Proof step e-7eb5590197b773bf

basis_map A007318 → concludes about Triangle whose (n,k)-th entry is 15^(n-k)*binomial(n,k). 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 (14 + x)^n. (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 26b313aa26ae2c04ee4b2b4268f439fecc372ee6d0e81258bf35493576e99e49, 6,860 bytes (1,385 compressed); download JSON

Cited by

• n-ff0214c333bfdcca (one_signed_coefficients)
• n-ff0214c333bfdcca (hadamard_kernel)
• n-ff0214c333bfdcca (real_rooted)