Proof step e-07dfe9939e4be29b

basis_map A007318 → concludes about basis_map_A007318 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": "A007318",
  "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 8217d29e16c768051edb5347ffc3478721f530f1df8d85f90052080212d5f5f6, 10,164 bytes (2,286 compressed); download JSON

Cited by

• n-261c6497576cc5f7 (real_rooted)
• n-261c6497576cc5f7 (one_signed_coefficients)
• n-261c6497576cc5f7 (hadamard_kernel)
• n-261c6497576cc5f7 (interlacing)