Proof step e-a6f64f0979a8db40

basis_map A013610 → concludes about basis_map_A013610 of Triangle of central factorial numbers |t(2n,2n-2k)| read by rows. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013610",
  "operation": "basis_map"
}

Premises

• Triangle of central factorial numbers |t(2n,2n-2k)| read by rows. (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" } } }
• { "claim": "interlacing", "from_index": 1, "kind": "weak", "orientation": "unordered" }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map, SHA-256 d138ccec96ba657f36af441f22b599bdffb58dfdbef3b91fd0a8df1378259a5c, 10,208 bytes (2,285 compressed); download JSON

Cited by

• n-5ffbcfe26ecef156 (one_signed_coefficients)
• n-5ffbcfe26ecef156 (hadamard_kernel)
• n-5ffbcfe26ecef156 (interlacing)
• n-5ffbcfe26ecef156 (real_rooted)