Real-rooted atlas

Proof step

Geometric basis map (elementary)

Image under a basis map u^k -> P_k A007318

Concludes
Triangle of coefficients, read by rows, where the n-th row forms the polynomial P(n,x) = {Sum_{k=1..n} 1/(k+x)}*{Product_{k=1..n} (k+x)}.
Premises
Theorem
polytool ?
Checked
polytool replayed · Lean not attempted
Technical details
Step id
e-07b4c15a87e8fc72 · 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"
    }
  }
}
{
  "claim": "interlacing",
  "from_index": 1,
  "kind": "weak",
  "orientation": "unordered"
}
Certificate
basis_map, SHA-256 bf8947b34a78c4534a00ed1fa4169b06972ff3d8ed72596a8279278b10fb0e37, 15,367 bytes (2,953 compressed); download
polytool replayed the certificate when the step was written.
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