Proof step e-c62e3171974f4f9c

basis_map A007318 → concludes about basis-map coefficients of Riordan array (1+2x,x(1+x)). shifted by x -> -x + 0 JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A007318",
  "operation": "basis_map"
}

Premises

• basis-map coefficients of Triangle read by rows: T(n,k) = binomial(k,n-k). shifted by x -> -x + 0 (sequence)
  uses: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]

Claims

• { "claim": "real_rooted", "from_index": 0, "region": { "upper": { "closed": true, "value": "0" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map, SHA-256 e62655ca23a140371a5a84d42b8abad304e02cf5be456fd92b083b81a73464d7, 6,862 bytes (1,387 compressed); download JSON

Cited by

• n-74c1e94669ff21ff (real_rooted)
• n-74c1e94669ff21ff (one_signed_coefficients)
• n-74c1e94669ff21ff (hadamard_kernel)