The generating function is an infinite product:
To evaluate the infinite product, you can use SageMath with the following commands:
typeset_mode(True)
(1/x)*prod(((1+x^(n-1/2))^(32)/(1-x^n)^8) for n in (1..oo))
a = (1/x)*prod(((1+x^(n-1/2))^(32)/(1-x^n)^8) for n in (1..200))
F = a.taylor(x,0,6)
g = "+".join(map(latex, sorted([f for f in F.operands()], key=lambda exp:exp.degree(x))))
g
— Me@2019-01-11 11:52:33 AM
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2019.01.11 Friday (c) All rights reserved by ACHK