Proof step e-fc612a08cfe0bbb6

basis_map A007318 → concludes about Even-numbered rows of Pascal's triangle. 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 Irregular triangle read by rows formed by taking every other row of the Delannoy array (A008288) regarded as a tr… (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 35601ad245e3504ab1a579084bd405a22a874a555a4fec529ee8621d39b25b6b, 6,875 bytes (1,387 compressed); download JSON

Cited by

• n-08f49539099949d5 (real_rooted)
• n-08f49539099949d5 (one_signed_coefficients)
• n-08f49539099949d5 (hadamard_kernel)