Half Binomial Coeff recurrence

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_recurrence (n : ℕ) :
    (n + 1 : ℝ) * halfBinomialCoeff (n + 1) =
      ((1 / 2 : ℝ) - n) * halfBinomialCoeff n := by sorry













end D1Bound5
end