preserver_image / reversal, shift 1
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
4 sequences
-
A030528: Triangle read by rows: T(n,k) = binomial(k,n-k).
1 · 1, 1 · 0, 2, 1 · 0, 1, 3, 1 … row sums 1, 2, 3, 5, 8, 13, 21, 34, …
-
A288874: Row reversed version of triangle A201637 (second-order Eulerian triangle).
A201637 → reverse (shift +1)1 · 0, 1 · 0, 2, 1 · 0, 6, 8, 1 … row sums 1, 1, 3, 15, 105, 945, 10395, 135135, …
-
A123125: Triangle of Eulerian numbers T(n,k), 0 <= k <= n, read by rows.
A173018 → reverse (shift +1)1 · 0, 1 · 0, 1, 1 · 0, 1, 4, 1 … row sums 1, 1, 2, 6, 24, 120, 720, 5040, …
-
A048993: Triangle of Stirling numbers of 2nd kind, S(n,k), n >= 0, 0 <= k <= n.
A106800 → reverse (shift +1)1 · 0, 1 · 0, 1, 1 · 0, 1, 3, 1 … row sums 1, 1, 2, 5, 15, 52, 203, 877, …