refine' (this.div (Stirling.tendsto_stirlingSeq_sqrt_pi.pow 2) (by positivity)).congr' _
this✝¹ : 0 < π
this✝ : (Real.sqrt π)⁻¹ = Real.sqrt π / Real.sqrt π ^ 2
this : Tendsto (fun n => Stirling.stirlingSeq (2 * n)) atTop (𝓝 (Real.sqrt π))
⊢ Tendsto (fun n => ↑(centralBinom n) * Real.sqrt ↑n / 4 ^ n) atTop (𝓝 (Real.sqrt π / Real.sqrt π ^ 2))
this✝¹ : 0 < π
this✝ : (Real.sqrt π)⁻¹ = Real.sqrt π / Real.sqrt π ^ 2
this : Tendsto (fun n => Stirling.stirlingSeq (2 * n)) atTop (𝓝 (Real.sqrt π))
⊢ ((fun n => Stirling.stirlingSeq (2 * n)) / fun x => Stirling.stirlingSeq x ^ 2) =ᶠ[atTop] fun n =>
    ↑(centralBinom n) * Real.sqrt ↑n / 4 ^ n