Real-rooted atlas

Proof step

Product of real-rooted factors (elementary)

A fixed real-rooted factor times a proved family factor [1+1], exponent 1 n + 0

Concludes
Irregular triangle T(n, k) = [x^k]( p(n, x) ), where p(n, x) = (1/x)*(1-x)^n*(1+x)^(n+2)*( Sum_{j >= 0} j^(n+1)*x^j ), read by rows.
Premises
Theorem
polytool ?
Checked
polytool replayed · Lean not attempted
Technical details
Step id
e-f25539c5a8b7f259 · JSON
Operation
A fixed real-rooted factor times a proved family
{
  "exponent_offset": 0,
  "exponent_slope": 1,
  "factor": [
    "1",
    "1"
  ],
  "operation": "row_factor"
}
Claims
{
  "claim": "real_rooted",
  "from_index": 0,
  "region": {
    "upper": {
      "closed": true,
      "value": "0"
    }
  }
}
Certificate
row_factor, SHA-256 2128867e9e2cbff16cb1bac9f825c11ee0c7376f63f6d472a6c88356d8786176, 4,808 bytes (1,442 compressed); download
polytool replayed the certificate when the step was written.
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