SUMS OF PRODUCTS OF POSITIVE INTEGERS

Although formulas for, and numerical values of, sums of powers of positive integers appear in any number of handbooks and reference volumes devoted to mathematics, few relationships can be found involving sums of products of positive integers. Included in this paper are a number of formulas for sums of products of two and of three variables. Since sums of products occur frequently, in such diverse fields as combinatorial analysis, numerical approximation of double integrals and complexity of algorithms, these formulas should be useful in a number of applications. Two examples are given illustrating the usefulness of the formulas.