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In 2021, Merca proposed a stronger version of the conjecture, that is, for positive integers $1\\leq S<R$ with $k\\geq 1$, the coefficient of $q^n$ in\n  the theta series\n  \\[\n  \\frac{(-1)^{k} \\sum_{j=k}^{\\infty}(-1)^j q^{R j(j+1) / 2}\\left(q^{-Sj}-q^{( j+1) S}\\right)}{\\left(q^S, q^{R-S}; q^R\\right)_{\\infty}}\n  \\]\n  is nonnegative. 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