Real-rooted atlas

Proof step

Geometric basis map (elementary)

Image under a basis map u^k -> P_k A013610

Concludes
basis_map_A013610 of basis_map_A013609 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-def8a3ad9bd5c098 · JSON
Operation
Image under a basis map u^k -> P_k
{
  "map": "A013610",
  "operation": "basis_map"
}
Claims
{
  "claim": "real_rooted",
  "from_index": 1,
  "region": {
    "upper": {
      "closed": true,
      "value": "0"
    }
  }
}
{
  "claim": "interlacing",
  "from_index": 2,
  "kind": "weak",
  "orientation": "unordered"
}
Certificate
basis_map, SHA-256 dee6c875d9ebde6e3cf72acf04cac652e73620e7b2d551cd616e8152c76e58aa, 10,542 bytes (2,339 compressed); download
polytool replayed the certificate when the step was written.
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