Real-rooted atlas

Proof step

Geometric basis map (elementary)

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

Concludes
shift_x_plus_one of derivative of Triangle T(n,k) read by rows: multiply row n of Pascal's triangle (A007318) by the n-th Catalan number (A000108).
Premises
Theorem
polytool ?
Checked
polytool replayed · Lean not attempted
Technical details
Step id
e-2b8102501002cba4 · JSON
Operation
Image under a basis map u^k -> P_k
{
  "map": "A007318",
  "operation": "basis_map"
}
Claims
{
  "claim": "real_rooted",
  "from_index": 1,
  "region": {
    "upper": {
      "closed": true,
      "value": "0"
    }
  }
}
{
  "claim": "interlacing",
  "from_index": 3,
  "kind": "weak",
  "orientation": "unordered"
}
Certificate
basis_map, SHA-256 f64b60bf6a9c68dddf1298bad19c425904dbe9286ec6ba637d104099c8b8a355, 15,441 bytes (2,861 compressed); download
polytool replayed the certificate when the step was written.
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