Real-rooted atlas

Proof step

Geometric basis map (elementary)

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

Concludes
basis_map_A013610 of Triangle read by rows: T(n,k) = binomial(n-2, k-1) + n*binomial(n-1, k-1), 1 <= k <= n, starting with T(1, 1) = 1.
Premises
Theorem
polytool ?
Checked
polytool replayed · Lean not attempted
Technical details
Step id
e-e5c14e4f16404560 · JSON
Operation
Image under a basis map u^k -> P_k
{
  "map": "A013610",
  "operation": "basis_map"
}
Claims
{
  "claim": "real_rooted",
  "from_index": 0,
  "region": {
    "upper": {
      "closed": true,
      "value": "0"
    }
  }
}
Certificate
basis_map, SHA-256 7d23b2e7c9b9980d522b69a1c6ff265f64cfe72e4620e328b162d73be33a8ee7, 13,329 bytes (2,569 compressed); download
polytool replayed the certificate when the step was written.
Cited by