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MMO 130 Moscow MO 1947 coeffiient of x^{20} in (1+x^2 -x^3)^{1000}

Source:

July 20, 2019
algebrapolynomialcoefficients

Problem Statement

Which of the polynomials, (1+x2−x3)1000(1+x^2 -x^3)^{1000} or (1−x2+x3)1000(1-x^2 +x^3)^{1000}, has the greater coefficient of x20x^{20} after expansion and collecting the terms?
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