MSC:  11Y35  Analytic computations 

11Y55  Calculation of integer sequences 
Abstract:
In 1770, Euler looked for positive integers n and m such that n(n+1)/2 = m^{2}.
Integer solutions for this equation produce what he called squaretriangular numbers.
In this paper, we present a new explicit formula for this kind of numbers
and establish a link with balancing numbers.