Real-rooted atlas

Proof step

Affine-current basis map theorem

Image under a basis map u^k -> P_k A008288

Concludes
basis_map_A008288 of basis_map_A013610 of Triangle T(n,k) read by rows: multiply row n of Pascal's triangle (A007318) by the n-th Catalan number (A000108).
Premises
Theorem
polytool RealRooted orderTwoConstants_nonneg_iff ?
Checked
polytool replayed · Lean not attempted
Technical details
Step id
e-0c5eb7e17f6b9f42 · JSON
Operation
Image under a basis map u^k -> P_k
{
  "map": "A008288",
  "operation": "basis_map"
}
Claims
{
  "claim": "real_rooted",
  "from_index": 1,
  "region": {
    "lower": {
      "closed": true,
      "exact": {
        "radicand": "2",
        "rational_part": "-3",
        "sqrt_coefficient": "-2"
      },
      "value": "-1564556493/268435456"
    },
    "upper": {
      "closed": true,
      "exact": {
        "radicand": "2",
        "rational_part": "-3",
        "sqrt_coefficient": "2"
      },
      "value": "-46056243/268435456"
    }
  }
}
Certificate
basis_map, SHA-256 3ea69985577f2ebebdfaae2056ce986ed7e71cd001d218405c010cdf465b0d12, 19,193 bytes (3,260 compressed); download
polytool replayed the certificate when the step was written.
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