Abstract
We study the asymptotic form of the Gopakumar-Vafa invariants at all genera for Calabi-Yau toric threefolds which have the structure of fibration of the A_n singularity over P^1. We claim that the asymptotic form is the inverse Laplace transform of the corresponding instanton amplitude in the prepotential of N=2 SU(n+1) gauge theory coupled to external graviphoton fields, which is given by the logarithm of the Nekrasov's partition function.
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