MathDB

The expressions a \plus{} b \plus{} c, ab \plus{} ac \plus{} 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) \equal{} abc \plus{} abd \plus{} acd \plus{} 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.)

Problem Statement