Proof step e-bd56c468ffc76132

basis_map A007318 → concludes about basis_map_A007318 of Triangle T(n,k) = n!*binomial(n-1, k-1) for 1 <= k <= n, read by rows. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• Triangle T(n,k) = n!*binomial(n-1, k-1) for 1 <= k <= n, read by rows. (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 21d78849a80463e091ba0f80681e5548d5e31f41325ff70ad674fba1d9478cb9, 7,400 bytes (1,613 compressed); download JSON

Cited by

• n-df44f407d23e429d (real_rooted)
• n-df44f407d23e429d (one_signed_coefficients)
• n-df44f407d23e429d (hadamard_kernel)