Proof step e-cdc351e4a2e06a48

basis_map A013609 → concludes about basis_map_A013609 of Triangle of coefficients in expansion of (x+1)*(x+3)*...*(x + 2n - 1) in rising powers of x. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• Triangle of coefficients in expansion of (x+1)*(x+3)*...*(x + 2n - 1) in rising powers of 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 d1fce5bd5e7a1b9a4627cf9e4464c4572a7f2854d1505ca0735b558e500d1580, 7,412 bytes (1,621 compressed); download JSON

Cited by

• n-c2e61578a2a87aa5 (real_rooted)
• n-c2e61578a2a87aa5 (one_signed_coefficients)
• n-c2e61578a2a87aa5 (hadamard_kernel)