ISL 1989 Problem 43

The expressions $a + b + c, ab + ac + bc,$ and $abc$ are called the elementary symmetric expressions on the three letters $a, b, c;$ symmetric because if we interchange any two letters, say $a$ and $c,$ the expressions remain algebraically the same. The common degree of its terms is called the order of the expression. Let $S_k(n)$ denote the elementary expression on $k$ different letters of order $n;$ for example $S_4(3) = abc + abd + acd + bcd.$ There are four terms in $S_4(3).$ How many terms are there in $S_{9891}(1989)?$ (Assume that we have $9891$ different letters.)