108, 324, 324 … row sums 0, 3, 24, 144, 768, 3840, 18432, 86016, …