Proof step e-095baa2a9dfe188f

basis_map A007318 → concludes about binomial JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A007318",
  "operation": "basis_map"
}

Premises

• a(n) = 1 if n is of the form m(m+3)/2, otherwise 0. (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 05446ba52f33fa49b6e1de7dedb11b2753869f8d6d869e6e382f0b89318c03c6, 6,855 bytes (1,380 compressed); download JSON

Cited by

• n-c8c19eba9d68881f (one_signed_coefficients)
• n-c8c19eba9d68881f (hadamard_kernel)
• n-c8c19eba9d68881f (real_rooted)