Proof step

Geometric basis map (elementary)

Image under a basis map u^k -> P_k A007318

Concludes

Triangle T(n, k) read by rows, T(n, k) = n!*binomial(n, k).

Premises

Triangle read by rows: row n consists of n zeros followed by n!.
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]

Theorem

polytool ?

Checked

polytool replayed · Lean not attempted

Technical details

Step id

e-bacfe2979349856c · JSON

Operation

Image under a basis map u^k -> P_k

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

Claims

{
  "claim": "real_rooted",
  "from_index": 0,
  "region": {
    "upper": {
      "closed": true,
      "value": "0"
    }
  }
}

Certificate

basis_map, SHA-256 e8113d39044c97e0cc9888eb2e47c8efc05b05cb148164294e1c5d7738069192, 7,643 bytes (1,689 compressed); download

polytool replayed the certificate when the step was written.

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