Proof step e-3d86f7db70abac1a

basis_map A007318 → concludes about shift_x_plus_one of Square array read by antidiagonals downwards: T(n,k), n>=0, k>=0, in which column 0 is equal to A057427: 0, 1, 1, 1, ..., and for k > 0 col… JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A007318",
  "operation": "basis_map"
}

Premises

• Square array read by antidiagonals downwards: T(n,k), n>=0, k>=0, in which column 0 is equal to A057427: 0, 1, 1, 1, ..., and for k > 0 col… (sequence)
  uses: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]

Claims

• { "claim": "real_rooted", "from_index": 0, "region": { "upper": { "closed": true, "value": "0" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map, SHA-256 0cd9560b7bc5c6bf9de7aca49f642e43c72da788f5bbc7925fed1707b2177d9a, 11,642 bytes (2,069 compressed); download JSON

Cited by

• n-634d40a3ea7efaff (one_signed_coefficients)
• n-634d40a3ea7efaff (hadamard_kernel)
• n-634d40a3ea7efaff (real_rooted)