Proof step e-796ce5140a0b4b04

basis_map A008288 → concludes about Square array of Delannoy numbers D(i,j) (i >= 0, j >= 0) read by antidiagonals. JSON

Theorem

Affine-current basis map theorem polytool RealRooted orderTwoConstants_nonneg_iff ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A008288",
  "operation": "basis_map"
}

Premises

• basis-map coefficients of Square array of binomial coefficients T(n,k) = binomial(n,k), n >= 0, k >= 0, read by downward antidiagonals. (sequence)
  uses: Every row P_n, n >= 1, is zero or real-rooted with all roots in [0, 0]

Claims

• { "claim": "real_rooted", "from_index": 1, "region": { "lower": { "closed": true, "value": "-1564556493/268435456" }, "upper": { "closed": true, "value": "-46056243/268435456" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map, SHA-256 58f92b11de764a3c912e390668290bd798639302d0d8c5a313009817373ce6f5, 14,350 bytes (2,251 compressed); download JSON

Cited by

• n-811c78acf96cbc19 (one_signed_coefficients)
• n-811c78acf96cbc19 (hadamard_kernel)
• n-811c78acf96cbc19 (real_rooted)