Smarandache sums of products

Abstract

Keywords The Smarandache sum, stirling numbers, properties of sequences. Introduction This paper deals with the sums of products of flrst n natural numbers, taken r at a time. Many interesting results about the summations are obtained. Mr. Rama- subramanian (1) has already made some work in this direction. This paper is an extension of his work. In next part, the sums of odd and even natural numbers are discussed, and also of natural numbers, not necessarily beginning with one. After that, properties of sequences, arising out of these sums are obtained. Interestingly, the numbers thus obtained are Stirlings numbers. 1.1 Deflnition. The Smarandache sum of products is denoted by S(n;r), and is deflned as sum of products of flrst n natural numbers, taken r at a time, without repeatition, rn. For example: S(4;1) = 1 + 2 + 3 + 4 = 10,