Proof step e-65b163cdbb61d2ab

basis_map A013609 → concludes about basis_map_A013609 of Triangle T(n,k) with the coefficient of [x^k] of the polynomial (2*(x+1)^2)^n in row n, column k, 0<=k<=2n. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013609",
  "operation": "basis_map"
}

Premises

• Triangle T(n,k) with the coefficient of [x^k] of the polynomial (2*(x+1)^2)^n in row n, column k, 0<=k<=2n. (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 ed721279817601818b04e35285f92425e1e8cbe08eed3ac01cb524af5f5db9c6, 6,877 bytes (1,395 compressed); download JSON

Cited by

• n-32191567c95f77cc (real_rooted)
• n-32191567c95f77cc (one_signed_coefficients)
• n-32191567c95f77cc (hadamard_kernel)