Proof step e-4ae5a85742c09b47

basis_map A007318 → concludes about basis_map_A007318 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": "A007318",
  "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 824bef88cc419d1eee0eda304704c4b5db02fd99b5ce8f574e034f9bf0122bae, 7,412 bytes (1,616 compressed); download JSON

Cited by

• n-fdb0bda32eba4618 (real_rooted)
• n-fdb0bda32eba4618 (one_signed_coefficients)
• n-fdb0bda32eba4618 (hadamard_kernel)