Half Binomial Coeff interior abs sum

import Mathlib.Algebra.BigOperators.NatAntidiagonal
import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.Normed.Ring.Basic
import Mathlib.Analysis.SpecificLimits.Normed
import Mathlib.Data.Sym.Basic
import Mathlib.Data.Sym.Card
import Mathlib.RingTheory.Binomial
import Mathlib.RingTheory.MvPolynomial.Symmetric.Defs
import Definitions.Def_D1Bound5_HalfBinomialCoefficients_Definitions

section
open Finset

namespace D1Bound5








theorem _root_.D1Bound5.halfBinomialCoeff_interior_abs_sum (k : ℕ) :
    (∑ ij ∈ Finset.antidiagonal k,
      |halfBinomialCoeff (ij.1 + 1) * halfBinomialCoeff (ij.2 + 1)|) =
        2 * |halfBinomialCoeff (k + 2)| := by sorry



end D1Bound5
end