Proof step e-01d2a4c51ed4f80c

basis_map A007318 → concludes about shift_x_plus_one of Triangle read by rows: triangle of repeated stepped binomial coefficients. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• Triangle read by rows: triangle of repeated stepped binomial coefficients. (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 6534b169b306d43b2252a01e19b9fe090aa049ad9f5b270522fbf3f0d4b2820f, 6,925 bytes (1,402 compressed); download JSON

Cited by

• n-b4a66ef190cb2745 (one_signed_coefficients)
• n-b4a66ef190cb2745 (hadamard_kernel)
• n-b4a66ef190cb2745 (real_rooted)