Real-rooted atlas

Proof step

Geometric basis map (elementary)

Image under a basis map u^k -> P_k A013609

Concludes
basis_map_A013609 of basis_map_A013610 of Triangle T(n,k) with the coefficient of [x^k] of the polynomial (2*(x+1)^2)^n in row n, column k, 0<=k<=2n.
Premises
Theorem
polytool ?
Checked
polytool replayed · Lean not attempted
Technical details
Step id
e-fb3370d90f6eaa17 · JSON
Operation
Image under a basis map u^k -> P_k
{
  "map": "A013609",
  "operation": "basis_map"
}
Claims
{
  "claim": "real_rooted",
  "from_index": 0,
  "region": {
    "upper": {
      "closed": true,
      "value": "0"
    }
  }
}
Certificate
basis_map, SHA-256 7ce7445d18d3fdd0e21f33f90b620ac2e786b4ec472d4fe368e7106b13f5ff5b, 6,889 bytes (1,401 compressed); download
polytool replayed the certificate when the step was written.
Cited by