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 Triangle read by rows: T(n,k) is the number of flattened Catalan words of length n with exactly k runs of descents.
Premises
Theorem
polytool ?
Checked
polytool replayed · Lean not attempted
Technical details
Step id
e-d8004c7e185a4c2a · 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 6f135a5d93dabf04ef055b92e0ca1b946bb4cd4e32075941cfb8b7e14a74e44b, 11,870 bytes (2,212 compressed); download
polytool replayed the certificate when the step was written.
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