We investigate a relationship between MacMahon's generalized sum-of-divisors
functions and Chebyshev polynomials of the first kind. This determines a
recurrence relation to compute these functions, as well as proving a conjecture
of MacMahon about their general form by relating them to quasi-modular forms.
These functions arise as solutions to a curve-counting problem on Abelian
surfaces.Comment: 6 Page