Proof step e-0d826cc18bc3a95c

basis_map A008288 → concludes about basis_map_A008288 of T(n,k) = binomial(n,k)*binomial(n+k,k), 0 <= k <= n, triangle read by rows. 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

• T(n,k) = binomial(n,k)*binomial(n+k,k), 0 <= k <= n, triangle read by rows. (sequence)
  uses: Every row P_n, n >= 1, is zero or real-rooted with all roots in [-1, 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 9dbd62e08f56d968e702f6f164e3fd48b70a343bf1df7fa1008ab056e715b7ca, 24,095 bytes (3,184 compressed); download JSON

Cited by

• n-59aff779bb582ee4 (real_rooted)
• n-59aff779bb582ee4 (one_signed_coefficients)
• n-59aff779bb582ee4 (hadamard_kernel)