Enumerative Geometry of Calabi-Yau 5-Folds

The original recursions for A2(d) ≡ nd(ψ̃, H) and B1(d1, d2) ≡ nd1d2(|;H2) do not involve any of the other terms. Using Lemma 1, the formulas (A.2) and (A.3) can be shown to satisfy the two recursions. The original formula for A1(d) ≡ nd(ψ̃H) expresses A1(d) in terms of B1(d1, d2). The formula (A.1) follows from (A.3) and Lemma 2. Originally, there are also the terms nd(ψ̃H,H ), but it is not hard to see that nd(ψ̃H,H ) = dnd(ψ̃H ) ∀ d≥3;