Proof step

Geometric basis map (elementary)

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

Concludes

Triangle read by rows: T(n,k) = (2^(n+1)-1)*binomial(n,k).

Premises

Triangle read by rows, (n-1) zeros followed by 2^n - 1.
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-7b3d5e46dee7f2c5 · 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 e0c6a576d399d27c71ebfc64ac4c66413de3520b96cbd5dfb4c7963fc0b695a9, 12,290 bytes (2,331 compressed); download

polytool replayed the certificate when the step was written.

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