Putnam 1990 B5

Is there an infinite sequence $a_0, a_1, a_2, \dots$ of nonzero real numbers such that for $n = 1, 2, 3, \dots$ the polynomial $$p_n(x) = a_0 + a_1x + a_2x^2 + \cdots + a_nx^n$$ has exactly $n$ distinct real roots?