Proof step

Geometric basis map (elementary)

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

Concludes

shift_x_plus_one of Riordan array (1+2x,x(1+x)).

Premises

Riordan array (1+2x,x(1+x)).
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]

Theorem

polytool ?

Checked

polytool replayed · Lean not attempted

Technical details

Step id

e-58f27a1f5024c805 · 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 3210c475d22a29aa8c0404621bc8dfbcc30c6f54d1b4469d4696495f1bfdcb79, 14,464 bytes (2,774 compressed); download

polytool replayed the certificate when the step was written.

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