filter_upwards [eventually_gt_atTop (0 : ℕ)] with n hn
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
case h
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))
n : ℕ
hn : 0 < n
⊢ ((fun n => Stirling.stirlingSeq (2 * n)) / fun x => Stirling.stirlingSeq x ^ 2) n =
    ↑(centralBinom n) * Real.sqrt ↑n / 4 ^ n