Proof step e-f48c153b749c881a

basis_map A007318 → concludes about basis_map_A007318 of Triangle read by rows: T(n,k) = 2^floor(n/2)*binomial(n-1,k-1). 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: T(n,k) = 2^floor(n/2)*binomial(n-1,k-1). (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 df120574af8de8250cef78d773b98a264aa48302c61d4f1ceb35600f778d2cd4, 6,925 bytes (1,408 compressed); download JSON

Cited by

• n-3f5f8a84df712aee (real_rooted)
• n-3f5f8a84df712aee (one_signed_coefficients)
• n-3f5f8a84df712aee (hadamard_kernel)