Proof step e-83332bc01455e815

basis_map A007318 → concludes about Triangle T(n, k) read by rows, T(n, k) = n!*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 read by rows: row n consists of n zeros followed by 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 f6eb1a0b4a0beb21e5dd6353d21cfc51d40693adcee19838a57a6fc481882730, 7,409 bytes (1,613 compressed); download JSON

Cited by

• n-cb5d49e71e46f2ed (one_signed_coefficients)
• n-cb5d49e71e46f2ed (hadamard_kernel)
• n-cb5d49e71e46f2ed (real_rooted)