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The following expansion works correctly under versions 7, 10.2, 11.0

 eta[q_] := q^(1/24)*QPochhammer[q];
 CoefficientList[Series[q^(-5/8)*(eta[q^3]*eta[q^6])^3/(eta[q]*eta[q^2])^4, {q, 0, 20}], q]

 (* {1, 4, 18, 53, 163, 414, 1059, 2431, 5553, 11844, 25013, 50391, 100362, 193136, 367371, 680705, 1247247, 2238408, 3975218, 6941384, 12003156} *)

But in version 11.3 I get an error message

 (* CoefficientList::poly: ((q^3)^(1/8) (q^6)^(1/8))/((q^2)^(1/6) q^(19/24))+(4 (q^3)^(1/8) (q^6)^(1/8) q^(5/24))/(q^2)^(1/6)+(18 (q^3)^(1/8) (q^6)^(1/8) q^(29/24))/(q^2)^(1/6)+<<431>> q^(31/24)+O[q]^(481/24) is not a polynomial. *)

Why ?

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    $\begingroup$ I think it's just a matter of not simplifying fractional exponents: CoefficientList[ Series[q^(-5/8)*(eta[q^3]*eta[q^6])^3/(eta[q]*eta[q^2])^4, {q, 0, 20}, Assumptions -> {q > 0}], q] works in 11.3. $\endgroup$ – ulvi Apr 16 '18 at 8:19

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