Proof step e-0b3719baa0dde23e

basis_map A007318 → concludes about basis_map_A007318 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": "A007318",
  "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 3981d079ea6ba1002d975cf5e0952ba93b12cdfe95c5a7575f35034b10a47379, 10,208 bytes (2,282 compressed); download JSON

Cited by

• n-6a1d0871f44aed3c (real_rooted)
• n-6a1d0871f44aed3c (one_signed_coefficients)
• n-6a1d0871f44aed3c (hadamard_kernel)
• n-6a1d0871f44aed3c (interlacing)