Balancing numbers which are products of consecutive integers

In 1999 A. BEHERA and G. K. PANDA defined balancing numbers as follows. A positive integer n is called a balancing number if 1 + 2 + . . . + (n - 1) = (n + 1) (n + 2) . . . + (n + k) for some k is an element of N. The sequence of balancing numbers is denoted by B-m for m is an element of N. In this paper we show that the Diophantine equation B-m = x(x + 1)(x + 2)(x + 3)(x + 4) has no solution with m >= 0 and x is an element of Z. We follow the ideas described in [13], that is we combine Baker's method and the so-called Mordell-Weil sieve to obtain all solutions.