Proof step

Geometric basis map (elementary)

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

Concludes

Triangle whose (i,j)-th entry is binomial(i,j)*11^(i-j)*5^j.

Premises

basis_map_A007318 of Triangle of coefficients in expansion of (1+5x)^n.
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-4b3c9ceb7c3808db · 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 ad43c6c05c2998f47d658ea50d46cb7d0e872ff5b81777f3df5521aca60b5322, 6,916 bytes (1,408 compressed); download

polytool replayed the certificate when the step was written.

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