Proof step e-b8e0a0fa3ba7bf57

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, "exact": { "radicand": "2", "rational_part": "-3", "sqrt_coefficient": "-2" }, "value": "-1564556493/268435456" }, "upper": { "closed": true, "exact": { "radicand": "2", "rational_part": "-3", "sqrt_coefficient": "2" }, "value": "-46056243/268435456" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map, SHA-256 81996fee9e69515ee61ae8c647337f01188d9a23b435f730d4065f7bceac7e37, 14,489 bytes (2,267 compressed); download JSON

Cited by

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