Proof step e-1de26a40255316f7

basis_map A007318 → concludes about Triangle whose (i,j)-th entry is binomial(i,j)*2^i. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• Infinite lower triangular matrix with 2^k in the right diagonal and the rest zeros. Triangle, T(n,k), n zeros followed by the term 2^k. Tri… (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 0b9d62b8b54adbe5e4aabff080ff17490e27795c96d65348f36a68150f6bccff, 6,855 bytes (1,387 compressed); download JSON

Cited by

• n-d28ad9841fc73317 (one_signed_coefficients)
• n-d28ad9841fc73317 (hadamard_kernel)
• n-d28ad9841fc73317 (real_rooted)