preserver_image / hadamard_multiplier, 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
5 sequences
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A055151: Triangular array of Motzkin polynomial coefficients.
narayana → γ (shift +1)1 · 1 · 1, 1 · 1, 3 … row sums 1, 1, 2, 4, 9, 21, 51, 127, …
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A331333: Interpolating the factorial and the powers of 2. Triangle read by rows, T(n, k) for 0 <= k <= n.
A013609 → ⊙ 1/k!1 · 1, 2 · 2, 8, 4 · 6, 36, 36, 8 … row sums 1, 3, 14, 86, 648, 5752, 58576, 671568, …
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A391403: Triangle read by rows: T(n,k) is k-th entry of the gamma-vector of the n-dimensional cyclohedron, 0 <= k <= floor(n/2).
A011973 → ⊙ C(n,k)1 · 1 · 1, 2 · 1, 6 … row sums 1, 1, 3, 7, 19, 51, 141, 393, …
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A111910: Square array read by antidiagonals: S(p,q) = (p+q+1)!(2p+2q+1)!/((p+1)!(2p+1)!(q+1)!(2q+1)!) (p,q>=0).
A091044 → ⊙ C(n+2,k+1)1 · 1, 1 · 1, 5, 1 · 1, 14, 14, 1 … row sums 1, 2, 7, 30, 146, 772, 4331, 25398, …
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A181543: Triangle of cubed binomial coefficients, T(n,k) = C(n,k)^3, read by rows.
A008459 → ⊙ C(n,k)1 · 1, 1 · 1, 8, 1 · 1, 27, 27, 1 … row sums 1, 2, 10, 56, 346, 2252, 15184, 104960, …