Proof step e-09b769bb10417be2

basis_map A007318 → concludes about shift_x_plus_one of Riordan array ((1+x)^3,x). JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• Riordan array ((1+x)^3,x). (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 69a13680c3ae08a3d12c28e16d7100ef070a29b5f65300933b0ca1e2830e1924, 6,917 bytes (1,401 compressed); download JSON

Cited by

• n-9aa9e3dd2403bca2 (one_signed_coefficients)
• n-9aa9e3dd2403bca2 (hadamard_kernel)
• n-9aa9e3dd2403bca2 (real_rooted)