Proof step e-107a218257e6f127

basis_map A007318 → concludes about Triangle whose (i,j)-th entry is binomial(i,j)*12^(i-j)*11^j. 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+11x)^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 ed278f75ffce7487f3dfb1f3d9f4aeaa1e81bf84332447de76316105bb95d04b, 6,923 bytes (1,403 compressed); download JSON

Cited by

• n-344e4bfa9933088a (one_signed_coefficients)
• n-344e4bfa9933088a (hadamard_kernel)
• n-344e4bfa9933088a (real_rooted)