Coefficient of x2x^2

Let C\color{#EC7300}{C} be the coefficient of x2\color{#20A900}{x^2} in (1x)(1+2x)(13x)(1+4x)(1+14x)(115x)\color{#69047E}{(1-x)(1+2x)(1-3x)(1+4x)\cdots (1+14x)(1-15x)}. Find C\color{#EC7300}{|C|}.

[2004 AIME 1 Problem 7]

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