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MR1134625 05A30 (11B65)
Friedman, Jane; Zeilberger, Doron A generalization of Odlyzko's conjecture: the coefficients of $(1-q)^j/((1-q^{2n})\cdots(1-q^{2n+2j}))$ alternate in sign. Proc. Amer. Math. Soc. 118 (1993), no. 3, 1013.
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