Proof step e-4c344817bd191837

basis_map A007318 → concludes about shift_x_plus_one of basis-map coefficients of Square array of binomial coefficients T(n,k) = binomial(n,k), n >= 0, k >= 0, read by downward antidiagonals. shi… JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• basis-map coefficients of Square array of binomial coefficients T(n,k) = binomial(n,k), n >= 0, k >= 0, read by downward antidiagonals. shi… (sequence)
  uses: Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 0]

Claims

• { "claim": "real_rooted", "from_index": 1, "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 f54804f1ca29938399f054961f4df94f2009809debccdb92cc6f0fc32af66863, 6,862 bytes (1,390 compressed); download JSON

Cited by

• n-94ecad1fe442c5e0 (one_signed_coefficients)
• n-94ecad1fe442c5e0 (hadamard_kernel)
• n-94ecad1fe442c5e0 (real_rooted)