Proof step e-2866478407d5f715

basis_map A130595 → concludes about Triangle of generalized Stirling numbers of the first kind read by rows: T(n, k) = (-1)^(n+k)*Sum_{m=0..n} Stirling1(n, m) * binomial(m, k), where Stirling1 is… JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A130595",
  "operation": "basis_map"
}

Premises

• Triangle of unsigned Stirling numbers of the first kind (see A048994), read by rows, T(n,k) for 0 <= k <= n. (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": {} }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map, SHA-256 5219990a5f5eb8dd3fef0349ada805c89cd8c823493925fced70b48cef71c8b4, 6,717 bytes (1,582 compressed); download JSON

Cited by

• n-af47a5bf0b42b546 (real_rooted)