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 shift_x_plus_one of Triangle read by rows: T(n,k) = ((n+1)(n+2)/2) * binomial(n,k) (0 <= k <= n).
Premises
Theorem
polytool ?
Checked
polytool replayed · Lean not attempted
Technical details
Step id
e-40f965714ec70af6 · 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 087a2cad429cf7ddab3d9a12587b1c25c5bc6d71f7b855d004e7b4a604c6f976, 12,511 bytes (2,189 compressed); download
polytool replayed the certificate when the step was written.
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