Proof step e-ad9ddfe0012b7a14

basis_map A013610 → concludes about basis_map_A013610 of Triangle of coefficients in expansion of (1+x)*(1+3x)*(1+5x)*(1+7x)*...*(1+(2n-1)x). 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 coefficients in expansion of (1+x)*(1+3x)*(1+5x)*(1+7x)*...*(1+(2n-1)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" } } }
• { "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 64cce4d75bb84f7f0f72289212c0095094a1186c63b69b7942454df818c2f195, 10,164 bytes (2,291 compressed); download JSON

Cited by

• n-00bc3b0d8b47bf75 (real_rooted)
• n-00bc3b0d8b47bf75 (one_signed_coefficients)
• n-00bc3b0d8b47bf75 (hadamard_kernel)
• n-00bc3b0d8b47bf75 (interlacing)